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<h2>SL Paper 1</h2><div class="question">
<p>The graph shows the variation with time <em>t</em> of the temperature <em>T</em> of two samples, X and Y. X and Y have the same mass and are initially in the solid phase. Thermal energy is being provided to X and Y at the same constant rate.</p>
<p><img src="data:image/png;base64,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"></p>
<p>What is the correct comparison of the specific latent heats <em>L</em><sub>X</sub> and <em>L</em><sub>Y</sub> and specific heat capacities in the liquid phase <em>c</em><sub>X</sub> and <em>c</em><sub>Y</sub> of X and Y?</p>
<p><img 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"></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Two pulses are travelling towards each other.</p>
<p><img src="data:image/png;base64,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"></p>
<p>What is a possible pulse shape when the pulses overlap?</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAhcAAAGLCAYAAAB0lbDtAAAgAElEQVR4Ae3df4xmVXkH8GeWRG2DawM2ZRcSSUMW/6FBISZtSN2o7LY2VGJbMQrBCklbhVKJQDTUP6opSgiJkVb+YZsKmmKxoZKKrLjBhNiUssZok+KWNKRdWZOSja4boU2caS67w8zuzHvn/XHuveec+yEhO/Pee8+Pz3NmfPzOu8PSysrKSviHAAECBAgQIJBIYFuicQxDgAABAgQIEHhZQHPhIBAgQIAAAQJJBTQXSTkNRoAAAQIECGgunAECBAgQIEAgqYDmIimnwQgQIECAAAHNhTNAgAABAgQIJBXYtLlYPrQv9i4txdLOj8eBY8tJJzQYAQIE0gm8FIf2vSeWmu9XG/7dG7ftOxCHjvsels7bSASmE9ikuXgpnn3y6/H9m++IOy76Vjz29NHpRnIXAQIEBhP4g7jvBy9G82t7Vv/9+fOfiHO+dVPsvunh+KH+YrDKmHicAhubi2Pfjvtu/8+45nfeH+++6ty48zNfjUO+MMd5OuyaQMEC23b8elx37RUR+/4uHnv2pYJ3YukEyhM4rblYjmNPPx73x57Ye+m5ccFlvxV79n89nvSFWV5lrZgAgRMCOy6I8895FQ0CBHoUOK25OBpPP7Y/4pp3xKXbt8W2C34jrtrznXjwyedCeDF7VZqfAd9zzz2zP+gJAgQWFlg+8s9x3xePxS0P3xi7t5/2rW7h0esfYON7WDZ7X4vX5nE6fPhw9QfolK+45UNfjc/cGXHN3l+L7c3Wt50fl1315th/+xfiCW/snOsw3HjjjXH0qPetzIXnIQJTC/x9XHfhL5zyps4zdl4WN+/7j/jR4Z/Ez6Yex43rBVbfv+LPtffyLGpxyy23xM9+Vv+JXNdcnHgj5/4dzY9Ezjp5vl5z4kcjR/Z7Y+f6r7gZPv7c5z4XX/rSl2Z4wq0ECMwusPENnSs//ff4yq0Rd/7eR+Pegz+efUhPECAwt8Bac7H8XDz54JMRR+6It7/ujFf+H8AZF14X++Ng3P/Y9+LY3NOM98H3ve99Ib0Yb/3tfECBM98YV153VeyJf4q7v/wd378GLIWpxydwsrlYjmNPfCFu33/Zhr/OtbLy8/jJNz8Wcee98dAh77ie9YicddZZIb2YVc39BNIIbDvn/Lh4R5qxjEKAwPQCJ5uLk2/k/OB7Y+8Frznt6W2x/dJ3xDU7nvTGztNkpv1UejGtlPsIpBVY/tFz8d0jl6y9jyzt8EYjQGCCwInm4tj34rH7I655/2/GuWs/KFl7ZPub4z03vzn2P/jteNZfG1lzmfIj6cWUUG4jkFLg+DPx8H0Pxv7d74/3vGX1fWQpJzAWAQKTBLZFvBSHHro37ryw7Qvwl+JNv/vu2LP/r+O+J16I1V8PvvO2A36OOUn2tNelF6eB+JRAUoGNf1tk6bU3xb9ceGM8/aUPxyVnrv4E+JnYt3en/7RBUnuDEdgosLTS/L0a/3Qi0Pz95/W8q7/z4oYbbuhkPoMSIEAglcDp379SjTv2cW699da4/vrrY9euXVVTbPZDkKo3POTmpBdD6pubAAECBPoS0Fz0JR0R3nvRI7apCBAgQGAwAc1Fz/TSi57BTUeAAAECvQtoLnoml170DG46AgQIEOhdQHPRO3mE9GIAdFMSIECAQG8CmoveqNcmkl6sWfiIAAECBOoT0FwMVFPpxUDwpiVAgACBzgU0F50Tbz6B9GJzF68SIECAQPkCmosBayi9GBDf1AQIECDQmYDmojParQeWXmxt5A4CBAgQKE9AczFwzaQXAxfA9AQIECCQXEBzkZx0tgGlF7N5uZsAAQIE8hfQXGRQI+lFBkWwBAIECBBIJqC5SEY5/0DSi/ntPEmAAAEC+QloLjKpifQik0JYBgECBAgsLKC5WJgwzQDSizSORiFAgACB4QU0F8PX4JUVSC9eofABAQIECBQsoLnIqHjSi4yKYSkECBAgMLeA5mJuum4elF5042pUAgQIEOhPQHPRn/VUM0kvpmJyEwECBAhkLKC5yLA40osMi2JJBAgQIDC1gOZiaqr+bpRe9GdtJgIECBBIL6C5SG+aZETpRRJGgxAgQIDAAAKaiwHQp5lSejGNknsIECBAIEcBzUWOVTm5JulFxsWxNAIECBCYKKC5mEgz/AXpxfA1sAICBAgQmF1AczG7Wa9PSC965TYZAQIECCQQ0FwkQOxyCOlFl7rGJkCAAIEuBDQXXagmHlN6kRjUcAQIECDQqYDmolPeNINLL9I4GoUAAQIE+hHQXPTjvPAs0ouFCQ1AgAABAj0JaC56gl50GunFooKeJ0CAAIG+BDQXfUknmEd6kQDREAQIECDQuYDmonPidBNIL9JZGokAAQIEuhPQXHRn28nI0otOWA1KgAABAgkFNBcJMfsYSnrRh7I5CBAgQGARAc3FInoDPSu9GAjetAQIECAwlYDmYiqmvG6SXuRVD6shQIAAgVMFNBenehTzmfSimFJZKAECBEYnoLkotOTSi0ILZ9kECBAYgYDmouAiSy8KLp6lEyBAoGIBzUXBxZVeFFw8SydAgEDFApqLwosrvSi8gJZPgACBCgU0F4UXVXpReAEtnwABAhUKaC4qKKr0ooIi2gIBAgQqEtBcVFBM6UUFRbQFAgQIVCSguaikmNKLSgppGwQIEKhAQHNRQRGbLUgvKimkbRAgQKACAc1FBUVc3YL0YlXCnwQIECAwpIDmYkj9xHNLLxKDGo4AAQIE5hLQXMzFlu9D0ot8a2NlBAgQGIuA5qKySksvKiuo7RAgQKBAAc1FgUXbasnSi62EXCdAgACBLgU0F13qDjS29GIgeNMSIECAwMsCmotKD4L0otLC2hYBAgQKENBcFFCkeZYovZhHzTMECBAgkEJAc5FCMdMxpBeZFsayCBAgULmA5qLiAksvKi6urREgQCBjAc1FxsVJsTTpRQpFYxAgQIDALAKai1m0CrxXelFg0SyZAAEChQtoLgov4DTLl15Mo+QeAgQIEEgloLlIJZnxONKLjItjaQQIEKhQQHNRYVE325L0YjMVrxEgQIBAFwKaiy5UMxxTepFhUSyJAAEClQpoLiot7Gbbkl5spuI1AgQIEEgtoLlILZrxeNKLjItjaQQIEKhIQHNRUTGn2Yr0Yhol9xAgQIDAIgKai0X0CnxWelFg0SyZAAEChQloLgorWIrlSi9SKBqDAAECBCYJaC4myVT8uvSi4uLaGgECBDIQ0FxkUIQhliC9GELdnAQIEBiHgOZiHHXesEvpxQYSLxAgQIBAIgHNRSLIEoeRXpRYNWsmQIBA/gKai/xr1NkKpRed0RqYAAECoxbQXIy6/BHSi5EfANsnQIBABwKaiw5QSxpSelFStayVAAECZQhoLsqoU6erlF50ymtwAgQIjE5AczG6km/csPRio4lXCBAgQGB+Ac3F/HZVPSm9qKqcNkOAAIFBBTQXg/LnM7n0Ip9aWAkBAgRKF9BclF7BhOuXXiTENBQBAgRGLKC5GHHxT9+69OJ0EZ8TIECAwDwCmot51Cp+RnpRcXFtjQABAj0JaC56gi5lGulFKZWyTgIECOQroLnItzaDrUx6MRi9iQkQIFCFgOaiijKm3YT0Iq2n0QgQIDA2Ac3F2Co+5X6lF1NCuY0AAQIENghoLjaQeKERkF44BwQIECAwr4DmYl65ETwnvRhBkW2RAAECHQhoLjpArWVI6UUtlbQPAgQI9CuguejXu7jZpBfFlcyCCRAgMLiA5mLwEuS9AOlF3vWxOgIECOQooLnIsSqZrUl6kVlBLIcAAQKZC2guMi9QDsuTXuRQBWsgQIBAOQKai3JqNehKpReD8pucAAECRQloLooq13CLlV4MZ29mAgQIlCaguSitYgOuV3oxIL6pCRAgUJCA5qKgYg29VOnF0BUwPwECBMoQ0FyUUadsVim9yKYUFkKAAIFsBTQX2ZYmz4VJL/Ksi1URIEAgJwHNRU7VKGQt0otCCmWZBAgQGEhAczEQfMnTSi9Krp61EyBAoHsBzUX3xlXOIL2osqw2RYAAgSQCmoskjOMbRHoxvprbMQECBKYV0FxMK+W+DQLSiw0kXiBAgACBiNBcOAZzC0gv5qbzIAECBKoW0FxUXd7uNye96N7YDAQIEChNQHNRWsUyW6/0IrOCWA4BAgQyENBcZFCE0pcgvSi9gtZPgACBtAKai7SeoxxNejHKsts0AQIEJgpoLibSuDCLgPRiFi33EiBAoG4BzUXd9e1td9KL3qhNRIAAgewFNBfZl6icBUovyqmVlRIgQKBLAc1Fl7ojG1t6MbKC2y4BAgQmCGguJsB4eT4B6cV8bp4iQIBATQKai5qqmcFepBcZFMESCBAgMLCA5mLgAtQ4vfSixqraEwECBKYX0FxMb+XOKQWkF1NCuY0AAQKVCmguKi3s0NuSXgxdAfMTIEBgOAHNxXD2Vc8svai6vDZHgACBVgHNRSuPi4sISC8W0fMsAQIEyhXQXJRbu+xXLr3IvkQWSIAAgU4ENBedsBp0VUB6sSrhTwIECIxHQHMxnloPslPpxSDsJiVAgMCgApqLQfnHMbn0Yhx1tksCBAisCmguViX82ZmA9KIzWgMTIEAgSwHNRZZlqW9R0ov6ampHBAgQmCSguZgk4/WkAtKLpJwGI0CAQNYCmousy1PX4qQXddXTbggQIDBJQHMxScbryQWkF8lJDUiAAIEsBTQXWZal3kVJL+qtrZ0RIEBgVUBzsSrhz14EpBe9MJuEAAECgwpoLgblH+fk0otx1t2uCRAYj4DmYjy1zman0otsSmEhBAgQ6ERAc9EJq0G3EpBebCXkOgECBMoV0FyUW7uiVy69KLp8Fk+AAIFWAc1FK4+LXQpIL7rUNTYBAgSGE9BcDGc/+pmlF6M/AgAIEKhUQHNRaWFL2Zb0opRKWScBAgSmF9BcTG/lzg4EpBcdoBqSAAECAwtoLgYugOkjpBdOAQECBOoS0FzUVc8idyO9KLJsFk2AAIGJApqLiTQu9CkgvehT21wECBDoVkBz0a2v0acUkF5MCeU2AgQIFCCguSigSGNZovRiLJW2TwIEahfQXNRe4YL2J70oqFiWSoAAgRYBzUULjkv9C0gv+jc3IwECBFILaC5SixpvIQHpxUJ8HiZAgEAWApqLLMpgEesFpBfrNXxMgACB8gQ0F+XVrPoVSy+qL7ENEiBQuYDmovICl7o96UWplbNuAgQIRGgunIIsBaQXWZbFoggQIDCVgOZiKiY3DSEgvRhC3ZwECBBYXEBzsbihEToSkF50BGtYAgQIdCyguegY2PCLCUgvFvPzNAECBIYQ0FwMoW7OqQWkF1NTuZEAAQLZCGgusimFhUwSkF5MkvE6AQIE8hTQXORZF6taJyC9WIfhQwIECBQgoLkooEiWGCG9cAoIECBQjoDmopxajXql0otRl9/mCRAoTEBzUVjBxrxc6cWYq2/vBAiUJKC5KKlaI1+r9GLkB8D2CRAoRkBzUUypLLQRkF44BwQIEMhfQHORf42scJ2A9GIdhg8JECCQqcDSysrKSqZr23RZS0tLm76e64uF8ebKeMq6jh49GmefffYpr+X+iXOQe4W6X19p37saEec2/bkYyzkorrlIX2ojEiBAgAABAikF/FgkpaaxCBAgQIAAgdBcOAQECBAgQIBAUgHNRVJOgxEgQIAAAQKaC2eAAAECBAgQSCqguUjKaTACBAgQIEBAc+EMECBAgAABAkkFNBdJOQ1GgAABAgQIaC6cAQIECBAgQCCpgOYiKafBCBAgQIAAAc2FM0CAAAECBAgkFdBcJOU0GAECBAgQIKC5cAYIECBAgACBpAKai6ScBiNAgAABAgQ0F84AAQIECBAgkFRAc5GU02AECBAgQICA5sIZIECAAAECBJIKaC6SchqMAAECBAgQ0Fw4AwQIECBAgEBSAc1FUk6DESBAgAABApoLZ4AAAQIECBBIKqC5SMppMAIECBAgQEBz4QwQIECAAAECSQU0F0k5DUaAAAECBAhoLpwBAgQIECBAIKnAxubi+KE48NBdce3OpVhaOvHvzmvviocOHIrjSac2GAECBBYVWI5jBz4eO09+r1r9nnXiz4vi2rsejAOHji06iecJEJhRYF1zsRzHD/1D3HbFO+OT//or8acH/zdWVlZiZeUn8cTVZ8QjV++OK+56SoMxI7DbCRDoQ+CSuPWb/3Pye1bzfWslVn76lbg6vhZX7/5I7HtGg9FHFcxBYFVgrbk4/nTc+0c3xP2/emc8cMc1ccmOV528Z3vsuvym+KtHbom45UPxyQMvrD7rTwIECOQrcOauuPzmv4h7fvupuO5P7ouDx5fzXauVEahM4GRzsRzHnno47n7isvjUbe+Mc9dajpPb3RZnvum9cdfDfx57z1ttOiqTsB0CBOoT2PaGuPK2j8SeJ74YX37qaH37s6PiBI4eHcc5PNlGHI2nH9sfR3ZcEOefM6F52LYjLnnXu+Jtu7YXV0wLJkBgvALbzjk/Lt7xfHz3uRdCdjHec5DDzl988cU4++yz4/Dhwzksp9M1nGgull+I5777fMRFF8R5Z26ILTpdgMEJECDQvcCR+P4Pnveese6hzdAi8Oijj7589bzzzmu5q45LOok66mgXBAgQIJCxQJNafPrTn854hWmXdqK52Pb6OP/inRHffzYOe9NTWmGjESCQgcCOuOjCnXFmBiuxhHEKNKnF7t27R7P5k8nFWXHp3j2x48iz8dyP/m/i5pePHIx/9PsuJvq4QIBAbgLLcezpx+P+Izvj4vNfH6La3OozjvWsphbXX3/9ODYcsfq1ti22v+XKuHn3k3H7Z74WP9zwrqflOP7M38YfXvKB+OqPXx2/OBoeGyVAoGiB5f+Ox7/4SBzZ86G4bvfri96KxZcrsJpa7Nq1q9xNzLjytUb+zEvjjz9/R1z+6A1x9cfuj4NHVhOMY3HoG5+ND7/tY/FfH7g7PnXlG1Y7khmncjsBAgR6FDh+KL5x9yfihkffEvd99vdj19p3ux4XYaqxC4wxtWhqvu7LbVuc+cZr428OPhJ/duG/xUd3vvrkr/9+Xex+4OdxxQNPxCN/eXnsOPnE8qF9sXdpKXbediD87ruxf/nYP4GhBQ7GnW//5Vf+kwUv//rv194Yj5/1B/HIwc/HB9+47q/QLz8T+/bujKWdH48DxzbEtENvxPyVCYwxtWhKuLTS/J5c/xAgQIAAAQJJBZrU4q1vfWs88MADsfojkabxHcP/7K5LLpKaGowAAQIECIxaYKypRVN0ycWoj77NEyBAgEAXApulFs08kosutI1JgAABAgRGIDDm1KIpr+RiBIfcFgkQIECgP4FJqUWzAslFf3UwEwECBAgQqEZg7KlFU0jJRTXH2UYIECBAYGiBttSiWZvkYugKmZ8AAQIECBQmILU4UTDJRWEH13IJECBAIE+BrVKLZtWSizxrZ1UECBAgQCBLAanFWlkkF2sWPiJAgAABAnMJTJNaNANLLubi9RABAgQIEBifgNTi1JpLLk718BkBAgQIEJhJYNrUohlUcjETrZsJECBAgMA4BaQWG+suudho4hUCBAgQIDCVwCypRTOg5GIqVjcRIECAAIHxCkgtNq+95GJzF68SIECAAIFWgVlTi2YwyUUrqYsECBAgQGDcAlKLyfWXXEy2cYUAAQIECGwqME9q0QwkudiU04sECBAgQICA1KL9DEgu2n1cJUCAAAECpwjMm1o0g0guTqH0CQECBAgQINAISC22PgeSi62N3EGAAAECBF4WWCS1aAaQXDhIBAgQIECAwCkCUotTOCZ+IrmYSOMCAQIECBBYE1g0tWhGklysefqIAAECBAiMXkBqMf0RkFxMb+VOAgQIEBipQIrUoqGTXIz0ANk2AQIECBA4XUBqcbpI++eSi3YfVwkQIEBg5AKpUouGUXIx8sNk+wQIECBAoBGQWsx+DiQXs5t5ggABAgRGIpAytWjIJBcjOTi2SYAAAQIEJglILSbJtL8uuWj3cZUAAQIERiqQOrVoGCUXIz1Mtk2AAAECBBoBqcX850ByMb+dJwkQIECgUoEuUouGSnJR6YGxLQIECBAgsJWA1GIrofbrkot2H1cJECBAYGQCXaUWDaPkYmSHyXYJECBAgEAjILVY/BxILhY3NAIBAgQIVCLQZWrREEkuKjkotkGAAAECBKYVkFpMK9V+n+Si3cdVAgQIEBiJQNepRcMouRjJYbJNAgQIECDQCEgt0p0DyUU6SyMRIECAQKECfaQWDY3kotADYtkECBAgQGBWAanFrGLt90su2n1cJUCAAIHKBfpKLRpGyUXlh8n2CBAgQIBAIyC1SH8OJBfpTY1IgAABAoUI9JlaNCSSi0IOhmUSIECAAIF5BaQW88q1Pye5aPdxlQABAgQqFeg7tWgYJReVHibbIkCAAAECjYDUortzILnoztbIBAgQIJCpwBCpRUMhucj0QFgWAQIECBBYVEBqsahg+/OSi3YfVwkQIECgMoGhUouGUXJR2WGyHQIECBAg0AhILbo/B5KL7o3NQIAAAQKZCAyZWjQEkotMDoJlECBAgACBVAJSi1SS7eNILtp9XCVAgACBSgSGTi0aRslFJYfJNggQIECAQCMgtejvHEgu+rM2EwECBAgMJJBDatFsXXIx0AEwLQECBAgQSC0gtUgt2j6e5KLdx1UCBAgQKFwgl9SiYZRcFH6YLJ8AAQIECDQCUov+z4Hkon9zMxIgQIBATwI5pRbNliUXPRXeNAQIECBAoCsBqUVXsu3jSi7afVwlQIAAgUIFckstGkbJRaGHybIJECBAgEAjILUY7hxILoazNzMBAgQIdCSQY2rRbFVy0VHBDUuAAAECBLoWkFp0Ldw+vuSi3cdVAgQIEChMINfUomGUXBR2mCyXAAECBAg0AlKL4c+B5GL4GlgBAQIECCQSyDm1aLYouUhUaMMQIECAAIG+BKQWfUm3zyO5aPdxlQABAgQKEcg9tWgYJReFHCbLJECAAAECjYDUIp9zILnIpxZWQoAAAQJzCpSQWjRbk1zMWWCPESBAgACBvgWkFn2Lt88nuWj3cZUAAQIEMhcoJbVoGCUXmR8myyNAgAABAo2A1CK/cyC5yK8mVkSAAAECUwqUlFo0W5JcTFlYtxEgQIAAgaEEpBZDybfPK7lo93GVAAECBDIVKC21aBglF5keJssiQIAAAQKNgNQi33Mguci3NlZGgAABAhMESkwtmq1ILiYU1MsECBAgQGBoAanF0BVon19y0e7jKgECBAhkJlBqatEwSi4yO0yWQ4AAAQIEGgGpRf7nQHKRf42skAABAgROCpScWjRbkFw4ygQIECBAIDMBqUVmBZmwHMnFBBgvEyBAgEBeAqWnFo2m5CKvM2U1BAgQIDByAalFOQdAclFOrayUAAECoxWoIbVoiie5GO0RtnECBAgQyE1AapFbRdrXI7lo93GVAAECBAYWqCW1aBglFwMfJtMTIECAAIFGQGpR3jmQXJRXMysmQIDAaARqSi2aokkuRnN0bZQAAQIEchWQWuRamfZ1SS7afVwlQIAAgYEEakstGkbJxUCHybQECBAgQKARkFqUew4kF+XWzsoJECBQrUCNqUVTLMlFtUfWxggQIEAgdwGpRe4Val+f5KLdx1UCBAgQ6Fmg1tSiYZRc9HyYTEeAAAECBBoBqUX550ByUX4N7YAAAQLVCNScWjRFklxUc1RthAABAgRKEZBalFKp9nVKLtp9XCVAgACBngRqTy0aRslFT4fJNAQIECBAoBGQWtRzDiQX9dTSTggQIFCswBhSi6Y4kotij6iFEyBAgEBpAlKL0irWvl7JRbuPqwQIECDQscBYUouGUXLR8WEyPAECBAgQaASkFvWdA8lFfTW1IwIECBQjMKbUoimK5KKYo2mhBAgQIFCqgNSi1Mq1r1ty0e7jKgECBAh0JDC21KJhlFx0dJgMS4AAAQIEGgGpRb3nQHJRb23tjAABAtkKjDG1aIohucj2SFoYAQIECJQuILUovYLt65dctPu4SoAAAQKJBcaaWjSMkovEh8lwBAgQIECgEZBa1H8OJBf119gOCRAgkI3AmFOLpgiSi2yOooUQIECAQC0CUotaKtm+D8lFu4+rBAgQIJBIYOypRcMouUh0mAxDgAABAgQaAanFeM6B5GI8tbZTAgQIDCYgtThBL7kY7AiamAABAgRqE5Ba1FbR9v1ILtp9XCVAgACBBQWkFmuAkos1Cx8RIECAAIG5BaQWc9MV+6DkotjSWTgBAgTyF5BanFojycWpHj4jQIAAAQIzC0gtZiar4gHJRRVltAkCBAjkJyC12FgTycVGE68QIECAAIGpBaQWU1NVd6PkorqS2hABAgSGF5BabF4DycXmLl4lQIAAAQJbCkgttiSq+gbJRdXltTkCBAj0LyC1mGwuuZhs4woBAgQIEJgoILWYSDOaC5KL0ZTaRgkQINC9gNSi3Vhy0e7jKgECBAgQ2CAgtdhAMsoXJBejLLtNEyBAIL2A1GJrU8nF1kbuIECAAAECrwhILV6hGP0HkovRHwEABAgQWFxAajGdoeRiOid3ESBAgACBkFo4BOsFJBfrNXxMgAABAjMLSC2mJ5NcTG/lTgIECBAYsYDUYsTFn7B1ycUEGC8TIECAwNYCUoutjdbfIblYr+FjAgQIECCwiYDUYhMUL4XkwiEgQIAAgbkEpBazs0kuZjfzBAECBAiMSEBqMaJiz7hVycWMYG4nQIAAgQipxXynQHIxn5unCBAgQGAEAlKLERR5gS1KLhbA8ygBAgTGKCC1mL/qkov57TxJgAABAhULSC0qLm6irUkuEkEahgABAmMQkFosVmXJxWJ+niZAgACBCgWkFhUWtYMtSS46QDUkAQIEahSQWixeVcnF4oZGIECAAIGKBKQWFRWz461ILjoGNjwBAgRqEJBapKmi5CKNo+68LvMAAAEuSURBVFEIECBAoAIBqUUFRexxC5KLHrFNRYAAgRIFpBbpqia5SGdpJAIECBAoWEBqUXDxBlq65GIgeNMSIECgBAGpRdoqSS7SehqNAAECBAoUkFoUWLQMliy5yKAIlkCAAIEcBaQW6asiuUhvakQCBAgQKEhAalFQsTJbquQis4JYDgECBHIQkFp0UwXJRTeuRiVAgACBAgSkFgUUKeMlSi4yLo6lESBAYAgBqUV36mNJLoprLprC+IdAaQIrKyulLdl6EwuU+L3LuU18CCJiLOeguOYifamNSIAAAQIECKQU2JZyMGMRIECAAAECBDQXzgABAgQIECCQVEBzkZTTYAQIECBAgIDmwhkgQIAAAQIEkgpoLpJyGowAAQIECBDQXDgDBAgQIECAQFKB/wdupVoVUU9o7AAAAABJRU5ErkJggg=="></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A thin-walled cylinder of weight <em>W</em>, open at both ends, rests on a flat surface. The cylinder has a height <em>L</em>, an average radius <em>R</em> and a thickness <em>x</em> where <em>R</em> is much greater than <em>x</em>.</p>
<p><img src="data:image/png;base64,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"></p>
<p>What is the pressure exerted by the cylinder walls on the flat surface?</p>
<p>A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{W}{{2\pi Rx}}">
<mfrac>
<mi>W</mi>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mi>R</mi>
<mi>x</mi>
</mrow>
</mfrac>
</math></span></p>
<p>B. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{W}{{\pi {R^2}x}}">
<mfrac>
<mi>W</mi>
<mrow>
<mi>π</mi>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>x</mi>
</mrow>
</mfrac>
</math></span></p>
<p>C. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{W}{{\pi {R^2}}}">
<mfrac>
<mi>W</mi>
<mrow>
<mi>π</mi>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>D. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{W}{{\pi {R^2}L}}">
<mfrac>
<mi>W</mi>
<mrow>
<mi>π</mi>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>L</mi>
</mrow>
</mfrac>
</math></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>The pressure of a fixed mass of an ideal gas in a container is decreased at constant temperature. For the molecules of the gas there will be a decrease in </p>
<p>A. the mean square speed.<br>B. the number striking the container walls every second. <br>C. the force between them. <br>D. their diameter.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>B</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A substance in the gas state has a density about <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math> times less than when it is in the liquid state. The diameter of a molecule is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>. What is the best estimate of the average distance between molecules in the gas state?</p>
<p>A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></p>
<p>B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mi>d</mi></math></p>
<p>C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mi>d</mi></math></p>
<p>D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn><mi>d</mi></math></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>B</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>This question gives good discrimination at HL but less so at SL. Teacher comments felt that the question was too mathematical but it can be noted that it asks for an estimation of the average distance which is related to the cube root of the volume and 1000 is 103. At both levels option D proved a popular alternative suggesting that candidates were forgetting the cube root.</p>
</div>
<br><hr><br><div class="question">
<p>When 40 kJ of energy is transferred to a quantity of a liquid substance, its temperature increases by 20 K. When 600 kJ of energy is transferred to the same quantity of the liquid at its boiling temperature, it vaporizes completely at constant temperature. What is</p>
<p style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>specific latent heat of vaporization</mtext><mtext>specific heat capacity of the liquid</mtext></mfrac></math></p>
<p>for this substance?</p>
<p>A. 15 K<sup>−1</sup></p>
<p>B. 15 K</p>
<p>C. 300 K<sup>−1</sup></p>
<p>D. 300 K</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A fixed mass of an ideal gas in a closed container with a movable piston initially occupies a volume <em>V</em>. The position of the piston is changed, so that the mean kinetic energy of the particles in the gas is doubled and the pressure remains constant.</p>
<p>What is the new volume of the gas?</p>
<p>A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{V}{4}">
<mfrac>
<mi>V</mi>
<mn>4</mn>
</mfrac>
</math></span></p>
<p>B. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{V}{2}">
<mfrac>
<mi>V</mi>
<mn>2</mn>
</mfrac>
</math></span></p>
<p>C. 2<em>V</em></p>
<p>D. 4<em>V</em></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>What does the constant <em>n</em> represent in the equation of state for an ideal gas <em>pV = nRT</em>?</p>
<p>A. The number of atoms in the gas</p>
<p>B. The number of moles of the gas</p>
<p>C. The number of molecules of the gas</p>
