A Level H2 Physics Thermal Physics Quiz

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A-Level Physics H2 Quiz - Thermal Physics

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

Duration: 45 minutes
Total Marks: 45

Instructions:

1. Answer all questions.
2. Write your answers in the spaces provided.
3. Show all working clearly. Marks may be awarded for correct working even if the final answer is incorrect.
4. Use $g = 9.81 \text{ m s}^{-2}$ where necessary.
5. The molar gas constant $R = 8.31 \text{ J mol}^{-1} \text{ K}^{-1}$.
6. The Avogadro constant $N_A = 6.02 \times 10^{23} \text{ mol}^{-1}$.

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Section A: Temperature and Internal Energy (Questions 1–5)

1. Define the term internal energy of a system.
[2]

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2. State two assumptions of the kinetic theory of gases regarding the motion of molecules.
[2]

(a) ___________________________________________________________________

(b) ___________________________________________________________________

3. Explain, in terms of molecular behavior, why the internal energy of an ideal gas depends only on its temperature.
[2]

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4. A student claims that if the temperature of a gas increases from $20^\circ\text{C}$ to $40^\circ\text{C}$, the average kinetic energy of its molecules doubles. Explain why this statement is incorrect.
[2]

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5. Two objects, A and B, are in thermal contact. Object A is at $80^\circ\text{C}$ and Object B is at $20^\circ\text{C}$.
(a) State the direction of net thermal energy flow.
[1]

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(b) State the condition required for thermal equilibrium to be reached.
[1]

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Section B: Ideal Gas Laws and Kinetic Theory (Questions 6–12)

6. A fixed mass of an ideal gas occupies a volume of $2.0 \times 10^{-3} \text{ m}^3$ at a pressure of $1.5 \times 10^5 \text{ Pa}$ and a temperature of $300 \text{ K}$. Calculate the number of moles of gas present.
[3]

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7. Using the data from Question 6, calculate the total number of molecules in the gas.
[2]

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8. The gas in Question 6 is heated at constant volume until its pressure doubles. Calculate the new temperature of the gas in Kelvin.
[2]

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9. Explain, using the kinetic theory of gases, why the pressure of the gas increases when it is heated at constant volume.
[3]

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10. Show that the mean square speed $\langle c^2 \rangle$ of gas molecules is related to the pressure $p$ and density $\rho$ by the equation: $p = \frac{1}{3} \rho \langle c^2 \rangle$ You may start from the kinetic theory equation $pV = \frac{1}{3} N m \langle c^2 \rangle$.
[2]

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11. Calculate the root-mean-square (r.m.s.) speed of nitrogen molecules ($N_2$) at a temperature of $300 \text{ K}$.
(Molar mass of $N_2 = 28.0 \text{ g mol}^{-1}$)
[3]

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12. Sketch a graph showing the distribution of molecular speeds for a gas at temperature $T_1$ and at a higher temperature $T_2$ on the same axes. Label the axes and the curves clearly.
[3]

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Section C: Thermodynamics and First Law (Questions 13–20)

13. State the First Law of Thermodynamics, defining all symbols used.
[2]

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14. A gas expands from a volume of $0.02 \text{ m}^3$ to $0.05 \text{ m}^3$ against a constant external pressure of $1.0 \times 10^5 \text{ Pa}$. Calculate the work done by the gas.
[2]

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15. During the expansion in Question 14, $5000 \text{ J}$ of thermal energy is supplied to the gas. Calculate the change in internal energy of the gas.
[2]

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16. An ideal gas undergoes an isothermal expansion.
(a) State what happens to the internal energy of the gas.
[1]

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(b) Explain why thermal energy must be supplied to the gas during this process.
[2]

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17. Distinguish between an adiabatic process and an isothermal process.
[2]

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18. On a $p-V$ diagram, the curve for an adiabatic expansion is steeper than the curve for an isothermal expansion starting from the same point. Explain why this is the case.
[3]

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19. 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]

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(b) Suggest one reason why the actual efficiency of a real engine is lower than this theoretical maximum.
[1]

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20. A fixed mass of gas is compressed rapidly in a cylinder fitted with a piston.
(a) State whether the process is approximately adiabatic or isothermal.
[1]

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(b) Explain what happens to the temperature of the gas during this compression.
[2]

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End of Quiz

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

1. Define the term internal energy of a system. [2]

• Answer: The sum of the random kinetic energy [1] and potential energy [1] of the molecules/atoms within the system.
• Note: Must mention both KE and PE. "Random" is key for KE.

