SL Paper 2
A sample of vegetable oil, initially in the liquid state, is placed in a freezer that transfers thermal energy from the sample at a constant rate. The graph shows how temperature of the sample varies with time .
The following data are available.
Mass of the sample
Specific latent heat of fusion of the oil
Rate of thermal energy transfer
Calculate the thermal energy transferred from the sample during the first minutes.
Estimate the specific heat capacity of the oil in its liquid phase. State an appropriate unit for your answer.
The sample begins to freeze during the thermal energy transfer. Explain, in terms of the molecular model of matter, why the temperature of the sample remains constant during freezing.
Calculate the mass of the oil that remains unfrozen after minutes.
A mass of 1.0 kg of water is brought to its boiling point of 100 °C using an electric heater of power 1.6 kW.
A mass of 0.86 kg of water remains after it has boiled for 200 s.
The electric heater has two identical resistors connected in parallel.
The circuit transfers 1.6 kW when switch A only is closed. The external voltage is 220 V.
The molar mass of water is 18 g mol−1. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.
State one assumption of the kinetic model of an ideal gas.
Estimate the specific latent heat of vaporization of water. State an appropriate unit for your answer.
Explain why the temperature of water remains at 100 °C during this time.
The heater is removed and a mass of 0.30 kg of pasta at −10 °C is added to the boiling water.
Determine the equilibrium temperature of the pasta and water after the pasta is added. Other heat transfers are negligible.
Specific heat capacity of pasta = 1.8 kJ kg−1 K−1
Specific heat capacity of water = 4.2 kJ kg−1 K−1
Show that each resistor has a resistance of about 30 Ω.
Calculate the power transferred by the heater when both switches are closed.
Cold milk enters a small sterilizing unit and flows over an electrical heating element.
The temperature of the milk is raised from 11 °C to 84 °C. A mass of 55 g of milk enters the sterilizing unit every second.
Specific heat capacity of milk = 3.9 kJ kg−1 K−1
The milk flows out through an insulated metal pipe. The pipe is at a temperature of 84 °C. A small section of the insulation has been removed from around the pipe.
Estimate the power input to the heating element. State an appropriate unit for your answer.
Outline whether your answer to (a) is likely to overestimate or underestimate the power input.
Discuss, with reference to the molecules in the liquid, the difference between milk at 11 °C and milk at 84 °C.
State how energy is transferred from the inside of the metal pipe to the outside of the metal pipe.
The missing section of insulation is 0.56 m long and the external radius of the pipe is 0.067 m. The emissivity of the pipe surface is 0.40. Determine the energy lost every second from the pipe surface. Ignore any absorption of radiation by the pipe surface.
Describe one other method by which significant amounts of energy can be transferred from the pipe to the surroundings.
Define internal energy.
0.46 mole of an ideal monatomic gas is trapped in a cylinder. The gas has a volume of 21 m3 and a pressure of 1.4 Pa.
(i) State how the internal energy of an ideal gas differs from that of a real gas.
(ii) Determine, in kelvin, the temperature of the gas in the cylinder.
(iii) The kinetic theory of ideal gases is one example of a scientific model. Identify one reason why scientists find such models useful.
A large cube is formed from ice. A light ray is incident from a vacuum at an angle of 46˚ to the normal on one surface of the cube. The light ray is parallel to the plane of one of the sides of the cube. The angle of refraction inside the cube is 33˚.
Each side of the ice cube is 0.75 m in length. The initial temperature of the ice cube is –20 °C.
Calculate the speed of light inside the ice cube.
Show that no light emerges from side AB.
Sketch, on the diagram, the subsequent path of the light ray.
Determine the energy required to melt all of the ice from –20 °C to water at a temperature of 0 °C.
Specific latent heat of fusion of ice = 330 kJ kg–1
Specific heat capacity of ice = 2.1 kJ kg–1 k–1
Density of ice = 920 kg m–3
Outline the difference between the molecular structure of a solid and a liquid.