<p>D. The number of particles in the gas</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>B</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>The graph shows how the temperature of a liquid varies with time when energy is supplied to the liquid at a constant rate <em>P</em>. The gradient of the graph is <em>K </em>and the liquid has a specific heat capacity <em>c</em>.</p>
<p> <img src="images/Schermafbeelding_2018-08-12_om_09.24.20.png" alt="M18/4/PHYSI/SPM/ENG/TZ2/11"></p>
<p>What is the mass of the liquid?</p>
<p>A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{P}{{cK}}">
<mfrac>
<mi>P</mi>
<mrow>
<mi>c</mi>
<mi>K</mi>
</mrow>
</mfrac>
</math></span></p>
<p>B. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{PK}}{c}">
<mfrac>
<mrow>
<mi>P</mi>
<mi>K</mi>
</mrow>
<mi>c</mi>
</mfrac>
</math></span></p>
<p>C. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{Pc}}{K}">
<mfrac>
<mrow>
<mi>P</mi>
<mi>c</mi>
</mrow>
<mi>K</mi>
</mfrac>
</math></span></p>
<p>D. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{cK}}{P}">
<mfrac>
<mrow>
<mi>c</mi>
<mi>K</mi>
</mrow>
<mi>P</mi>
</mfrac>
</math></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Two identical containers X and Y each contain an ideal gas. X has <em>N</em> molecules of gas at an absolute temperature of <em>T</em> and Y has 3<em>N</em> molecules of gas at an absolute temperature of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>T</mi><mn>2</mn></mfrac></math> What is the ratio of the pressures <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>P</mi><mi>Y</mi></msub><msub><mi>P</mi><mi>X</mi></msub></mfrac></math>?</p>
<p style="text-align:center;"><img src="data:image/png;base64,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"></p>
<p>A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>6</mn></mfrac></math></p>
<p>B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac></math></p>
<p>C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac></math></p>
<p>D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A sealed cylinder of length <em>l </em>and cross-sectional area <em>A </em>contains <em>N </em>molecules of an ideal gas at kelvin temperature <em>T</em>.</p>
<p> <img src="images/Schermafbeelding_2018-08-10_om_16.26.56.png" alt="M18/4/PHYSI/SPM/ENG/TZ1/12"></p>
<p>What is the force acting on the area of the cylinder marked <em>A </em>due to the gas?</p>
<p>A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{NRT}}{l}">
<mfrac>
<mrow>
<mi>N</mi>
<mi>R</mi>
<mi>T</mi>
</mrow>
<mi>l</mi>
</mfrac>
</math></span></p>
<p>B. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{NRT}}{{lA}}">
<mfrac>
<mrow>
<mi>N</mi>
<mi>R</mi>
<mi>T</mi>
</mrow>
<mrow>
<mi>l</mi>
<mi>A</mi>
</mrow>
</mfrac>
</math></span></p>
<p>C. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{N{k_B}T}}{{lA}}">
<mfrac>
<mrow>
<mi>N</mi>
<mrow>
<msub>
<mi>k</mi>
<mi>B</mi>
</msub>
</mrow>
<mi>T</mi>
</mrow>
<mrow>
<mi>l</mi>
<mi>A</mi>
</mrow>
</mfrac>
</math></span></p>
<p>D. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{N{k_B}T}}{l}">
<mfrac>
<mrow>
<mi>N</mi>
<mrow>
<msub>
<mi>k</mi>
<mi>B</mi>
</msub>
</mrow>
<mi>T</mi>
</mrow>
<mi>l</mi>
</mfrac>
</math></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A sealed container contains a mixture of oxygen and nitrogen gas.<br>The ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{mass of an oxygen molecule}}}}{{{\text{mass of a nitrogen molecule}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>mass of an oxygen molecule</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>mass of a nitrogen molecule</mtext>
</mrow>
</mrow>
</mfrac>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{8}{7}">
<mfrac>
<mn>8</mn>
<mn>7</mn>
</mfrac>
</math></span>.</p>
<p>The ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{average kinetic energy of oxygen molecules}}}}{{{\text{average kinetic energy of nitrogen molecules}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>average kinetic energy of oxygen molecules</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>average kinetic energy of nitrogen molecules</mtext>
</mrow>
</mrow>
</mfrac>
</math></span> is</p>
<p>A. 1.</p>
<p>B. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{7}{8}">
<mfrac>
<mn>7</mn>
<mn>8</mn>
</mfrac>
</math></span>.</p>
<p>C. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{8}{7}">
<mfrac>
<mn>8</mn>
<mn>7</mn>
</mfrac>
</math></span>.</p>
<p>D. dependent on the concentration of each gas.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A sealed container contains water at 5 °C and ice at 0 °C. This system is thermally isolated from its surroundings. What happens to the total internal energy of the system?</p>
<p>A. It remains the same.</p>
<p>B. It decreases.</p>
<p>C. It increases until the ice melts and then remains the same.</p>
<p>D. It increases.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A fixed mass of an ideal gas has a volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math>, a pressure of <em>p</em> and a temperature of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math>. The gas is compressed to the volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>V</mi><mn>6</mn></mfrac></math> and its pressure increases to 12<em>p</em>. What is the new temperature of the gas?</p>
<p><br>A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math></p>
<p>B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math></p>
<p>C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>333</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math></p>
<p>D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>606</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Two blocks, X and Y, are placed in contact with each other. Data for the blocks are provided.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>X has a mass <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></em>. What is the mass of Y?</p>
<p>A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>m</mi><mn>4</mn></mfrac></math></p>
<p>B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></p>
<p>C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi>m</mi></math></p>
<p>D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo> </mo><mi>m</mi></math></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>This question was very well answered by candidates, reinforced by the high difficulty index for both HL and SL groups. This is another question that requires the rearrangement of an equation to determine a relationship between variables; interestingly candidates showed greater success on this question than others of this type. This may be due to the fact that there was not an easy distractor included in the response options, requiring candidates to work through equation substitution and rearrangement to reach a final answer.</p>
</div>
<br><hr><br><div class="question">
<p>A sample of oxygen gas with a volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>0</mn><mo> </mo><msup><mtext>m</mtext><mn>3</mn></msup></math> is at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math>. The gas is heated so that it expands at a constant pressure to a final volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>0</mn><mo> </mo><msup><mtext>m</mtext><mn>3</mn></msup></math>. What is the final temperature of the gas?</p>
<p>A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>750</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math></p>
<p>B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>470</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math></p>
<p>C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>370</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math></p>
<p>D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>B</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A quantity of 2.00 mol of an ideal gas is maintained at a temperature of 127 ºC in a container of volume 0.083 m<sup>3</sup>. What is the pressure of the gas?</p>
<p>A. 8 kPa</p>
<p>B. 25 kPa</p>
<p>C. 40 kPa</p>
<p>D. 80 kPa</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A driver uses the brakes on a car to descend a hill at constant speed. What is correct about the internal energy of the brake discs?</p>
<p>A. The internal energy increases.</p>
<p>B. The internal energy decreases.</p>
<p>C. There is no change in the internal energy.</p>
