The graph shows the variation with time t of the temperature T 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.

What is the correct comparison of the specific latent heats L_X and L_Y and specific heat capacities in the liquid phase c_X and c_Y of X and Y?

D

Two pulses are travelling towards each other.

What is a possible pulse shape when the pulses overlap?

A

A thin-walled cylinder of weight W, open at both ends, rests on a flat surface. The cylinder has a height L, an average radius R and a thickness x where R is much greater than x.

What is the pressure exerted by the cylinder walls on the flat surface?

A.  $\frac{W}{2\pi Rx}$

B.  $\frac{W}{\pi R^{2}x}$

C.  $\frac{W}{\pi R^2}$

D.  $\frac{W}{\pi R^{2}L}$

A

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 

A. the mean square speed.
B. the number striking the container walls every second. 
C. the force between them. 
D. their diameter.

B

A substance in the gas state has a density about $1000$ times less than when it is in the liquid state. The diameter of a molecule is $d$. What is the best estimate of the average distance between molecules in the gas state?

A.  $d$

B.  $10d$

C.  $100d$

D.  $1000d$

B

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.

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

$\frac{\text{specific latent heat of vaporization}}{\text{specific heat capacity of the liquid}}$

for this substance?

A. 15 K⁻¹

B. 15 K

C. 300 K⁻¹

D. 300 K

D

A fixed mass of an ideal gas in a closed container with a movable piston initially occupies a volume V. 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.

What is the new volume of the gas?

A.  $\frac{V}{4}$

B.  $\frac{V}{2}$

C.  2V

D.  4V

C

What does the constant n represent in the equation of state for an ideal gas pV = nRT?

A. The number of atoms in the gas

B. The number of moles of the gas

C. The number of molecules of the gas

D. The number of particles in the gas

B

The graph shows how the temperature of a liquid varies with time when energy is supplied to the liquid at a constant rate P. The gradient of the graph is K and the liquid has a specific heat capacity c.

What is the mass of the liquid?

A.     $\frac{P}{cK}$

B.     $\frac{PK}{c}$

C.     $\frac{Pc}{K}$

D.     $\frac{cK}{P}$

A

Two identical containers X and Y each contain an ideal gas. X has N molecules of gas at an absolute temperature of T and Y has 3N molecules of gas at an absolute temperature of $\frac{T}{2}$ What is the ratio of the pressures $\frac{P_Y}{P_X}$?

A.   $\frac{1}{6}$

B.   $\frac{2}{3}$

C.   $\frac{3}{2}$

D.   $6$

C

A sealed cylinder of length l and cross-sectional area A contains N molecules of an ideal gas at kelvin temperature T.

What is the force acting on the area of the cylinder marked A due to the gas?

A.     $\frac{NRT}{l}$

B.     $\frac{NRT}{lA}$

C.     $\frac{N{k}_{B}T}{lA}$

D.     $\frac{N{k}_{B}T}{l}$

D

A sealed container contains a mixture of oxygen and nitrogen gas.
The ratio $\frac{\text{mass of an oxygen molecule}}{\text{mass of a nitrogen molecule}}$ is $\frac{8}{7}$.

The ratio $\frac{\text{average kinetic energy of oxygen molecules}}{\text{average kinetic energy of nitrogen molecules}}$ is

A.  1.

B.  $\frac{7}{8}$.

C.  $\frac{8}{7}$.

D.  dependent on the concentration of each gas.

A

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?

A.     It remains the same.

B.     It decreases.

C.     It increases until the ice melts and then remains the same.

D.     It increases.

A

A fixed mass of an ideal gas has a volume of $V$, a pressure of p and a temperature of $30 °\text{C}$. The gas is compressed to the volume of $\frac{V}{6}$ and its pressure increases to 12p. What is the new temperature of the gas?

A.  $15 °\text{C}$

B.  $60 °\text{C}$

C.  $333 °\text{C}$

D.  $606 °\text{C}$

C

Two blocks, X and Y, are placed in contact with each other. Data for the blocks are provided.

X has a mass $m$. What is the mass of Y?

A.  $\frac{m}{4}$

B.  $m$

C.  $4 m$

D.  $6 m$

C

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.

A sample of oxygen gas with a volume of $3.0 {\text{m}}^3$ is at $100 °\text{C}$. The gas is heated so that it expands at a constant pressure to a final volume of $6.0 {\text{m}}^3$. What is the final temperature of the gas?

A. $750 °\text{C}$

B. $470 °\text{C}$

C. $370 °\text{C}$

D. $200 °\text{C}$

B

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 m³. What is the pressure of the gas?

A. 8 kPa

B. 25 kPa

C. 40 kPa

D. 80 kPa

D

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?

