A Level H2 Physics Thermal Physics Quiz

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A-Level Physics H2 Quiz - Thermal Physics

Name: ____________________ Class: ____________________ Date: __________ Score: ________

Duration: 60 minutes
Total Marks: 50 marks

Instructions:

• Answer all questions.
• Show all necessary working for calculation questions.
• Use $g = 9.81 \text{ m s}^{-2}$, $R = 8.31 \text{ J K}^{-1} \text{ mol}^{-1}$, and $N_A = 6.02 \times 10^{23} \text{ mol}^{-1}$ where applicable.

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Section A: Fundamental Concepts (Questions 1–5)

Short answer and definition questions.

1. Define the term internal energy of a gas. [2]
   
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2. State the First Law of Thermodynamics in terms of energy changes. [2]
   
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3. Explain why the temperature of a gas increases when it is compressed adiabatically. [2]
   
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4. Distinguish between isothermal and adiabatic processes. [2]
   
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5. State the equation of state for an ideal gas and define each symbol used. [2]
   
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Section B: Ideal Gases and Kinetic Theory (Questions 6–12)

Calculations and conceptual applications.

6. A sample of helium gas occupies a volume of $2.0 \text{ m}^3$ at a pressure of $1.0 \times 10^5 \text{ Pa}$ and a temperature of $300 \text{ K}$. Calculate the number of moles of helium present. [2]
   
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7. Calculate the root-mean-square (r.m.s.) speed of the helium atoms in Question 6. (Molar mass of He = $4.0 \text{ g mol}^{-1}$) [3]
   
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8. Explain, using the kinetic theory of gases, why the pressure of a fixed mass of gas increases when its temperature is raised at constant volume. [3]
   
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9. A gas undergoes a process where its volume is doubled while the pressure is kept constant. If the initial temperature was $27^\circ\text{C}$, calculate the final temperature in Kelvin. [2]
   
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10. Describe the relationship between the average kinetic energy of a molecule and the absolute temperature of an ideal gas. [2]
    
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11. A container holds $0.5 \text{ mol}$ of an ideal gas. Calculate the total internal energy of the gas at $20^\circ\text{C}$. [2]
    
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12. Explain why the ideal gas law $pV = nRT$ is less accurate at very high pressures and very low temperatures. [3]
    
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Section C: Thermodynamics and Heat Engines (Questions 13–20)

Structured problems and data interpretation.

13. A gas is compressed isothermally from a volume of $0.8 \text{ m}^3$ to $0.4 \text{ m}^3$ at a constant pressure of $2.0 \times 10^5 \text{ Pa}$. Calculate the work done on the gas. [2]
    
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14. In a thermodynamic process, $500 \text{ J}$ of heat is added to a system, and the system does $200 \text{ J}$ of work on its surroundings. Calculate the change in internal energy. [2]
    
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15. A heat engine operates between a hot reservoir at $600 \text{ K}$ and a cold reservoir at $300 \text{ K}$. Calculate the maximum theoretical efficiency of this engine. [2]
    
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16. For the engine in Question 15, if $1000 \text{ J}$ of heat is extracted from the hot reservoir per cycle, calculate the amount of heat rejected to the cold reservoir. [3]
    
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17. Explain the role of a "working substance" in a heat pump. [2]
    
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18. A cylinder contains a gas. The gas is expanded rapidly such that no heat is exchanged with the surroundings. State the name of this process and explain the change in temperature. [3]
    
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19. Compare the efficiency of a real heat engine with a Carnot engine operating between the same two temperatures. Justify your answer. [3]
    
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20. A graph of pressure $p$ against volume $V$ shows a closed loop for a cyclic process. Explain what the area enclosed by the loop represents. [3]
    
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Answer Key - A-Level Physics H2 Quiz: Thermal Physics

1. Internal Energy: The sum of the random distribution of kinetic and potential energies associated with the molecules of the system. [2]

2. First Law of Thermodynamics: $\Delta U = q + w$ (or $\Delta U = Q - W$). The change in internal energy of a system is equal to the heat energy supplied to the system minus the work done by the system. [2]