<p>D. The internal energy is zero.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>This question was well answered by HL and SL candidates, although option C did prove to be a distraction for some.</p>
</div>
<br><hr><br><div class="question">
<p>A liquid is vaporized to a gas at a constant temperature.</p>
<p>Three quantities of the substance are the</p>
<p style="padding-left:60px;">I. total intermolecular potential energy<br>II. root mean square speed of the molecules<br>III. average distance between the molecules.</p>
<p>Which quantities are <strong>greater</strong> for the substance in the gas phase compared to the liquid phase?</p>
<p><br>A. I and II only</p>
<p>B. I and III only</p>
<p>C. II and III only</p>
<p>D. I, II and III</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>B</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Which assumption is part of the molecular kinetic model of ideal gases? </p>
<p><br>A. The work done on a system equals the change in kinetic energy of the system.</p>
<p>B. The volume of a gas results from adding the volume of the individual molecules.</p>
<p>C. A gas is made up of tiny identical particles in constant random motion.</p>
<p>D. All particles in a gas have kinetic and potential energy.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A quantity of an ideal gas is at a temperature <em>T</em> in a cylinder with a movable piston that traps a length <em>L</em> of the gas. The piston is moved so that the length of the trapped gas is reduced to <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mi>L</mi></mrow><mn>6</mn></mfrac></math> and the pressure of the gas doubles.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>What is the temperature of the gas at the end of the change?</p>
<p><br>A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>12</mn></mfrac><mi>T</mi></math><br><br>B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>5</mn></mfrac><mi>T</mi></math><br><br>C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>3</mn></mfrac><mi>T</mi></math><br><br>D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>12</mn><mn>5</mn></mfrac><mi>T</mi></math></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>Some comments queried that the Laws of Thermodynamics are not on the syllabus. This question was set as a test of Thermal Physics, topic 3, with option A coming from Mechanics, topic 2, not Thermodynamics.</p>
</div>
<br><hr><br><div class="question">
<p><span style="background-color:#ffffff;">A substance changes from the solid phase to the gas phase without becoming a liquid and without a change in temperature.<br></span></p>
<p><span style="background-color:#ffffff;">What is true about the internal energy of the substance and the total intermolecular potential energy of the substance when this phase change occurs?</span></p>
<p><span style="background-color:#ffffff;"><img 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"></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>This question has a low discrimination index at SL with more candidates choosing response D rather than the correct C. Candidates should remember that all information given in the question is important and the clue here is ‘without a change in temperature’. Thus the kinetic energy does not change so internal energy and potential energy will both have the same change and in addition energy must be provided to change the state of a solid.</p>
</div>
<br><hr><br><div class="question">
<p>A 700 W electric heater is used to heat 1 kg of water without energy losses. The specific heat capacity of water is 4.2 kJ kg<sup>–1</sup> K<sup>–1</sup>. What is the time taken to heat the water from 25 °C to 95 °C?</p>
<p> </p>
<p>A. 7 s</p>
<p>B. 30 s</p>
<p>C. 7 minutes</p>
<p>D. 420 minutes</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A gas storage tank of fixed volume <em>V</em> contains <em>N</em> molecules of an ideal gas at temperature <em>T</em>. The pressure at kelvin temperature <em>T</em> is 20 MPa. <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{N}{4}">
<mfrac>
<mi>N</mi>
<mn>4</mn>
</mfrac>
</math></span></span> molecules are removed and the temperature changed to 2<em>T</em>. What is the new pressure of the gas?</p>
<p>A. 10 MPa</p>
<p>B. 15 MPa</p>
<p>C. 30 MPa</p>
<p>D. 40 MPa</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p><span style="background-color:#ffffff;">The temperature of a fixed mass of an ideal gas changes from 200 °C to 400 °C.<br></span></p>
<p><span style="background-color:#ffffff;">What is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{mean kinetic energy of gas at 200 °C}}}}{{{\text{mean kinetic energy of gas at 400 °C}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>mean kinetic energy of gas at 200 °C</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>mean kinetic energy of gas at 400 °C</mtext>
</mrow>
</mrow>
</mfrac>
</math></span></span><span style="background-color:#ffffff;">?<br></span></p>
<p><span style="background-color:#ffffff;">A. 0.50<br></span></p>
<p><span style="background-color:#ffffff;">B. 0.70<br></span></p>
<p><span style="background-color:#ffffff;">C. 1.4<br></span></p>
<p><span style="background-color:#ffffff;">D. 2.0</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>B</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>Most candidates chose A having forgotten to convert from oC to K.</p>
</div>
<br><hr><br><div class="question">
<p><span style="background-color: #ffffff;">An ideal gas is in a closed container. Which changes to its volume and temperature when taken together must cause a decrease in the gas pressure?</span></p>
<p><img src="data:image/png;base64,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"></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p><span style="background-color: #ffffff;">Two flasks P and Q contain an ideal gas and are connected with a tube of negligible volume compared to that of the flasks. The volume of P is twice the volume of Q.</span></p>
<p><span style="background-color: #ffffff;"><img style="margin-right:auto;margin-left:auto;display: block;" src="data:image/png;base64,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" width="257" height="111"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">P is held at a temperature of 200 K and Q is held at a temperature of 400 K.</span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">What is mass of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>mass</mi><mo> </mo><mi>of</mi><mo> </mo><mi>gas</mi><mo> </mo><mi>in</mi><mo> </mo><mi mathvariant="normal">P</mi></mrow><mrow><mi>mass</mi><mo> </mo><mi>of</mi><mo> </mo><mi>gas</mi><mo> </mo><mi>in</mi><mo> </mo><mi mathvariant="normal">Q</mi></mrow></mfrac></math>?</span></span></p>
<p> </p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>8</mn></mfrac></math></span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>4</mn></mfrac></math></span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">C. 4</span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">D. 8</span></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p><span style="background-color:#ffffff;">A container holds 20 g of argon-40(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{18}^{40}{\text{Ar}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>18</mn>
</mrow>
<mrow>
<mn>40</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Ar</mtext>
</mrow>
</math></span>) and 40 g of neon-20 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{10}^{20}{\text{Ne}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>20</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Ne</mtext>
</mrow>
</math></span>) .<br></span></p>
<p><span style="background-color:#ffffff;">What is<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{number of atoms of argon -40}}}}{{{\text{number of atoms of neon -20}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>number of atoms of argon -40</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>number of atoms of neon -20</mtext>
</mrow>
</mrow>
</mfrac>
</math></span> in the container?<br></span></p>
<p><span style="background-color:#ffffff;">A. 0.25<br></span></p>
<p><span style="background-color:#ffffff;">B. 0.5<br></span></p>
<p><span style="background-color:#ffffff;">C. 2<br></span></p>