A.  The internal energy increases.

B.  The internal energy decreases.

C.  There is no change in the internal energy.

D.  The internal energy is zero.

A

This question was well answered by HL and SL candidates, although option C did prove to be a distraction for some.

A liquid is vaporized to a gas at a constant temperature.

Three quantities of the substance are the

I.   total intermolecular potential energy
II.  root mean square speed of the molecules
III. average distance between the molecules.

Which quantities are greater for the substance in the gas phase compared to the liquid phase?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

B

Which assumption is part of the molecular kinetic model of ideal gases? 

A.  The work done on a system equals the change in kinetic energy of the system.

B.  The volume of a gas results from adding the volume of the individual molecules.

C.  A gas is made up of tiny identical particles in constant random motion.

D.  All particles in a gas have kinetic and potential energy.

C

A quantity of an ideal gas is at a temperature T in a cylinder with a movable piston that traps a length L of the gas. The piston is moved so that the length of the trapped gas is reduced to $\frac{5L}{6}$ and the pressure of the gas doubles.

What is the temperature of the gas at the end of the change?

A.  $\frac{5}{12}T$

B.  $\frac{3}{5}T$

C.  $\frac{5}{3}T$

D.  $\frac{12}{5}T$

C

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.

A substance changes from the solid phase to the gas phase without becoming a liquid and without a change in temperature.

What is true about the internal energy of the substance and the total intermolecular potential energy of the substance when this phase change occurs?

C

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.

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^–1 K^–1. What is the time taken to heat the water from 25 °C to 95 °C?

A.   7 s

B.   30 s

C.   7 minutes

D.   420 minutes

C

A gas storage tank of fixed volume V contains N molecules of an ideal gas at temperature T. The pressure at kelvin temperature T is 20 MPa. $\frac{N}{4}$ molecules are removed and the temperature changed to 2T. What is the new pressure of the gas?

A. 10 MPa

B. 15 MPa

C. 30 MPa

D. 40 MPa

C

The temperature of a fixed mass of an ideal gas changes from 200 °C to 400 °C.

What is $\frac{\text{mean kinetic energy of gas at 200 °C}}{\text{mean kinetic energy of gas at 400 °C}}$?

A. 0.50

B. 0.70

C. 1.4

D. 2.0

B

Most candidates chose A having forgotten to convert from oC to K.

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?

D

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.

P is held at a temperature of 200 K and Q is held at a temperature of 400 K.

What is mass of $\frac{\mathrm{mass} \mathrm{of} \mathrm{gas} \mathrm{in} \mathrm{P}}{\mathrm{mass} \mathrm{of} \mathrm{gas} \mathrm{in} \mathrm{Q}}$?

A. $\frac{1}{8}$

B. $\frac{1}{4}$

C. 4

D. 8

C

A container holds 20 g of argon-40(${}_{18}^{40}\text{Ar}$)  and 40 g of neon-20 (${}_{10}^{20}\text{Ne}$) .

What is$\frac{\text{number of atoms of argon -40}}{\text{number of atoms of neon -20}}$ in the container?

A. 0.25

B. 0.5

C. 2

D. 4

A

An insulated tube is filled with a large number n of lead spheres, each of mass m. The tube is inverted s times so that the spheres completely fall through an average distance L each time. The temperature of the spheres is measured before and after the inversions and the resultant change in temperature is ΔT.

What is the specific heat capacity of lead?

A. $\frac{sgL}{nm\mathrm{\Delta }T}$

B. $\frac{sgL}{\mathrm{\Delta }T}$

C. $\frac{sgL}{n\mathrm{\Delta }T}$

D. $\frac{gL}{m\mathrm{\Delta }T}$

B

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^–1.

What is the time taken for all the water to vaporize?

A. 250 s

B. 400 s

C. 2500 s

D. 4000 s

B

This question was well answered by candidates.

A bicycle of mass $M$ comes to rest from speed $v$ using the back brake. The brake has a specific heat capacity of $c$ and a mass $m$. Half of the kinetic energy is absorbed by the brake.

What is the change in temperature of the brake?

A.  $\frac{M{v}^2}{4mc}$

B.  $\frac{M{v}^2}{2mc}$

C.  $\frac{m{v}^2}{4Mc}$

D.  $\frac{m{v}^2}{2Mc}$

A

An ideal gas of N molecules is maintained at a constant pressure p. The graph shows how the volume V of the gas varies with absolute temperature T.

What is the gradient of the graph?

A. $\frac{N}{p}$

B. $\frac{NR}{p}$

C. $\frac{N{k}_{\mathrm{B}}}{p}$

D. $\frac{N}{Rp}$

C

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?

A

A mass $m$ of a liquid of specific heat capacity $c$ flows every second through a heater of power $P$. What is the difference in temperature between the liquid entering and leaving the heater?

