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A Level H2 Physics Thermal Physics Quiz

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Questions

A-Level Physics H2 Quiz - Thermal Physics

Name: __________________________
Class: __________________________
Date: __________________________
Score: _______ / 45

Duration: 60 minutes
Total Marks: 45
Instructions:

Answer all questions.
Show all working clearly.
Use $g = 9.81 \text{ m s}^{-2}$ where applicable.
The data booklet is assumed to be available.

Section A: Multiple Choice & Short Concepts (Questions 1-5)

1. Which of the following statements correctly describes the internal energy of an ideal gas?
A. It is the sum of the kinetic and potential energies of the molecules.
B. It is proportional to the absolute temperature of the gas.
C. It depends on the volume of the gas at constant temperature.
D. It includes the intermolecular potential energy due to attractive forces.
[1]

2. A fixed mass of an ideal gas expands from volume $V_1$ to $V_2$ at constant pressure $p$ . The work done by the gas is:
A. $p(V_2 - V_1)$
B. $p(V_1 - V_2)$
C. $\frac{1}{2}p(V_2 + V_1)$
D. $0$
[1]

3. State the meaning of the term absolute zero in terms of the kinetic theory of gases.

[1]

4. The first law of thermodynamics is expressed as $\Delta U = q + w$ .
Define the symbols $q$ and $w$ in this equation, stating the sign convention for energy added to the system.
$q$ : ___________________________________________________________________
$w$ : ___________________________________________________________________
[2]

5. A quantity of ideal gas undergoes an isothermal expansion. Explain why the internal energy of the gas remains constant during this process.

[2]

Section B: Structured Concepts (Questions 6-10)

6. Two objects, A and B, are in thermal contact. Object A is at $50^\circ\text{C}$ and Object B is at $30^\circ\text{C}$ .
State the condition required for thermal equilibrium to be established between them.

[1]

7. The specific latent heat of vaporization of water is significantly larger than its specific latent heat of fusion.
Explain this difference in terms of molecular separation and work done against atmospheric pressure.

[2]

8. Brownian motion provides evidence for the kinetic model of matter.
Describe what is observed when smoke particles in air are viewed under a microscope.

[2]

9. Explain how the observation of Brownian motion supports the idea that air consists of moving molecules.

[3]

10. A student investigates the relationship between pressure $p$ and volume $V$ of a fixed mass of air at constant temperature. The data is plotted as $p$ against $1/V$ .
Explain why the graph of $p$ against $1/V$ is expected to be a straight line passing through the origin for an ideal gas.

[2]

Section C: Calculations & Applications (Questions 11-15)

11. A cylinder contains $0.20 \text{ mol}$ of an ideal monatomic gas at a pressure of $2.0 \times 10^5 \text{ Pa}$ and a volume of $4.0 \times 10^{-3} \text{ m}^3$ .
Calculate the temperature of the gas.
[2]

Answer space

12. The gas in Question 11 is heated at constant volume until its pressure doubles.
(i) Calculate the new temperature of the gas.
[1]

Answer space

(ii) Determine the thermal energy supplied to the gas. (For a monatomic ideal gas, $U = \frac{3}{2}nRT$ ).
[3]

Answer space

13. An ideal gas undergoes a cyclic process. During one part of the cycle, it undergoes an isothermal expansion at $T = 300 \text{ K}$ . The volume increases from $2.0 \times 10^{-3} \text{ m}^3$ to $6.0 \times 10^{-3} \text{ m}^3$ . The pressure at the start of the expansion is $3.0 \times 10^5 \text{ Pa}$ .
Calculate the work done by the gas during this expansion.
[3]

Answer space

14. In the same cycle as Question 13, the gas undergoes an isobaric compression.
State and explain whether the internal energy of the gas increases, decreases, or remains constant during an isobaric compression.