<p><span style="background-color:#ffffff;">D. 4</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>An insulated tube is filled with a large number <em>n</em> of lead spheres, each of mass <em>m</em>. The tube is inverted <em>s</em> times so that the spheres completely fall through an average distance <em>L</em> each time. The temperature of the spheres is measured before and after the inversions and the resultant change in temperature is <em>ΔT</em>.</p>
<p>What is the specific heat capacity of lead?</p>
<p style="text-align:center;"><img src="data:image/png;base64,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"> </p>
<p style="text-align:center;"> </p>
<p style="text-align:left;">A. <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{sgL}}{{nm\Delta T}}">
<mfrac>
<mrow>
<mi>s</mi>
<mi>g</mi>
<mi>L</mi>
</mrow>
<mrow>
<mi>n</mi>
<mi>m</mi>
<mi mathvariant="normal">Δ</mi>
<mi>T</mi>
</mrow>
</mfrac>
</math></span></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">B. <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{sgL}}{{\Delta T}}">
<mfrac>
<mrow>
<mi>s</mi>
<mi>g</mi>
<mi>L</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>T</mi>
</mrow>
</mfrac>
</math></span></span></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">C. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{sgL}}{{n\Delta T}}">
<mfrac>
<mrow>
<mi>s</mi>
<mi>g</mi>
<mi>L</mi>
</mrow>
<mrow>
<mi>n</mi>
<mi mathvariant="normal">Δ</mi>
<mi>T</mi>
</mrow>
</mfrac>
</math></span></span></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">D. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{gL}}{{m\Delta T}}">
<mfrac>
<mrow>
<mi>g</mi>
<mi>L</mi>
</mrow>
<mrow>
<mi>m</mi>
<mi mathvariant="normal">Δ</mi>
<mi>T</mi>
</mrow>
</mfrac>
</math></span></span></span></p>
<p style="text-align:left;"> </p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>B</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Boiling water is heated in a 2 kW electric kettle. The initial mass of water is 0.4 kg. Assume the specific latent heat of vaporization of water is 2 MJ kg<sup>–1</sup>.</p>
<p>What is the time taken for all the water to vaporize?</p>
<p>A. 250 s</p>
<p>B. 400 s</p>
<p>C. 2500 s</p>
<p>D. 4000 s</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>B</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>This question was well answered by candidates.</p>
</div>
<br><hr><br><div class="question">
<p>A bicycle of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math> comes to rest from speed <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> using the back brake. The brake has a specific heat capacity of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> and a mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math>. Half of the kinetic energy is absorbed by the brake.</p>
<p>What is the change in temperature of the brake?</p>
<p>A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>M</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mrow><mn>4</mn><mi>m</mi><mi>c</mi></mrow></mfrac></math></p>
<p>B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>M</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mi>m</mi><mi>c</mi></mrow></mfrac></math></p>
<p>C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mrow><mn>4</mn><mi>M</mi><mi>c</mi></mrow></mfrac></math></p>
<p>D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mi>M</mi><mi>c</mi></mrow></mfrac></math></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>An ideal gas of <em>N </em>molecules is maintained at a constant pressure <em>p</em>. The graph shows how the volume <em>V </em>of the gas varies with absolute temperature <em>T</em>.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>What is the gradient of the graph?</p>
<p>A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{N}{p}">
<mfrac>
<mi>N</mi>
<mi>p</mi>
</mfrac>
</math></span></p>
<p>B. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{NR}{p}">
<mfrac>
<mrow>
<mi>N</mi>
<mi>R</mi>
</mrow>
<mi>p</mi>
</mfrac>
</math></span></p>
<p>C. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{N{k_{\rm{B}}}}}{p}">
<mfrac>
<mrow>
<mi>N</mi>
<mrow>
<msub>
<mi>k</mi>
<mrow>
<mrow>
<mi mathvariant="normal">B</mi>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
<mi>p</mi>
</mfrac>
</math></span></p>
<p>D. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{N}{{Rp}}">
<mfrac>
<mi>N</mi>
<mrow>
<mi>R</mi>
<mi>p</mi>
</mrow>
</mfrac>
</math></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A fixed mass of an ideal gas is trapped in a cylinder of constant volume and its temperature is varied. Which graph shows the variation of the pressure of the gas with temperature in degrees Celsius?</p>
<p><img src="images/Schermafbeelding_2018-08-10_om_16.23.05.png" alt="M18/4/PHYSI/SPM/ENG/TZ1/10"></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> of a liquid of specific heat capacity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> flows every second through a heater of power <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math>. What is the difference in temperature between the liquid entering and leaving the heater?</p>
<p><br>A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><mi>c</mi></mrow><mi>P</mi></mfrac></math></p>
<p>B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>273</mn><mo>+</mo><mfrac><mrow><mi>m</mi><mi>c</mi></mrow><mi>P</mi></mfrac></math></p>
<p>C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>P</mi><mrow><mi>m</mi><mi>c</mi></mrow></mfrac></math></p>
<p>D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>273</mn><mo>+</mo><mfrac><mi>P</mi><mrow><mi>m</mi><mi>c</mi></mrow></mfrac></math></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A mass m of ice at a temperature of –5 °C is changed into water at a temperature of 50 °C.</p>
<p>Specific heat capacity of ice = <em>c</em><sub>i</sub><br>Specific heat capacity of water = <em>c</em><sub>w</sub><br>Specific latent heat of fusion of ice = <em>L</em></p>
<p>Which expression gives the energy needed for this change to occur?</p>
<p>A. 55 <em>m c</em><sub>w</sub> + <em>m L</em></p>
<p>B. 55 <em>m c</em><sub>i</sub> + 5 <em>m L</em></p>
<p>C. 5 <em>m c</em><sub>i</sub> + 50 <em>m c</em><sub>w</sub> + <em>m L</em></p>
<p>D. 5 <em>m c</em><sub>i</sub> + 50 <em>m c</em><sub>w</sub> + 5 <em>m L</em></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A piece of metal at a temperature of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math> is dropped into an equal mass of water at a temperature of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math> in a container of negligible mass. The specific heat capacity of water is four times that of the metal. What is the final temperature of the mixture?</p>
<p>A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>83</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math></p>
<p>B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>57</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math></p>
<p>C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math></p>
<p>D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>What are the units of the ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{specific heat capacity of copper}}}}{{{\text{specific latent heat of vaporization of copper}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>specific heat capacity of copper</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>specific latent heat of vaporization of copper</mtext>
</mrow>
</mrow>
</mfrac>
</math></span>?</p>
<p>A. no units</p>
<p>B. k</p>
<p>C. k<sup>–1</sup></p>
<p>D. k<sup>–2</sup></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Which aspect of thermal physics is best explained by the molecular kinetic model?</p>
<p>A. The equation of state of ideal gases</p>
<p>B. The difference between Celsius and Kelvin temperature</p>
<p>C. The value of the Avogadro constant</p>
<p>D. The existence of gaseous isotopes</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>An ideal gas is maintained at a temperature of 100 K. The variation of the pressure <em>P</em> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mtext>volume</mtext></mfrac></math> of the gas is shown.</p>