3. Adiabatic Compression: Work is done on the gas, increasing its internal energy. Since no heat escapes (adiabatic), this increase in internal energy manifests as an increase in temperature. [2]

4. Isothermal vs Adiabatic: Isothermal: Process occurs at constant temperature ($\Delta T = 0$). Adiabatic: Process occurs without heat exchange between the system and surroundings ($q = 0$). [2]

5. Equation of State: $pV = nRT$. $p$ = pressure (Pa), $V$ = volume ($\text{m}^3$), $n$ = number of moles (mol), $R$ = molar gas constant ($\text{J K}^{-1} \text{ mol}^{-1}$), $T$ = absolute temperature (K). [2]

6. Moles Calculation: $n = \frac{pV}{RT} = \frac{(1.0 \times 10^5)(2.0)}{(8.31)(300)} = \frac{200000}{2493} \approx 80.2 \text{ mol}$. [2]

7. r.m.s. Speed: $v_{\text{rms}} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3 \times 8.31 \times 300}{0.004}} = \sqrt{\frac{7479}{0.004}} = \sqrt{1869750} \approx 1367 \text{ m s}^{-1}$. [3]

8. Pressure Increase:

   • Higher temperature $\rightarrow$ higher average kinetic energy of molecules.
   • Molecules move faster $\rightarrow$ more frequent collisions with walls.
   • Greater change in momentum per collision $\rightarrow$ greater force exerted per unit area $\rightarrow$ higher pressure. [3]

9. Final Temperature: $T_1 = 27 + 273 = 300 \text{ K}$. $\frac{V_1}{T_1} = \frac{V_2}{T_2} \rightarrow T_2 = \frac{V_2 T_1}{V_1} = \frac{(2V_1)(300)}{V_1} = 600 \text{ K}$. [2]

10. KE and Temperature: The average kinetic energy of an ideal gas molecule is directly proportional to the absolute temperature ($T$) of the gas. [2]

11. Internal Energy: $U = \frac{3}{2}nRT = 1.5 \times 0.5 \times 8.31 \times (20 + 273) = 0.75 \times 8.31 \times 293 \approx 1833 \text{ J}$. [2]

12. Ideal Gas Law Limitations:

    • High pressure: Volume of molecules becomes significant compared to total volume (intermolecular spaces decrease).
    • Low temperature: Intermolecular forces of attraction become significant, causing the gas to deviate from "ideal" behavior (potential energy is no longer negligible). [3]

13. Work Done: $W = p\Delta V = (2.0 \times 10^5)(0.8 - 0.4) = 2.0 \times 10^5 \times 0.4 = 8.0 \times 10^4 \text{ J}$. [2]

14. Internal Energy Change: $\Delta U = q - w = 500 - 200 = 300 \text{ J}$. [2]

15. Efficiency: $\eta = 1 - \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 - \frac{300}{600} = 0.5$ or $50\%$. [2]

16. Heat Rejected: $\eta = \frac{Q_{\text{hot}} - Q_{\text{cold}}}{Q_{\text{hot}}} \rightarrow 0.5 = \frac{1000 - Q_{\text{cold}}}{1000}$ $500 = 1000 - Q_{\text{cold}} \rightarrow Q_{\text{cold}} = 500 \text{ J}$. [3]

17. Working Substance: A fluid (usually a refrigerant) that can easily change phase between liquid and gas at moderate temperatures, allowing it to absorb heat from a cold space and release it to a hot space via compression/expansion. [2]

18. Adiabatic Expansion:

    • Process: Adiabatic expansion.
    • Explanation: The gas does work on the surroundings. This work is done at the expense of the internal energy of the gas. Since no heat enters, internal energy decreases, leading to a drop in temperature. [3]

19. Real vs Carnot:

    • Real engines are less efficient than Carnot engines.
    • Justification: Carnot engines are idealized and reversible; real engines have irreversibilities such as friction, heat leakage, and non-quasi-static processes. [3]

20. p-V Loop Area:

    • The area represents the net work done by (or on) the gas during one complete cycle.
    • If clockwise, the gas does net work on surroundings. [3]