2. State two assumptions of the kinetic theory of gases regarding the motion of molecules. [2]

• Answer: (Any two of the following)
  • Molecules move in random directions / random motion. [1]
  • Collisions between molecules and with walls are perfectly elastic. [1]
  • Intermolecular forces are negligible except during collisions. [1]
  • The volume of the molecules is negligible compared to the volume of the container. [1]
  • Time of collision is negligible compared to time between collisions. [1]

3. Explain, in terms of molecular behavior, why the internal energy of an ideal gas depends only on its temperature. [2]

• Answer:
  • For an ideal gas, there are no intermolecular forces, so the potential energy is zero (or constant). [1]
  • Therefore, internal energy consists only of kinetic energy, which is directly proportional to the absolute temperature. [1]

4. A student claims that if the temperature of a gas increases from $20^\circ\text{C}$ to $40^\circ\text{C}$, the average kinetic energy of its molecules doubles. Explain why this statement is incorrect. [2]

• Answer:
  • Average kinetic energy is proportional to absolute temperature (Kelvin), not Celsius. [1]
  • $20^\circ\text{C} = 293 \text{ K}$ and $40^\circ\text{C} = 313 \text{ K}$. The ratio is $313/293 \approx 1.07$, not 2. [1]

5. Two objects, A and B, are in thermal contact. Object A is at $80^\circ\text{C}$ and Object B is at $20^\circ\text{C}$.

• (a) State the direction of net thermal energy flow. [1]
  • Answer: From A to B (or from hot to cold).
• (b) State the condition required for thermal equilibrium to be reached. [1]
  • Answer: When both objects are at the same temperature.

6. Calculate the number of moles of gas present. [3]

• Answer:
  • Use $pV = nRT$
  • $n = \frac{pV}{RT}$
  • $n = \frac{(1.5 \times 10^5)(2.0 \times 10^{-3})}{(8.31)(300)}$
  • $n = \frac{300}{2493} \approx 0.120 \text{ mol}$
• Marks: 1 for formula, 1 for substitution, 1 for answer ($0.12$ or $0.120$).

7. Calculate the total number of molecules in the gas. [2]

• Answer:
  • $N = n \times N_A$
  • $N = 0.120 \times 6.02 \times 10^{23}$
  • $N \approx 7.22 \times 10^{22}$ molecules
• Marks: 1 for method, 1 for answer.

8. Calculate the new temperature of the gas in Kelvin. [2]

• Answer:
  • At constant volume, $p \propto T$ (Pressure Law).
  • $\frac{p_1}{T_1} = \frac{p_2}{T_2}$
  • Since $p_2 = 2p_1$, then $T_2 = 2T_1$.
  • $T_2 = 2 \times 300 = 600 \text{ K}$.
• Marks: 1 for reasoning/ratio, 1 for answer.

9. Explain, using the kinetic theory of gases, why the pressure of the gas increases when it is heated at constant volume. [3]

• Answer:
  • Temperature increase means molecules have higher average kinetic energy / speed. [1]
  • Molecules collide with the walls more frequently. [1]
  • Each collision involves a greater change in momentum (greater force per collision). [1]
  • (Result: Greater average force per unit area = higher pressure).

10. Show that $p = \frac{1}{3} \rho \langle c^2 \rangle$. [2]

• Answer:
  • Start with $pV = \frac{1}{3} N m \langle c^2 \rangle$. [1]
  • Density $\rho = \frac{\text{total mass}}{V} = \frac{Nm}{V}$.
  • Rearrange equation: $p = \frac{1}{3} \frac{Nm}{V} \langle c^2 \rangle$.
  • Substitute $\rho$: $p = \frac{1}{3} \rho \langle c^2 \rangle$. [1]