<p style="text-align:center;"><img 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3TgiNSxm0+dnVNG3AUJSlJA+xo+iWwMAMQAs+Df5JSZzLLs7HFklgGtiOIszGlnaobuu3mQ3ZI8zuEG7Tux02mJu6CrLnSOIxoDAFGuvHy7nVkWCATsFuZ1141yrgBoDd8IWZzjdsy0M/+of8rarMySRzU7vauOVc7T4KwlGly0QYuzekl1JZox5HaVz15v3dLVwfmXTefnSGbcVRWnHmPeVzPmFZ0n8/jjTzhHAHDuffDBByouXmdnl91888266KLjH8+AaJKRkeEceZApztq9g9tC8zIHhDLnbQsddE59VvFAKLXXgND04tqmEx9vDuX16xlKnVcR+qzpjO3z3Y+GbnTHRTImQr169XSOYl9ZWZlzFPuYa2yK9bkePnw4tHz5cvtxqbi4mPs2RjFX76CtaTm2+/9paVW9qgp/rBQnn+y7WfNUb/3vmZkZSppRorrOPnXrKB05ENBh598ZwYP1qpVP3bueL0UyBgCiiJtZVlVVFc4sA9C2KM4sHdLvkL92j2qb3d4uuUMJ1v+uL9qq2sVZSuyQpMtv6K3G12q0L5xX9qne2VFhlXAXK7lnF+sdRTAGAKKAySwz2y6ZzLL8/Hwyy4CziOIsYglKHzVC8f4Fmrtspw6ZdWrVG7Vkdbnix4zX9X06RTgGALzNzSxLSUmxF/ynpqY6VwCcDRRnEYuTb/itWlkwSnvmZColKUkpI3NVMWiOVt4zRj3sr2QkYwDAm0xm2YQJE+xtl1ateozMMuAcoVw4iaZW547jX10Zl6j0qQXaGG5/7tLGgslKTzzPGWCJZAwAeIjJLDPbLpnMspycm+0Wpkn6B3BuUJwBQDv27LOb7Mwyn89HZhngERRnANAOmawys+3SokWP2NsumWNamIA3UJwBQDtiWpgrVqzQpEk3KTMzU2vWrGHbJcBjKM4AoJ0wmWWmhWkyy4qLS8gsAzyK4gwAYpybWVZQUKCioofILAM8juIMAGKUaWGazLK0tIEaMmSIli5dSmYZEAUozgAgBpnMMrPtksks27r1ZbuFyYJ/IDpQnAFADDEtTDezbNasWWSWAVGI4gwAYoTJLDPbLrmZZUOHDnWuAIgmFGcAEOVMC9PklK1du47MMiAGUJwBQJRyM8tMC9Nkli1cuJDMMiAGUJwBQBQqKyuzM8tM0j+ZZUBsoTgDgChiijGTWTZ//ny7hZmbm0tmGRBjKM4AIAq4mWUZGVeGM8toYQKxieIMADzObLvkZpb5/TvILANiHMUZAHiUm1k2c+avw5lltDCB2EdxBgAeZFqYJrPMBMiSWQa0LxRnAOAhbmZZaWmpveB/ypQptDCBdobiDAA8wCz4NzllJrMsO3scmWVAO0ZxBgDnmNl2yWSWBQIBu4V53XWjnCsA2iOKMwA4R9zMskWLHglnltHCBEBxBgBnmbvtkptZtmbNGlqYAMIozgDgLHIzy6qqqsKZZQDQHMUZAJwFJrPMtDBNZll+fj6ZZQBOiuIMANqYm1mWkpJiL/hPTU11rgDAl1GcAUAbMZllEyZMsLddWrXqMTLLAESE4gwAWplZ8G+2XTKZZTk5N9stTJP0DwCRoDgDgFbkZpb5fD4yywB8LRRnANAKTGaZ2XbJzSwzx7QwAXwdFGcAcAZMC/OZZ0o1adJNyszMJLMMwBmjOAOAr8lklpkWZk1NjYqLS8gsA9AqKM4A4DS5mWUFBQUqKnpIOTm/JLMMQKs5eXEW2KL8/hcpKenE2xDNKCpTXdAZF/apqpdMVv/8LQo4Z77wd5XMGKiktHmqPOacOs4x1ZXc3sLHcj5eYYkq6446Y9tKUIeqN6lwxpCTf9xgnSqX52v0V31ukYwBEJVMC9NklqWlDbS3XVq6dCmZZQBa3UmKs6AClc9rXePVuve5v6m2dk/4VrPtfvV4+jd66MUDzlhH8F29tK5O40Z9Xz7n1OnLUtG2mi9/vNJcZeWsUvWXCsLWE3xvve4ce7tKu+fpuaraLz7utIdVech8YOtr8uICTc7foUFFz6mqxc8tkjEAopHJLDPbLpnMsq1bX7ZbmCz4B9AWTlKcHdW+mrfUmDZKw/p0cs41iUtM1YhBR7Ru0+vHP0N26H3rwStRyT27OCdaR1zitbrzrp8o3v+YnvIfcs62tk/11jNP6OnGwZo4bbSSu8RZH/dq3fqrUVLVBr2w+7A1pl6Vm563vibZmja2r8ws4xKHaerEwZK/XDv3m6cEIxkDIJqYFqabWTZr1iwyywC0uZaLM/tZsHLFD+it7hGtSnOeaUv+cjHXsqOq2/I7jU7qq9FznmuhRdpcnDr7uqqjGnUg8Kn1tmk/btGS/BudtqG53aj85dtP8X6+SiclT1up2tqVmpZ8ks//WK1e2VBzwtekky4ZOEgJ8mv7mw2RjQEQNUxmmdl2yc0sGzp0qHMFANpOy6WX/SzYd1puUQZe16Z1OuGaecboJSWPy1CfUxZzVnG163H9+y3LpWkLtOSekUr8yn/zqd7ZUWF9hIvtZ+Wa2o+/1OpvztK2mj2qrSnX2jsv1Lr82V9utX5tpgB8Sg89vEnxY27RT9K6SIcDOnBE6tjNp87OKCPuggQlKaB9DZ9ENgaA55kWpskpW7t2HZllAM66Fsoid71ZUzHUXLCuTEV3/JvWXX2nbhvezTlrCX6omtekAb2/fbI+qeNzBXat1Kys32nP+EgKs6Oqq1yrJavLrSJpvK7voy/aj1OHNf3buEQN+l8/VLJqtOGVWp1x4zC4S0vG9lfKyNu1/N0f6JbpVzV9nMMN2tfYNKS5uAu66kLnOKIxADzLLPhfsWKF3cI0mWULFy4kswzAWfeNkMU5dphXXU7XyDkvOG83k/Iz3XtbtkbfkH5cURWsXqKssW/rjpfv0TW+lqot82rNGzTzmfqmN+N/oWXHjTWv1pylITNLnLebu1xT7/0XTfun4fZasCYBVW95QTsbPrc++Nt6Kn+enrGKooTZ61U+O10dnFFnxrRe/0PTfrpevYue1IKrKpUz5Hbr/Z/wMepKNGPIHKlogxZfVWEdn2JMVi/nZBPTlj2Zxx9/wjkC0NZef/11/fd/P6yrrsrQjTfeaLcyAcSujIwM58iDTHF2nM/fDD164/dC/fI2hz52Tn21T0K7H510ivG1oeLpA0K9evUM9cu8PjSy1/dCmfO2hQ46V0Ohz0LvF99mXb8tVPz+Z865ln3+/rOh32R+zxp7RWj6vMdCxcXrQ5s3Lw5Nt9536rwK6z21Iudr0evGR0O7P9ocyuv35Y/x+e5HQzf2GhCaXlwbCn0cwZgIma9Ve1FWVuYcxT7m6j179uwJ3X333aHx48eHdu/e7Zw9Pe3pfjX4Po5NzNU7vvw0l73eTEpO/kf71Yandkh7q+siGx//Cy1c85j+Y3aKqgrn68lqs8D/dBzQiw/9f1ry7mgV/c9ftXj2RGVl3ajhPb+p/c6IVhXXWV0v7CjV1utgJ5+6WYdHDgRkXrvpCh6sV6186t71fKlzBGMAeIKbWZaRcWU4s4wWJgAv+FJxFtxXo9caB2vcsItPsX7MYb9AIDGy8R27ytc5QWk/+ZnGxL+guQ9s1Hun9QrLT9SwL2BVjpfrssTznHNBHdr7tqx68gwc0Jb8Hyip/xxtCTT7hIKH1bD/iOKv+q4Sz0vS5Tf0VuNrNdoXHnL8ixXUIYIxAM45s+2Sm1nm9+8gswyAp5xQT32qt17aJH98H/Xu7hY/X+V0IzSaxPUYozn3Z0tP36d719da7yVSFyjpsj6S///oKb+JpTAvGHhMc3//uMw6/BOfsYpcggZnT1BK40atWPeGmtLUAqpev1Kr/SnKyblGPeISlD5qhOL9CzR32U5rjHlF58ZmL1Yw849kDIBzxc0smznz1+HMMrZdAuA1JxRnpkX5ruLHjVB6iwv7T9QUVquI89Bc56nHdVOUk/Kxnn64RH47gT8SXZV+8+9VNPWYCrO+r6Sk72pIXpWS//V+zU6LP+EZq9MRpy7pv9KSkjxd9tefK8XOTkvR2Ke66V+fW6rZ6V3tMb7ht2plwSjtmZNpjUlSyshcVQyao5X3jLGKt6b3c+oxAM4F08I0mWUmQJbMMgBe1sKrNeEF5lWcZvuq9mDr1q3eftVMK2KuZ5/JLJs3b559fMcdd7TJurL2dL8afB/HJubqHTyXAyAmmQX/JqfMZJZlZ48jswxA1KA4AxBzzLZLo0dnKhAI2C3M664b5VwBAO+jOAMQM/bu3au8vDwtWvSIve1Sbm4ur8IEEHUozgBEPXfbJTezbM2aNbQwAUQtijMAUc3NLKuqqgpnlgFANKM4AxCVTGaZaWGazLL8/HwyywDEDIozAFHHzSxLSUmxF/ynpqY6VwAg+lGcAYgaJrNswoQJ9rZLq1Y9pilTprDgH0DMoTgD4Hlmwb/ZdslkluXk3Gy3ME3SPwDEIoozAJ7mZpb5fD4yywC0CxRnADzJZJbdcsst4cwyc0wLE0B7QHEGwFPczLJJk25SZmYmmWUA2h2KMwCeYTLLTAvTZJYVF5eQWQagXaI4A3DOuZllBQUFKip6iMwyAO0axRmAc8a0ME1mWVraQHvbpaVLl5JZBqDdozgDcE6YzDKz7ZLJLNu69WW7hcmCfwCgOANwlpkWpptZNmvWLDLLAOAEFGcAzhqTWWa2XXIzy4YOHepcAQC4KM4AtDnTwjQ5ZWvXriOzDABOgeIMQJtxM8tMC9Nkli1cuJDMMgA4BYozAG3i9ddftzPLTNI/mWUAEDmKMwCtyhRjJrPsiSfW2C3M3NxcMssA4DRQnAFoFW5mWUbGlXZmWV5ePi1MAPgaKM4AnDGz7ZKbWeb377BbmB07dnSuAgBOB8UZgK/NzSybOfPX4cwyWpgAcGYozgB8LaaFaTLLTIAsmWUA0HoozgCcFjezrLS01F7wP2XKFDLLAKAVUZwBiIhZ8G9yykxmWXb2ODLLAKCNUJwBOCWz7ZLJLAsEAnYL87rrRjlXAACtjeIMwEm5mWWLFj0SziyjhQkAbYviDMCXuNsuuZlla9asoYUJAGcJxRmA47iZZVVVVeHMMgDA2UNxFnZUdZUrlT+6r5KSLrJv/WfMU0llnYLOCAXrVLk8X6Od60lJQzSjsESVdUedAZZIxgAeZDLLTAvTZJbl5+eTWQYA5wjFmS2oQ5UPa1rWg9o35lFtq9mj2qrndH/3zZqZdYserGywxwReXKDJ+Ts0qOg5VdXuUc22+9WjNFdZOatUbVdwkYwBvMfNLEtJSbEX/KempjpXAABnG8WZrV7la9eoKmGibr11qBLNV6VLX2Xl/oumxm/XorV+BawxlZueV2NatqaN7asu1pC4xGGaOnGw5C/Xzv3H7Pdz6jGAd5jMsgkTJtjbLq1a9RiZZQDgARRntm66puCvqvXfofQOzimjs0/dOkqN+xp0+FitXtlQo/gBvdU9/FXrpEsGDlKC/Nr+ZoMUyRjAA8yCf7Ptksksy8m52W5hmqR/AMC5R3H2FYLv7NDmeinhsiR1OxzQgSNSx24+dXauG3EXJChJAe1r+ESKZAxwjrmZZT6fj8wyAPAgirOTapD/qf8jv67WrB+lqMPhBu1rdC41E3dBV13oHCuSMcA5YjLLzLZLbmaZOaaFCQDeQ3HWIvMCgWXKK9yrMUX366fJnZzzQPRxM8smTbpJmZmZZJYBgMd9I2RxjmGzCrNdKzUr63fak7NCT86+wl7Yr8AW5V85RRty1qt8drrcpWnB6iXKGjlPFxZt0OIRb516TFYv52wTE7dxMo8//oRzBHw9f/vb3/Tgg/M1YMAATZx4k93KBABIGRkZzpEHmeIMriOh97ctDE3v971Q5m+eDb3/uXPa+KwiNC+1Z6hf3ubQx84p47OKB0KpvYaF8jZ/ENmYCPXq1dM5in1lZWXOUew7W3P98MMPQ3fffXdo/PjxIb/f75w9u7hfYxf3bWxirt5BWzMsoF1LZura7ELtGb9AS+4Z2RSp4eqQpMtv6K3G12q0L5xX9qne2VGhel2s5J5dIhsDtCHTwjSZZWlpA+1tl5YuXUpmGQBEGYoz21G9V/IbZc15ShozV38+sTCzJSh91AjF+xdo7rKdOmTan9UbtWR1ueLHjNf1fcy6tEjGAG3DZJaZbZdMZtnWrS/b2y6x4B8Aog/FmXHsdT1+z1qZF1o2Pn27rurtbr3k3NLmqfJYnHzDb9XKglHaMydTKUlJShmZq4pBc7TynjHqYX8lIxkDtC6z7ZKbWTZr1iwyywAgylEuGB3SNdu/R7W1J7m54bRxiUqfWqCN4Wu7tLFgstITz2t6P0YkY4BWYjLLzLZLbmbZ0KFDnSsAgGhFcQZEIdPCNDlla9euI7MMAGIMxRkQRdzMMtPCNJllCxcuJLMMAGIMxRkQJcrKyuxtl0zSf3Fxib3gHwAQeyjOAI8zxVheXp7mz59vtzBzc3OVkJDgXAUAxBqKM8Cj3MyyjIwrw5lltDABIPZRnAEe9Oqrr4Yzy/z+HWSWAUA7QnEGeIibWTZz5q/DmWW0MAGgfaE4AzzCtDBNZpkJkCWzDADaL4oz4BxzM8tKS0vtBf9TpkyhhQkA7RjFGXCOmAX/JqfMZJZlZ48jswwAYKM4A84Bs+2SySwLBAJ2C/O660Y5VwAA7R3FGXAWffDBB3Zm2aJFj4Qzy2hhAgCaozgDzgJ326Xbb7/Vzixbs2YNLUwAQIsozoA25maWVVVV6ZFH/sS2SwCAr0RxBrQRk1lmWpgmsyw/P9/OLPP5fM5VAABaRnEGtAE3sywlJcVe8J+amupcAQDgq1GcAa3IZJZNmDDB3nZp1arHyCwDAJw2ijOgFZgF/2bbJZNZlpNzs93CNEn/AACcLooz4Ay5mWVmPRmZZQCAM0VxBnxNe/futbddcjPLzDEtTADAmaI4A06Tm1k2adJNyszMJLMMANCqKM6A02Ayy0wL02SWFReXkFkGAGh1FGdABNzMsoKCAhUVPWQv+E9ISHCuAgDQeijOgK9gWpgmsywtbaC97dLSpUvJLAMAtCmKM+AkTGaZ2XbJZJZt3fqy3cJkwT8AoK1RnAEnMC1MN7Ns1qxZZJYBAM4qijOgGZNZZrZdcjPLhg4d6lwBAODsoDgDLKaFaXLK1q5dR2YZAOCcojhDu+ZmlpkWpsksW7hwIZllAIBziuIM7VZZWZmdWWaS/sksAwB4BcUZ2h1TjJnMsvnz59stzNzcXDLLAACeQXGGdsPNLMvIuDKcWUYLEwDgNRRnaBfMtktuZpnfv4PMMgCAZ1GctahBlYU/VtKMEtU5Z2zBOlUuz9fopIuUZN+GaEZhiSrrjjoDLJGMwVnjZpbNnPnrcGYZLUwAgJdRnH1JQLuW3KXJhdudt11BBV5coMn5OzSo6DlV1e5Rzbb71aM0V1k5q1QdjHQMzhbTwjSZZSZAlswyAEC0oDhrJli3Xcvzb9F/Hk3TuC89uVKvyk3PqzEtW9PG9lUX60xc4jBNnThY8pdr5/5jEY5BW3Mzy0pLS+0F/1OmTKGFCQCIGhRnYX/X+n+/TSu/+Qv9btoQdXPOhh2r1SsbahQ/oLe6h79qnXTJwEFKkF/b32yIbAzajFnwb3LKTGZZdvY4MssAAFGJ4izsH3TZrY/pyXtHKrGlr8rhgA4ckTp286mzc8qIuyBBSQpoX8MnkY1BmzDbLpnMskAgYLcwr7tulHMFAIDoQnEW5lNyeh+7Fdmiww3a1+gcNxN3QVdd6BxHNAatys0sW7TokXBmGS1MAEA0+0bI4hzDdaxShYPHWrc/atviLCWac3UlmjHkdpXPXm/d0tXBHmixz8+RijZo8VUVpx6T1cs52cS8ovNkHn/8CecIJzpy5IheeGGL/vSnxbr99l/rhz8c7lwBAODUMjIynCMPMsUZTvBZRWheas9Qr+nFofedU6GPN4fy+vUMpc6rCH3mnDI+3/1o6MZeA0LTi2sjGxOhXr16Okexr6yszDmKjN/vD40fPz509913hz788EPnbHQ43blGM+Yau7hvYxNz9Q7ampHq7FO3jtKRAwEddk4ZwYP1qpVP3bueH9kYfG0ms8y0ME1mWX5+PpllAICYRHEWqQ5JuvyG3mp8rUb7wnlln+qdHRWq18VK7tklsjH4WtzMspSUFHvBf2pqqnMFAIDYQnEWsQSljxqheP8CzV22U4cU1KHqjVqyulzxY8br+j6dIhyD02EyyyZMmGBvu7Rq1WNklgEAYh7FWcTi5Bt+q1YWjNKeOZlKSUpSyshcVQyao5X3jFEP+ysZyRhEwmSWmW2XTGZZTs7NdgvTJP0DABDrKBda0iFds/17VOu+UtMVl6j0qQXaWGtds2+7tLFgstITz3MGWCIZg6/kZpb5fD4yywAA7Q7FGTzDZJaZbZfczDJzTAsTANDeUJzhnDOZZStWrNCkSTcpMzNTa9asYdslAEC7RXGGc+rVV1/VnXf+i6qqqlRcXKKsrCznCgAA7RPFGc4JN7OsoKBA//zPs8gsAwDAQXGGs8q8CtNklqWlDdSQIUO0dOlSXXrppc5VAABAcYazxmSW/exnP7Mzy7ZufdluYbLgHwCA41Gcoc2ZFqabWTZrVlMLk8wyAABaRnGGNmUyy8y2S25m2dChQ50rAACgJRRnaBOmhWlyytauXUdmGQAAp4HiDK3KLPg3mWWmhWkyyxYuXEhmGQAAp4HiDK2mrKzM3nbJJP2TWQYAwNdDcYYzZooxk1k2f/58u4WZm5tLZhkAAF8TxRm+NjezLCPjynBmGS1MAADODMUZvhaz7ZKbWeb37yCzDACAVkJxhtPiZpbNnPnrcGYZLUwAAFoPxRkiZlqYJrPMBMiSWQYAQNugOMMpuZllpaWl9oL/KVOm0MIEAKCNUJzhpMyCf5NTZjLLsrPHkVkGAMBZQHGGFpltl0xmWSAQsFuY1103yrkCAADaEsUZjuNmli1a9Eg4s4wWJgAAZw/FGWzutktuZtmaNWtoYQIAcA5QnCGcWVZVVRXOLAMAAOcGxVk7ZjLLTAvTZJbl5+eTWQYAgAdQnLVTbmZZSkqKveA/NTXVuQIAAM4lirN2xmSWTZgwwd52adWqx8gsAwDAYyjO2gmz4N9su2Qyy3JybrZbmCbpHwAAeAvFWTvgZpb5fD4yywAA8DiKsxhmMsvMtktuZpk5poUJAIC3UZzFIDezbNKkm5SZmUlmGQAAUYTiLMaYzDLTwjSZZcXFJWSWAQAQZSjOYoSbWVZQUKCioofILAMAIEpRnEU508I0mWVpaQPtbZeWLl1KZhkAAFGM4qy1BetUuTxfo5MuUpJ9G6IZhSWqrDvqDGg9JrPMbLtkMsu2bn3ZbmGy4B8AgOhGcdaqggq8uECT83doUNFzqqrdo5pt96tHaa6yclapOugMO0Omhelmls2aNYvMMgAAYgjFWauqV+Wm59WYlq1pY/uqi3UmLnGYpk4cLPnLtXP/saZhZ8Bklpltl9zMsqFDhzpXAABALKA4a03HavXKhhrFD+it7uGvbCddMnCQEuTX9jcbnHOnz7QwTU7Z2rXryCwDAOAcu/rq4fYTJm2B4qw1HQ7owBGpYzefOjunjLgLEpSkgPY1fOKciZybWWZamCazbOHChWSWAQBwjpn9qc0TJiYpwYS+tyaKs9Z0uEH7Gp3jZuIu6KoLnePTUVZWZmeWmTudzDIAALzDrPU2T5iYpISMjCvt5ITW8o2QxTnGmaor0Ywht6t89nrrlq4Ozumm83Okog1anNXLOdnEvKITAABEvxtuuNEu2M4UxVlrCmxR/pVTtCHn+OIsWL1EWSPn6cIWirOTMUXbrl3V7WJdmZlrbe0e563YxlxjU3uaq8F9G5uY69djlh8VFRXp6ac32CHwrZE1SluzNXX2qVtH6ciBgA47p4zgwXrVyqfuXU+v0GLBPwAA3uUuPzItTpOg0Foh8BRnralDki6/obcaX6vRvnCm2ad6Z0eF6nWxknuacA0AABDtzAsB5s+fbycoTJkypVWfUKE4a1UJSh81QvH+BZq7bKcOKahD1Ru1ZHW54seM1/V9OjnjAABANPvRj36kNWvWtEmCAsVZq4qTb/itWlkwSnvmZColKUkpI3NVMWiOVt4zRj34agMAEBPaMgSecqG1xSUqfWqBNtbusRcb1tbu0saCyUpPPM8ZAAAAcHIUZwAAAB5ClAYAAICH8MwZAACAh1CceUmwTpXL8zU66SI7IC8paYhmFJaosu6oMyAWBHWossia4+0qqTvmnDOOqq5ypfJH93XmfpH6z5inkso6619El2Dddi3PvzE8j6T+01VYUqm6ZhOJZExUOFSt5wqnq78zj5bus5iZ63EaVFn4Y2s+x38fx85c/66SGQO/mId7S5unSme6sXS/njiX/jMe1vbmj7ux8NhsdqoJf/5fvqUVVsq+a2Pm99CJv1PMPDap+lCzb1Avz9W0NeEFn4c+3vybUL9ePwrlFb8ZOmjOvP9s6DeZ3wv1uvHR0O7Pm0ZFt89DB99cFprer2eoV6/bQsXvf+act3y8OZTX73uhzLzi0O6D1mQ/3xva/JsfWeMmhR7d/YkzKAoc3BaaZ91n/aYvDG17/4h14uPQ7uLfhDJ7WXObt82+X0OhD0Kb84aFemX+JlS8+2Pr7SOh9zf/1h5z46NvWl+lKPH5u6HiX17xxTzC91lWaF7FR86gGJnrcazv44oHrTmc+H0cQ3N1fh5P/nnH0Fztn9lhoemPvn78427mg6EK81hkzSZmH5udx6temb8NbbYfr2Jlru7P6BWhXxa/2/T96D425222HpWbxnh5rjxz5hn1qtz0vBrTsjVtbF+ZuNq4xGGaOnGw5C/Xzv3Nn2WKQvZfKL/RpP/8SEPH9XVOuoIKVD6vdY2DNXHaaCV3sb4t43po+NRspek1/XXnB844r7PmUf4XLarqrZxbp+gK+xW6PiVnzdRdU7+jqkV/UXnA+qst8Lo2rftAaRMna2yyzxpznhKHj9fENOuu/usb2m+/L+8LvvW8/vz0x1/Mw7rPrrl1uq7Xdi194e2mv8JjZK7HOVShR/L+S1XOm2ExNNfgvhq91vgdDej97ZbbKzEz109V/eR8Fb47QlPG9Xced6/VnXf9RPFVG/TCbrPXS6w+Nh/Ve8+usB6vvqOpd/1K19iPV7Ey18Pa/cIG62d0iEZf1aPpe7hLf12d2VuNy5/U8/az3d6eK8WZVxyr1SsbahQ/oLe6h++VTrpk4CAlyK/tbzY456LRMdWt/52yVp6vO343RWndwlvCOw7rb6+8rMb4Purd/YvIkbhLBurahHq9tP0tBZxz3hYn3zX36o3aUs1ONz/qrk7ydYuXGuvVcDioY3+r1IYTf/HF9dTAa3tLL1XqTVPARYG45GlaX7tL66f1PekDSazM9QsNqnzkPhXqJ5o99fg/MmJnrkEd2vu2qq0/ja7o19U5d7yYmWvwXb20rlzx40Yo3efO5ISf41h9bA6U6b/uXiuNuVO3De/WdC6mfw+dwONzDX9KOMcOB3TgiNSxm0+dnVNG3AUJSrJKk30NnzhnolGculyWo+eezHP+OjvRpwocaLQm31W+zs2+JePi9a2keDXuazhur9KoE9yrHZtrpITvKqlbnHVXN+iI4tXN13zHiA664FvWA6RTwEWlQ7tU8tCf9Ex8tu75yfetGQVjbK5mveQy5RVKs++7WVcf90dGLM3V/WPpAz1111BnLU5fjc5f6azFiaG5Bhv1UW2j9dDToNeL3LWTzedqicnH5k9Vve4RLW+8Qjk513wRkB4zc+2s7119g1K0TRv/5z3rO9Zy6A29UGoVY2Ou05ALrZ9dj8+V4swrDjdon1WfnCjugq660DmOXlZxljywqV3Zok/UsK+F58biOqvrhR2dN6KV9QvdX6rVfilt1g1K62D9Ymuo15fvausXW9dvOcfRxnqgXzJZSSkjNXP5Pl1/y090lV2Ex9hc7XbmYqsyy9PN6Sd+/jE0V/ePCX1LP7j7WSdMe7seTP5/mjztYVUeOhY7cz1Qq531Uv1D9+nPmq7NNdZcazbrrm+uVpY9V+vXeiw+Nh96TU+tLrcelP63fpTW7NnRmJmr9TsnPUcP3Zusp2cOVW9TdKf8WIXv/kQL/2NsUzHq8blSnAFtyVmf9O6YuXr4pydv/0W3TkqettL+JV6z7X71ePrnuvbWEr0XTU+KnZLbzpyh+24eZK9PiVlxfTVt/S7VvvGwpvU168kMn/qOHq1hVf+le56s1ufO2VgRPyZP994+VInmB9Rd71q1RmvLrcot5rhrY63abFyG+sTkg9JRvVeSq7FzL9C9m6qa/sCo2aZl41/RTyf8sano9jiKM6/o3FXd453jZoIHG6Jz0fRpOV9du7u/BJoJHlbD/iPOG1Ho0E4tmXWb9Qv9Nq38g/PXmvUj17lrgr58Vx/TwYaPnOPo5S6obXz6CT3z1tEYmWvzduZPld7iM8Cxfb9+oVG1Hx3W+bEyV+dxt2PfJF3Y7G5tevakRhteqdWxmHtsdtrWGqxxwy4+vgiIlbm66+nGTdQ49w+McNG9WAue3ev5uVKceUVnn7p1lI4cCBy3vip4sF611l+t3bue75yJRc6C+SMNCjRfq+KsB4nv3vW4NQHRIFhXpqJZP9ecPWO1bMmvmv1Ct36J+7qqo/XQeCDwqXPOsH6xfXTA+hM+QV2br7uLOm5r64A+OhiMkbm6r/zarsKs7ztrsPopq3Cnda1EM4eka0bJ3hi/X5v7ZuzMtcs/Kjm5hd/QtnglfStecbH22Oy2rdNGaVif5msGLbEyV6dl+eX1ZKborlf5Ox9YRbe35xorjxbRr0OSLr+htxpfq9G+cH3yqd7ZUWF9K12s5J6x3EjprEsvv1LxjW+pZt8X4X/Bd3Zoc3289eD5j1HURgrq0K7lyrl2gv5gF2b/9qUXQXS4NF03xH+g12o+tEY73AfM5O+q50nX5nlJUIEtc9Q/6QfK32L9Qg5znj2J76dLrHnHxly7KH12qbP2yr29qZLZl1nXslS0rVKLs3rFyFwtgS3K73+R+udvOe5V0k3PKPTWDZcnqVOszDXu2+o94Duq37xD74Qn4s7VeTVqrD02739Df/U3KuHagbrkxLspVubaLUmXJTjHzTTdrwkafMl31MHjc42Sn6D2IEHpo0Yo3r9Ac5ft1CHrIe9Q9UYtWV2u+DHjdf2Jf+HElDj50kdoXPwLmjv3Ce0y6wEO7dL6JWvljx+tX1x/SdR8owbfW687s+7WM8pW0Z+/XJjZfN/XqHHfkX9uoZbtMr/+Aqpev1Kr/f+gMb8YESVrQKz7bPCNykn5QOtW/N+m+yz8PfuaUnKm6Loe1txjYq4RipW5+tKUnXOFGtet1jp7Hpbge3px+VpVu7ELMXO/dtPw2+7UmOoFemB9bVOh6Tz2hOcaY4/Nx957W+VugeKc+0KMzLXD9/WTe7J1pHStHnN3LHG+h/0pM3TrdT2tEx6fqxNGCy/4/P1QxbI8J3nc3Exi/opQhZ3cHCsOhirmXX9CsrpxJPR+xYpQnklnduefmRdaVvF+U7pzVHDn5t5/J96uD82raNoj4PP3t4WW5Zk0fffaj0J5y7aF3o+ytPHP368IFc/7RaifO49+vwjNe3a3nbbtipW5Hq/l7+OYmat5LCp+wNnNw9yuCE2f90zT7h2O2LlfPw8d3P1MaN70K046V/vrESOPzZ9VPBBK7TUslLf5A+fMCWJmrh+Hdj/7YLPv4Rbm4eG5fsP8n1OnAQAA4ByLpaYCAABA1KM4AwAA8BCKMwAAAA+hOAMAAPAQijMAAAAPoTgDAADwEIozAAAAD6E4AwAA8BCKMwAAAA+hOAMAAPAQijMAAAAPoTgDAADwEIozAAAAD6E4AwAA8BCKMwAAAA+hOAMQIxpUWfhjJc0oUZ1zBgCiEcUZgBgQ0K4ld2ly4XbnbQCIXhRnAKJasG67luffov88mqZxCc5JAIhiFGcAotjftf7fb9PKb/5Cv5s2RN2cswAQzSjOAESxf9Bltz6mJ+8dqUQezQDECB7OAEQxn5LT+6iL8xYAxAKKMwAAAA+hOAMAAPAQijMAAAAPoTgDAADwEIozAAAAD6E4A4BW96mql0xW//wtCjhnWl2wTtuLpqt/0kVKGv07bak76lwAEO0ozgDEhg7pmu3fo9rFWUp0Tp0zwXf10ro6jRv1ffmcU60t+NZG/fbpVK2s2q3nJr6hWY+9rmPONQDRjeIMAFrbofdVXZ2o5J5tl8AWlzxN6zfOVHqXozr40TElfSueB3QgRvCzDACtKqhA5fNalzxKw/p0cs4193eVzBiopNH5+nOh05a0bv1nPKzt1Tv1XPhcX43OL1H1oaDz71pi3tdwZS3qousu+wfnHIBoR3EGAK2qXpWbXlLyuAz1+apH2KonteajSdpcU6uqkn/Txc/8Ttkjf67HvjndOve2ti2bKi3P1b88+arKCzPtAu6LW6YKKw9Z76SXshbvUM1zN6rq5gV6MfBVhRyAaEFxBgCtKfihal6TBvT+9lc/wMb/RHfdea0S4+LUJS1TE9PirXOjNWXaVda585T4gzHKTGiU/6/v6qLZpaqt3dPs9n81PfAf6j+jRHXWu4rr0lXfbnqvAGLAN0IW5xgAWpV5lidWmSKpJcHqJcoa+7buePkeXeNrqTwzrcgbNLN8mkrK71B6h2bndK+2uS9oOFapwsFjrdsfvzjXXPA9bbnnl/rpklesoi5Tdy4r0O1XJPIXNxADKM4AoNWYCI3pGlt9s14uuOYkr9RspeIMQMzijywAaDWHtLe6TsnJ/6i2e50mgFhHcQYArSXwujatS9S4YRfz4Arga+PxAwBaxakiNAAgMhRnAKJDXYlmJF2ktMJKjybhH9W+mrfMyzTVnUdWAGeAFwQAiA6mOBtyu8pnr7du6bLX0QNADOLvOwAAAA+hOAPQxg5oS/4PlDR2iaqbB9gHd2nJ2L7qn79FAfP2oWptWZKv0W4Kfv/pKiypVF2LofcmemKgktLmqTLc4zymupLbm6XnO2O+zjZJwTpVLj/hc3muWua9AkBbozgD0MYSlD5qhOL9m/TSW58656z6562tWuf/jsaN+r58wVqV3DlZP537oSZuqlJt7dvatvASlc68SdMe3H5mRVHE2yRVq6k8a1Dlg7co6746jVlbrhr3c/n5ZN1ZUuuMAYC2Q3EGoI3FyZc+QuPiy7XupXed4uZTvfXSJvnjR2hUelcFXlysu5+Wxtyfp5/2NdGt5ynxmtt13+wUVRXO15PVXxR1py3ibZLe0H5reLC6RPcUVikt99+cxH3zufxKd009T0/fvZj9KwG0OYozAG3P932NGvcd+VeXym/ah8F39dK6csWPG6F03zH7VY6NStZVl13Y7EHJp0svH6B4vavqvWfw3FnHrvJ1dt5rXGd1vbCjNCxd/VrcWumY9u8sl1+9de3Ans0+l67qd0Wa1PiyXvnbYeccALQNijMAZ4HT2qxao7Xl9ce3NK2C6OBHB6wx31LXC5q/BjNOnX1d1VEB7Wv4xDnX1qzPpeEj6787VZjVr2m9mX3rrSEzS5qGAEAbozgDcBa4rc0ardu0TRXhlmaCda2DLvhWN+u/H6nhYPMEs6AOBxp0xCrfunc93znX1qzPpeu3rP9erXuf+5u9ufnxt1LNTmdjJgBti+IMwNlhtzZ7q7Fijf57tdvSNA9B56l77z6KV7X+Z+f+ZgvuA/rbK6+pURcruWckBVGD3tzud46/rg668LLBSlPz9XGG2dB8spKSJmvJmax/A4AIUJwBOEvc1uazeqbKbWkacfINn6H7x0hP332flu0ywRpHVbflj8orrFLK7Fn6p+QTt0P6ji77wQCpfrUWrNipQ2b89ie1Yl2Nc/3ri+szQr8Y8w/yz/0P/XF7nVWgmfe9RHPnlp/kcwGA1kVxBuAscVub1mG4pemIS1LWH1ZqWe63tXpUipKSvqsht7yjzKLHtOSfr9CXnzfrpOSfPqC1dw7QS3MylWKNv/a/D2rouMud62fAfC4L1qskL1FPZw9Wb/O5ZG9Q97wVJ/lcAKB1sX0TAACAh/DMGQAAgIdQnAEAAHgIxRkAAICHUJwBAAB4CMUZAACAh1CcAQAAeAjFGQAAgIdQnAEAAHiG9P8DElIy72lWjfYAAAAASUVORK5CYII="></p>
<p>What is the quantity of the gas?</p>
<p>A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup></mrow><mi>R</mi></mfrac><mo> </mo><mtext>mol</mtext></math></p>
<p>B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>200</mn><mi>R</mi></mfrac><mo> </mo><mtext>mol</mtext></math></p>
<p>C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>80</mn><mi>R</mi></mfrac><mo> </mo><mtext>mol</mtext></math></p>
<p>D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mrow><mn>5</mn><mi>R</mi></mrow></mfrac><mo> </mo><mtext>mol</mtext></math></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>This question tested candidate understanding of the relationship between the slope of a graph and the ideal gas law. SL candidates found this question more difficult than their HL counterparts, but in both groups of students, option C was the most frequent (and correct) answer.</p>