[2]

15. A heat engine operates between a hot reservoir at $600 \text{ K}$ and a cold reservoir at $300 \text{ K}$ .
(a) Calculate the maximum theoretical efficiency of this engine.
[2]

Answer space

(b) If the engine absorbs $1200 \text{ J}$ of energy from the hot reservoir in one cycle, calculate the maximum useful work output per cycle.
[2]

Answer space

Section D: Data-Based & Complex Problems (Questions 16-20)

16. An electric kettle has a power rating of $2.4 \text{ kW}$ . It contains $1.5 \text{ kg}$ of water at an initial temperature of $20^\circ\text{C}$ . The specific heat capacity of water is $4200 \text{ J kg}^{-1} \text{ K}^{-1}$ .
Calculate the time taken to heat the water from $20^\circ\text{C}$ to its boiling point of $100^\circ\text{C}$ . Assume no energy is lost to the surroundings.
[3]

Answer space

17. After the water in Question 16 reaches $100^\circ\text{C}$ , the kettle continues to operate for another $2.0$ minutes. The specific latent heat of vaporization of water is $2.26 \times 10^6 \text{ J kg}^{-1}$ .
Calculate the mass of water that is converted into steam during this time.
[3]

Answer space

18. In reality, the time taken to boil the water in Question 16 is longer than calculated.
Explain two reasons for this discrepancy.

[2]

19. A fixed mass of ideal gas is confined in a cylinder by a movable piston. The gas expands slowly against a constant external pressure of $1.0 \times 10^5 \text{ Pa}$ . During the expansion, the volume of the gas increases by $5.0 \times 10^{-4} \text{ m}^3$ , and $150 \text{ J}$ of thermal energy is supplied to the gas.
(a) Calculate the work done by the gas during the expansion.
[2]

Answer space

(b) Calculate the change in internal energy of the gas.
[2]

Answer space

20. In the experiment described in Question 10, the line of best fit for $p$ against $1/V$ does not pass exactly through the origin at very high pressures.
(a) Suggest one reason for this deviation from ideal gas behavior.

[1]

(b) The gradient of the straight line portion of the graph in Question 10 is found to be $2500 \text{ J}$ . If the temperature of the air is $300 \text{ K}$ , calculate the amount of gas in moles. ( $R = 8.31 \text{ J mol}^{-1} \text{ K}^{-1}$ ).
[3]

Answer space

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Answers

A-Level Physics H2 Quiz - Thermal Physics (Answer Key)

1. B
Reasoning: For an ideal gas, there are no intermolecular forces, so potential energy is zero. Internal energy is the sum of random kinetic energies, which is proportional to absolute temperature ( $U \propto T$ ).

2. A
Reasoning: Work done by gas at constant pressure is $W = p\Delta V = p(V_{final} - V_{initial})$ .

3. Absolute zero is the temperature at which the molecules of a gas have minimum kinetic energy (or zero kinetic energy in the classical ideal gas model).
[1 mark for reference to minimum/zero kinetic energy]

4.
$q$ : Thermal energy (heat) supplied to the system.
$w$ : Work done on the system.
[1 mark for each correct definition with sign convention implied or stated]

5.
For an ideal gas, internal energy depends only on temperature ( $U \propto T$ ).
In an isothermal process, the temperature remains constant.
Therefore, the internal energy remains constant.
[1 mark for U depends on T, 1 mark for T constant]

6.
There is no net flow of thermal energy between them (or they are at the same temperature).
[1 mark]

7.
Vaporization involves separating molecules completely from the liquid phase to the gas phase, requiring significant work against intermolecular forces.
Fusion only involves loosening the rigid structure of the solid, requiring less separation.
Additionally, vaporization involves a large increase in volume, doing work against atmospheric pressure, whereas fusion involves a negligible volume change.
[1 mark for separation/intermolecular forces, 1 mark for work against atmosphere]

8.
Smoke particles move in random, erratic, zig-zag motion.
[1 mark for random/erratic, 1 mark for continuous motion]

9.
The smoke particles are bombarded by air molecules.
The air molecules are moving randomly and at high speeds.
The unequal bombardment of smoke particles from different sides causes the erratic motion.
[1 mark for bombardment, 1 mark for random motion of air molecules, 1 mark for unequal forces]