The first scientists to identify alpha particles by a direct method were Rutherford and Royds. They knew that radium-226 () decays by alpha emission to form a nuclide known as radon (Rn).
Write down the missing values in the nuclear equation for this decay.
Rutherford and Royds put some pure radium-226 in a small closed cylinder A. Cylinder A is fixed in the centre of a larger closed cylinder B.
At the start of the experiment all the air was removed from cylinder B. The alpha particles combined with electrons as they moved through the wall of cylinder A to form helium gas in cylinder B.
The wall of cylinder A is made from glass. Outline why this glass wall had to be very thin.
Rutherford and Royds expected 2.7 x 1015 alpha particles to be emitted during the experiment. The experiment was carried out at a temperature of 18 °C. The volume of cylinder B was 1.3 x 10–5 m3 and the volume of cylinder A was negligible. Calculate the pressure of the helium gas that was collected in cylinder B.
Rutherford and Royds identified the helium gas in cylinder B by observing its emission spectrum. Outline, with reference to atomic energy levels, how an emission spectrum is formed.
The work was first reported in a peer-reviewed scientific journal. Outline why Rutherford and Royds chose to publish their work in this way.
A closed box of fixed volume 0.15 m3 contains 3.0 mol of an ideal monatomic gas. The temperature of the gas is 290 K.
When the gas is supplied with 0.86 kJ of energy, its temperature increases by 23 K. The specific heat capacity of the gas is 3.1 kJ kg–1 K–1.
Calculate the pressure of the gas.
Calculate, in kg, the mass of the gas.
Calculate the average kinetic energy of the particles of the gas.
Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.
The diagram below shows part of a downhill ski course which starts at point A, 50 m above level ground. Point B is 20 m above level ground.
A skier of mass 65 kg starts from rest at point A and during the ski course some of the gravitational potential energy transferred to kinetic energy.
At the side of the course flexible safety nets are used. Another skier of mass 76 kg falls normally into the safety net with speed 9.6 m s–1.
From A to B, 24 % of the gravitational potential energy transferred to kinetic energy. Show that the velocity at B is 12 m s–1.
Some of the gravitational potential energy transferred into internal energy of the skis, slightly increasing their temperature. Distinguish between internal energy and temperature.
The dot on the following diagram represents the skier as she passes point B.
Draw and label the vertical forces acting on the skier.
The hill at point B has a circular shape with a radius of 20 m. Determine whether the skier will lose contact with the ground at point B.
The skier reaches point C with a speed of 8.2 m s–1. She stops after a distance of 24 m at point D.
Determine the coefficient of dynamic friction between the base of the skis and the snow. Assume that the frictional force is constant and that air resistance can be neglected.
Calculate the impulse required from the net to stop the skier and state an appropriate unit for your answer.
Explain, with reference to change in momentum, why a flexible safety net is less likely to harm the skier than a rigid barrier.
An ideal monatomic gas is kept in a container of volume 2.1 × 10–4 m3, temperature 310 K and pressure 5.3 × 105 Pa.
The volume of the gas in (a) is increased to 6.8 × 10–4 m3 at constant temperature.
State what is meant by an ideal gas.
Calculate the number of atoms in the gas.
Calculate, in J, the internal energy of the gas.
Calculate, in Pa, the new pressure of the gas.
Explain, in terms of molecular motion, this change in pressure.
Liquid oxygen at its boiling point is stored in an insulated tank. Gaseous oxygen is produced from the tank when required using an electrical heater placed in the liquid.
The following data are available.
Mass of 1.0 mol of oxygen = 32 g
Specific latent heat of vaporization of oxygen = 2.1 × 105 J kg–1
An oxygen flow rate of 0.25 mol s–1 is needed.
Distinguish between the internal energy of the oxygen at the boiling point when it is in its liquid phase and when it is in its gas phase.
Calculate, in kW, the heater power required.
Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of 260 K.