</div>
<br><hr><br><div class="question">
<p>Energy is transferred to water in a flask at a rate <em>P</em>. The water reaches boiling point and then <em>P</em> is increased. What are the changes to the temperature of the water and to the rate of vaporization of the water after the change?</p>
<p><img 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"></p>
<p style="text-align:center;"> </p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Container X contains 1.0 mol of an ideal gas. Container Y contains 2.0 mol of the ideal gas. Y has four times the volume of X. The pressure in X is twice that in Y.</p>
<p>What is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{temperature of gas in X}}}}{{{\text{temperature of gas in Y}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>temperature of gas in X</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>temperature of gas in Y</mtext>
</mrow>
</mrow>
</mfrac>
</math></span>?</p>
<p> </p>
<p>A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4}">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math></span></p>
<p>B. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span></p>
<p>C. 1</p>
<p>D. 2</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Energy is supplied at a constant rate to a fixed mass of a material. The material begins as a solid. The graph shows the variation of the temperature of the material with time. </p>
<p><img src="data:image/png;base64,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" alt></p>
<p>The specific heat capacities of the solid, liquid and gaseous forms of the material are c<sub>s</sub> c<sub>l</sub> and c<sub>g</sub> respectively. What can be deduced about the values of c<sub>s</sub> c<sub>l</sub> and c<sub>g</sub>? </p>
<p>A. c<sub>s</sub> > c<sub>g</sub> > c<sub>l</sub> <br>B. c<sub>l</sub> > c<sub>s</sub> > c<sub>g <br></sub>C. c<sub>l</sub> > c<sub>g</sub> > c<sub>s</sub> <br>D. c<sub>g</sub> > c<sub>s</sub> > c<sub>l</sub></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A liquid is initially at its freezing point. Energy is removed at a uniform rate from the liquid until it freezes completely.<br>Which graph shows how the temperature <em>T</em> of the liquid varies with the energy <em>Q</em> removed from the liquid?</p>
<p><img 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"></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>What is the relation between the value of the unified atomic mass unit in grams and the value of Avogadro’s constant in mol<sup>−1</sup>?</p>
<p>A. Their ratio is 1.</p>
<p>B. Their product is 1.</p>
<p>C. Their sum is 1.</p>
<p>D. Their difference is 0.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>B</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>An ideal gas of constant mass is heated in a container of constant volume.</p>
<p>What is the reason for the increase in pressure of the gas?</p>
<p>A. The average number of molecules per unit volume increases.</p>
<p>B. The average force per impact at the container wall increases.</p>
<p>C. Molecules collide with each other more frequently.</p>
<p>D. Molecules occupy a greater fractional volume of the container.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>B</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>Many candidates chose option C which is a typical misconception that collision between molecules has something to do with pressure.</p>
</div>
<br><hr><br><div class="question">
<p>A 1.0 kW heater supplies energy to a liquid of mass 0.50 kg. The temperature of the liquid changes by 80 K in a time of 200 s. The specific heat capacity of the liquid is 4.0 kJ kg<sup>–1</sup> K<sup>–1</sup>. What is the average power lost by the liquid?</p>
<p>A. 0</p>
<p>B. 200 W</p>
<p>C. 800 W</p>
<p>D. 1600 W</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>B</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>What is true for an ideal gas?</p>
<p><br>A. <em>nRT = Nk</em><sub>B</sub><em>T</em></p>
<p>B. <em>nRT = k</em><sub>B</sub><em>T</em></p>
<p>C. <em>RT = Nk</em><sub>B</sub><em>T</em></p>
<p>D. <em>RT = k</em><sub>B</sub><em>T</em></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A container is filled with a mixture of helium and oxygen at the same temperature. The molar mass of helium is 4 g mol<sup>–1</sup> and that of oxygen is 32 g mol<sup>–1</sup>.</p>
<p>What is the ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{average speed of helium molecules}}}}{{{\text{average speed of oxygen molecules}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>average speed of helium molecules</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>average speed of oxygen molecules</mtext>
</mrow>
</mrow>
</mfrac>
</math></span>?</p>
<p> </p>
<p>A. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{8}">
<mfrac>
<mn>1</mn>
<mn>8</mn>
</mfrac>
</math></span></p>
<p>B. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{\sqrt 8 }}">
<mfrac>
<mn>1</mn>
<mrow>
<msqrt>
<mn>8</mn>
</msqrt>
</mrow>
</mfrac>
</math></span></p>
<p>C. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\sqrt 8 }">
<mrow>
<msqrt>
<mn>8</mn>
</msqrt>
</mrow>
</math></span></p>
<p>D. 8</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Under what conditions of pressure and temperature does a real gas approximate to an ideal gas?</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>C</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>A container that contains a fixed mass of an ideal gas is at rest on a truck. The truck now moves away horizontally at a constant velocity. What is the change, if any, in the internal energy of the gas and the change, if any, in the temperature of the gas when the truck has been travelling for some time?</p>
<p><img src="images/Schermafbeelding_2018-08-12_om_09.27.13.png" alt="M18/4/PHYSI/SPM/ENG/TZ2/12"></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p><span style="background-color: #ffffff;">A mass <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></em> of water is at a temperature of 290 K. The specific heat capacity of water is <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></em>. Ice, at its melting point, is added to the water to reduce the water temperature to the freezing point. The specific latent heat of fusion for ice is <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></em>. What is the minimum mass of ice that is required?</span></p>
<p><span style="background-color: #ffffff;">A. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>17</mn><mi>m</mi><mi>c</mi></mrow><mi>L</mi></mfrac></math></span></p>
<p><span style="background-color: #ffffff;">B. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>290</mn><mi>m</mi><mi>c</mi></mrow><mi>L</mi></mfrac></math></span></p>
<p><span style="background-color: #ffffff;">C. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>17</mn><mi>m</mi><mi>L</mi></mrow><mi>c</mi></mfrac></math></span></p>
<p><span style="background-color: #ffffff;">D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>290</mn><mi>m</mi><mi>L</mi></mrow><mi>c</mi></mfrac></math></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>A</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p><strong>System X</strong> is at a temperature of 40 °C. Thermal energy is provided to system X until it reaches a temperature of 50 °C. <strong>System Y</strong> is at a temperature of 283 K. Thermal energy is provided to system Y until it reaches a temperature of 293 K.</p>
<p>What is the difference in the thermal energy provided to both systems?</p>
<p>A. Zero</p>
<p>B. Larger for X</p>
<p>C. Larger for Y</p>
<p>D. Cannot be determined with the data given</p>
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<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>D</p>
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<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>This question gives good discrimination although slightly more candidates chose option A instead of the correct option D. It is unusual that the correct response is 'cannot be determined' but the lack of mass or specific heat capacity in the data should have alerted candidates that they were not able to work out or compare how much thermal energy was supplied.</p>
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