10.
Ideal gas law: $pV = nRT \Rightarrow p = (nRT) \times \frac{1}{V}$ .
If $T$ is constant, $nRT$ is constant.
Thus $p$ is directly proportional to $1/V$ , yielding a straight line through the origin.
[1 mark for equation/proportionality, 1 mark for constant gradient]

11.
Using $pV = nRT$ :
$T = \frac{pV}{nR} = \frac{(2.0 \times 10^5)(4.0 \times 10^{-3})}{0.20 \times 8.31}$
$T = \frac{800}{1.662} \approx 481 \text{ K}$
[1 mark for substitution, 1 mark for answer]

12.
(i) At constant volume, $p \propto T$ .
If pressure doubles, temperature doubles.
$T_{new} = 2 \times 481 = 962 \text{ K}$
[1 mark]

(ii) $\Delta U = \frac{3}{2}nR\Delta T$
$\Delta T = 962 - 481 = 481 \text{ K}$
$\Delta U = 1.5 \times 0.20 \times 8.31 \times 481$
$\Delta U \approx 1200 \text{ J}$ (or $1.2 \text{ kJ}$ )
[1 mark for $\Delta T$ , 1 mark for formula, 1 mark for answer]

13.
Work done in isothermal expansion:
$W = nRT \ln(\frac{V_2}{V_1}) = p_A V_A \ln(\frac{V_B}{V_A})$
$W = (3.0 \times 10^5)(2.0 \times 10^{-3}) \ln(\frac{6.0}{2.0})$
$W = 600 \ln(3) \approx 600 \times 1.099 = 659 \text{ J}$
[1 mark for formula, 1 mark for substitution, 1 mark for answer]

14.
Decreases.
Process is isobaric compression. Volume decreases, so from $pV=nRT$ , temperature must decrease.
Since $U \propto T$ , internal energy decreases.
[1 mark for decrease, 1 mark for explanation linking V, T and U]

15.
(a) Efficiency $\eta = 1 - \frac{T_c}{T_h} = 1 - \frac{300}{600} = 1 - 0.5 = 0.5$ or $50\%$ .
[1 mark for formula, 1 mark for answer]

(b) $W = \eta \times Q_h = 0.5 \times 1200 = 600 \text{ J}$ .
[1 mark for substitution, 1 mark for answer]

16.
Energy required $Q = mc\Delta \theta = 1.5 \times 4200 \times (100 - 20) = 1.5 \times 4200 \times 80 = 504,000 \text{ J}$ .
Time $t = \frac{Q}{P} = \frac{504,000}{2400} = 210 \text{ s}$ .
[1 mark for Q calc, 1 mark for formula, 1 mark for answer]

17.
Energy supplied in 2 mins: $E = P \times t = 2400 \times (2 \times 60) = 288,000 \text{ J}$ .
Mass $m = \frac{E}{L_v} = \frac{288,000}{2.26 \times 10^6} \approx 0.127 \text{ kg}$ .
[1 mark for E calc, 1 mark for formula, 1 mark for answer]

18.

Energy loss to the surroundings (air/kettle body) via conduction/convection/radiation.
Energy absorbed by the kettle material itself (not just the water).
[1 mark each]

19.
(a) $W = p\Delta V = 1.0 \times 10^5 \times 5.0 \times 10^{-4} = 50 \text{ J}$ .
[1 mark for formula, 1 mark for answer]

(b) First Law: $\Delta U = q + w$ .
Sign convention: Heat supplied $q = +150 \text{ J}$ . Work done by gas is $50 \text{ J}$ , so work done on gas $w = -50 \text{ J}$ .
$\Delta U = 150 - 50 = +100 \text{ J}$ .
[1 mark for signs, 1 mark for answer]

20.
(a) At high pressures, the volume of the gas molecules themselves is not negligible compared to the container volume, OR intermolecular forces become significant.
[1 mark]

(b) Gradient $k = nRT$ .
$2500 = n \times 8.31 \times 300$
$n = \frac{2500}{2493} \approx 1.00 \text{ mol}$
[1 mark for identifying gradient, 1 mark for substitution, 1 mark for answer]