11. Calculate the r.m.s. speed of nitrogen molecules at $300 \text{ K}$. [3]

• Answer:
  • Molar mass $M = 28.0 \text{ g mol}^{-1} = 0.028 \text{ kg mol}^{-1}$.
  • Formula: $\frac{1}{2} M \langle c^2 \rangle = \frac{3}{2} RT \Rightarrow c_{rms} = \sqrt{\frac{3RT}{M}}$
  • $c_{rms} = \sqrt{\frac{3 \times 8.31 \times 300}{0.028}}$
  • $c_{rms} = \sqrt{\frac{7479}{0.028}} = \sqrt{267107}$
  • $c_{rms} \approx 517 \text{ m s}^{-1}$
• Marks: 1 for formula, 1 for conversion of mass, 1 for answer.

12. Sketch Maxwell-Boltzmann distribution. [3]

• Answer:
  • Axes: y-axis = Number of molecules (or fraction), x-axis = Speed. [1]
  • Curve $T_1$: Starts at origin, rises to peak, tails off asymptotically to x-axis. [1]
  • Curve $T_2$: Peak is lower and shifted to the right (higher speed) compared to $T_1$. Area under both curves is equal. [1]

13. State the First Law of Thermodynamics. [2]

• Answer:
  • $\Delta U = Q + W$ (or $\Delta U = Q - W$ depending on convention, must define).
  • $\Delta U$: Change in internal energy. [0.5]
  • $Q$: Thermal energy supplied to the system. [0.5]
  • $W$: Work done on the system. [1]
  • (If using $\Delta U = Q - W$, $W$ is work done by the system).

14. Calculate the work done by the gas. [2]

• Answer:
  • $W = p \Delta V$
  • $W = 1.0 \times 10^5 \times (0.05 - 0.02)$
  • $W = 1.0 \times 10^5 \times 0.03 = 3000 \text{ J}$
• Marks: 1 for formula/sub, 1 for answer.

15. Calculate the change in internal energy. [2]

• Answer:
  • $\Delta U = Q - W_{by}$ (Using convention where $W_{by}$ is work done by gas)
  • $Q = +5000 \text{ J}$ (supplied)
  • $W_{by} = +3000 \text{ J}$
  • $\Delta U = 5000 - 3000 = +2000 \text{ J}$
• Marks: 1 for correct signs/logic, 1 for answer.

16. Isothermal expansion.

• (a) State what happens to internal energy. [1]
  • Answer: Internal energy remains constant ($\Delta U = 0$).
• (b) Explain why thermal energy must be supplied. [2]
  • Answer:
    • Gas does work during expansion ($W_{by} > 0$). [1]
    • Since $\Delta U = 0$, $Q = W_{by}$. Energy must be supplied as heat to compensate for the work done, keeping temperature constant. [1]

17. Distinguish between adiabatic and isothermal processes. [2]

• Answer:
  • Adiabatic: No thermal energy enters or leaves the system ($Q=0$). [1]
  • Isothermal: Temperature remains constant ($\Delta T = 0$, so $\Delta U = 0$ for ideal gas). [1]

18. Explain why adiabatic curve is steeper than isothermal on p-V diagram. [3]

• Answer:
  • In isothermal expansion, $T$ is constant, so $p$ decreases only due to volume increase ($p \propto 1/V$). [1]
  • In adiabatic expansion, gas does work at the expense of internal energy, so $T$ decreases. [1]
  • The drop in temperature causes an additional decrease in pressure, making the pressure drop faster for the same volume increase. [1]

19. Heat engine efficiency.

• (a) Calculate maximum theoretical efficiency. [2]
  • Answer:
    • $\eta = 1 - \frac{T_C}{T_H}$
    • $\eta = 1 - \frac{300}{600} = 1 - 0.5 = 0.5$ or $50\%$
• (b) Suggest one reason for lower actual efficiency. [1]
  • Answer: Friction / Heat loss to surroundings / Irreversible processes / Energy used to move engine parts.

20. Rapid compression.

• (a) State whether adiabatic or isothermal. [1]
  • Answer: Adiabatic.
• (b) Explain temperature change. [2]
  • Answer:
    • Work is done on the gas ($W > 0$). [1]
    • Since $Q \approx 0$, $\Delta U = W$. Internal energy increases, so temperature increases. [1]