State one assumption of the kinetic model of an ideal gas that does not apply to oxygen.
The graph shows the variation with temperature T of the pressure P of a fixed mass of helium gas trapped in a container with a fixed volume of 1.0 × 10−3 m3.
Deduce whether helium behaves as an ideal gas over the temperature range 250 K to 500 K.
Helium has a molar mass of 4.0 g. Calculate the mass of gas in the container.
A second container, of the same volume as the original container, contains twice as many helium atoms. The graph of the variation of P with T is determined for the gas in the second container.
Predict how the graph for the second container will differ from the graph for the first container.
A quantity of 0.24 mol of an ideal gas of constant volume 0.20 m3 is kept at a temperature of 300 K.
State what is meant by the internal energy of an ideal gas.
Calculate the pressure of the gas.
The temperature of the gas is increased to 500 K. Sketch, on the axes, a graph to show the variation with temperature T of the pressure P of the gas during this change.
A container is filled with 1 mole of helium (molar mass 4 g mol−1) and 1 mole of neon (molar mass 20 g mol−1). Compare the average kinetic energy of helium atoms to that of neon atoms.
A container of volume 3.2 × 10-6 m3 is filled with helium gas at a pressure of 5.1 × 105 Pa and temperature 320 K. Assume that this sample of helium gas behaves as an ideal gas.
A helium atom has a volume of 4.9 × 10-31 m3.
The molar mass of helium is 4.0 g mol-1. Show that the mass of a helium atom is 6.6 × 10-27 kg.
Estimate the average speed of the helium atoms in the container.
Show that the number of helium atoms in the container is about 4 × 1020.
Calculate the ratio .
Explain, using your answer to (d)(i) and with reference to the kinetic model, why this sample of helium can be assumed to be an ideal gas.
A tube of constant circular cross-section, sealed at one end, contains an ideal gas trapped by a cylinder of mercury of length 0.035 m. The whole arrangement is in the Earth’s atmosphere. The density of mercury is 1.36 × 104 kg m–3.
When the mercury is above the gas column the length of the gas column is 0.190 m.
The tube is slowly rotated until the gas column is above the mercury.
The length of the gas column is now 0.208 m. The temperature of the trapped gas does not change during the process.
A solid cylinder of height h and density ρ rests on a flat surface.
Show that the pressure pc exerted by the cylinder on the surface is given by pc = ρgh.
Show that (po + pm) × 0.190 = where
po = atmospheric pressure
pm = pressure due to the mercury column
T = temperature of the trapped gas
n = number of moles of the trapped gas
A = cross-sectional area of the tube.
Determine the atmospheric pressure. Give a suitable unit for your answer.
Outline why the gas particles in the tube hit the mercury surface less often after the tube has been rotated.
A fixed mass of an ideal gas is contained in a cylinder closed with a frictionless piston. The volume of the gas is 2.5 × 10−3 m3 when the temperature of the gas is 37 °C and the pressure of the gas is 4.0 × 105 Pa.
Energy is now supplied to the gas and the piston moves to allow the gas to expand. The temperature is held constant.
Calculate the number of gas particles in the cylinder.
Discuss, for this process, the changes that occur in the density of the gas.
Discuss, for this process, the changes that occur in the internal energy of the gas.
The air in a kitchen has pressure 1.0 × 105 Pa and temperature 22°C. A refrigerator of internal volume 0.36 m3 is installed in the kitchen.
The refrigerator door is closed. The air in the refrigerator is cooled to 5.0°C and the number of air molecules in the refrigerator stays the same.
With the door open the air in the refrigerator is initially at the same temperature and pressure as the air in the kitchen. Calculate the number of molecules of air in the refrigerator.
Determine the pressure of the air inside the refrigerator.
The door of the refrigerator has an area of 0.72 m2. Show that the minimum force needed to open the refrigerator door is about 4 kN.
Comment on the magnitude of the force in (b)(ii).