A.  $\frac{mc}{P}$

B.  $273+\frac{mc}{P}$

C.  $\frac{P}{mc}$

D.  $273+\frac{P}{mc}$

C

A mass m of ice at a temperature of –5 °C is changed into water at a temperature of 50 °C.

Specific heat capacity of ice = c_i
Specific heat capacity of water = c_w
Specific latent heat of fusion of ice = L

Which expression gives the energy needed for this change to occur?

A.  55 m c_w + m L

B.  55 m c_i + 5 m L

C.  5 m c_i + 50 m c_w + m L

D.  5 m c_i + 50 m c_w + 5 m L

C

A piece of metal at a temperature of $100 °\text{C}$ is dropped into an equal mass of water at a temperature of $15 °\text{C}$ 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?

A.  $83 °\text{C}$

B.  $57 °\text{C}$

C.  $45 °\text{C}$

D.  $32 °\text{C}$

D

What are the units of the ratio $\frac{\text{specific heat capacity of copper}}{\text{specific latent heat of vaporization of copper}}$?

A.     no units

B.     k

C.     k^–1

D.     k^–2

C

Which aspect of thermal physics is best explained by the molecular kinetic model?

A. The equation of state of ideal gases

B. The difference between Celsius and Kelvin temperature

C. The value of the Avogadro constant

D. The existence of gaseous isotopes

A

An ideal gas is maintained at a temperature of 100 K. The variation of the pressure P and $\frac{1}{\text{volume}}$ of the gas is shown.

What is the quantity of the gas?

A.  $\frac{2\times {10}^5}{R} \text{mol}$

B.  $\frac{200}{R} \text{mol}$

C.  $\frac{80}{R} \text{mol}$

D.  $\frac{4}{5R} \text{mol}$

C

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.

Energy is transferred to water in a flask at a rate P. The water reaches boiling point and then P is increased. What are the changes to the temperature of the water and to the rate of vaporization of the water after the change?

D

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.

What is $\frac{\text{temperature of gas in X}}{\text{temperature of gas in Y}}$?

A.   $\frac{1}{4}$

B.   $\frac{1}{2}$

C.   1

D.   2

C

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. 

The specific heat capacities of the solid, liquid and gaseous forms of the material are c_s c_l and c_g respectively. What can be deduced about the values of c_s c_l and c_g? 

A. c_s > c_g > c_l 
B. c_l > c_s > c_g 
C. c_l > c_g > c_s 
D. c_g > c_s > c_l

D

A liquid is initially at its freezing point. Energy is removed at a uniform rate from the liquid until it freezes completely.
Which graph shows how the temperature T of the liquid varies with the energy Q removed from the liquid?

A

What is the relation between the value of the unified atomic mass unit in grams and the value of Avogadro’s constant in mol⁻¹?

A. Their ratio is 1.

B. Their product is 1.

C. Their sum is 1.

D. Their difference is 0.

B

An ideal gas of constant mass is heated in a container of constant volume.

What is the reason for the increase in pressure of the gas?

A.  The average number of molecules per unit volume increases.

B.  The average force per impact at the container wall increases.

C.  Molecules collide with each other more frequently.

D.  Molecules occupy a greater fractional volume of the container.

B

Many candidates chose option C which is a typical misconception that collision between molecules has something to do with pressure.

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^–1 K^–1. What is the average power lost by the liquid?

A. 0

B. 200 W

C. 800 W

D. 1600 W

B

What is true for an ideal gas?

A.  nRT = Nk_BT

B.  nRT = k_BT

C.  RT = Nk_BT

D.  RT = k_BT

A

A container is filled with a mixture of helium and oxygen at the same temperature. The molar mass of helium is 4 g mol^–1 and that of oxygen is 32 g mol^–1.

What is the ratio $\frac{\text{average speed of helium molecules}}{\text{average speed of oxygen molecules}}$?

A.   $\frac{1}{8}$

B.   $\frac{1}{\sqrt{8}}$

C.   $\sqrt{8}$

D.   8

C

Under what conditions of pressure and temperature does a real gas approximate to an ideal gas?

C

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?

A

A mass $m$ of water is at a temperature of 290 K. The specific heat capacity of water is $c$. 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 $L$. What is the minimum mass of ice that is required?

A. $\frac{17mc}{L}$

B. $\frac{290mc}{L}$

C. $\frac{17mL}{c}$

D. $\frac{290mL}{c}$

A

System X is at a temperature of 40 °C. Thermal energy is provided to system X until it reaches a temperature of 50 °C. System Y is at a temperature of 283 K. Thermal energy is provided to system Y until it reaches a temperature of 293 K.

What is the difference in the thermal energy provided to both systems?

A.  Zero

B.  Larger for X

C.  Larger for Y

D.  Cannot be determined with the data given

D

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.