A Level H2 Physics Thermal Physics Quiz

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A-Level Physics H2 Quiz - Thermal Physics

Name: __________________________
Class: __________________________
Date: __________________________
Score: ________ / 65

Duration: 1 hour 15 minutes
Total Marks: 65

Instructions:

• Answer all questions.
• Use $R = 8.31\text{ J mol}^{-1}\text{ K}^{-1}$ and $k_B = 1.38 \times 10^{-23}\text{ J K}^{-1}$ where necessary.
• Show all working clearly.
• Give your answers to an appropriate number of significant figures.

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Section A: Temperature, Heat, and Internal Energy (Questions 1–7)

1. Define the term absolute zero. [1]
   
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2. A metal block of mass 2.0 kg and specific heat capacity $385\text{ J kg}^{-1}\text{ K}^{-1}$ is heated from $20^\circ\text{C}$ to $80^\circ\text{C}$. Calculate the heat energy absorbed by the block. [2]
   
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3. Explain the relationship between the internal energy of an ideal gas and its absolute temperature. [2]
   
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4. A sample of water is heated at a constant rate. Describe the change in temperature of the water as it reaches its boiling point and continues to receive heat. [3]
   
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5. Distinguish between heat and internal energy. [2]
   
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6. A 50g piece of ice at $0^\circ\text{C}$ is mixed with 200g of water at $40^\circ\text{C}$. Calculate the final equilibrium temperature of the mixture. (Specific latent heat of fusion of ice = $3.34 \times 10^5\text{ J kg}^{-1}$) [4]
   
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7. Explain why the temperature of a gas decreases during an adiabatic expansion. [3]
   
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Section B: First Law of Thermodynamics (Questions 8–14)

8. State the First Law of Thermodynamics in terms of internal energy, heat, and work. [2]
   
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9. A gas expands from a volume of $1.0 \times 10^{-3}\text{ m}^3$ to $3.0 \times 10^{-3}\text{ m}^3$ 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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10. During a thermodynamic process, 500 J of heat is added to a system, and the system does 200 J of work on its surroundings. Calculate the change in internal energy of the system. [2]
    
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11. An ideal gas undergoes an isothermal expansion. (a) What is the change in internal energy of the gas? [1] (b) If 1200 J of heat is supplied to the gas, how much work is done by the gas? [2]
    
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12. Describe a process in which the internal energy of a system remains constant while heat is exchanged. [2]
    
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13. A cylinder contains an ideal gas. The gas is compressed adiabatically. (a) Does the temperature of the gas increase or decrease? [1] (b) Explain your answer to (a) using the First Law of Thermodynamics. [3]
    
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14. 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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Section C: Ideal Gases and Kinetic Theory (Questions 15–20)

15. State two assumptions made in the kinetic theory of an ideal gas. [2]
    
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16. A container holds 0.5 moles of an ideal gas at $27^\circ\text{C}$ and $2.0 \times 10^5\text{ Pa}$. Calculate the volume of the container. [3]
    
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17. Calculate the root-mean-square (rms) speed of Helium atoms (molar mass $4.0 \times 10^{-3}\text{ kg mol}^{-1}$) at $100^\circ\text{C}$. [3]
    
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18. A fixed mass of an ideal gas is kept at a constant temperature. If the pressure is increased by 25%, by what percentage does the volume decrease? [3]
    
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19. Explain how the pressure of an ideal gas is related to the change in momentum of the gas molecules colliding with the walls of the container. [4]
    
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20. A gas is compressed from volume $V$ to $V/2$ while the temperature is kept constant. (a) What happens to the pressure of the gas? [1] (b) What happens to the average kinetic energy of the molecules? [1] (c) Explain your answer to (b). [2]
    
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A-Level Physics H2 Quiz - Thermal Physics (Answer Key)

Section A: Temperature, Heat, and Internal Energy

1. Absolute zero is the lowest possible temperature (0 K), at which the internal energy of an ideal gas is minimum (or the molecules have zero kinetic energy). [1]
2. $Q = mc\Delta T = 2.0 \times 385 \times (80 - 20) = 2.0 \times 385 \times 60 = 46,200\text{ J}$ (or $4.62 \times 10^4\text{ J}$). [2]
3. For an ideal gas, there are no intermolecular forces; therefore, internal energy consists solely of the sum of the random kinetic energies of the molecules. Internal energy is directly proportional to the absolute temperature. [2]
4. As water reaches its boiling point, the temperature remains constant at $100^\circ\text{C}$ despite continued heating. [1] The energy supplied is used to break the intermolecular bonds (latent heat of vaporization) [1] rather than increasing the average kinetic energy of the molecules. [1]
5. Internal energy is the total energy (kinetic + potential) stored within a system. [1] Heat is the energy transferred between two bodies due to a temperature difference. [1]
6. Heat lost by water = Heat gained by ice. $m_w c_w (40 - T) = m_i L_f + m_i c_w (T - 0)$ $0.2 \times 4180 \times (40 - T) = 0.05 \times 3.34 \times 10^5 + 0.05 \times 4180 \times T$ $33440 - 83.6T = 16700 + 209T$ $16740 = 302.6T \implies T \approx 55.3^\circ\text{C}$ (Wait, calculation check: $0.2 \times 4180 \times 40 = 33440$. $0.05 \times 334000 = 16700$. $33440 - 16700 = 16740$. $T = 16740 / (83.6 + 209) = 57.3^\circ\text{C}$). [4]
7. In an adiabatic expansion, no heat enters or leaves the system ($Q=0$). [1] The gas does work on the surroundings, which requires energy. [1] This energy is taken from the internal energy of the gas, causing the temperature to drop. [1]

Section B: First Law of Thermodynamics

8. $\Delta U = Q - W$ (or $\Delta U = Q + W$ depending on sign convention). [2] "The change in internal energy of a system is equal to the heat added to the system minus the work done by the system."
9. $W = P\Delta V = 1.0 \times 10^5 \times (3.0 \times 10^{-3} - 1.0 \times 10^{-3}) = 1.0 \times 10^5 \times 2.0 \times 10^{-3} = 200\text{ J}$. [2]
10. $\Delta U = Q - W = 500 - 200 = 300\text{ J}$. [2]
11. (a) $\Delta U = 0$ (since $T$ is constant for an ideal gas). [1] (b) $0 = Q - W \implies W = Q = 1200\text{ J}$. [2]
12. An isothermal process (for an ideal gas). [1] Heat is added to the system, but the system does an equal amount of work on the surroundings, keeping $\Delta U = 0$. [1]
13. (a) Increase. [1] (b) In adiabatic compression, $Q = 0$. [1] Work is done on the gas ($W$ is negative). [1] By $\Delta U = Q - W$, $\Delta U$ increases, leading to a rise in temperature. [1]
14. $\eta = 1 - \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 - \frac{300}{600} = 0.5$ or $50\%$. [2]

Section C: Ideal Gases and Kinetic Theory

15. Any two: (1) Molecules are point masses (negligible volume). (2) No intermolecular forces (except during collisions). (3) Collisions are perfectly elastic. (4) Motion is random. [2]
16. $PV = nRT \implies V = \frac{nRT}{P} = \frac{0.5 \times 8.31 \times (27 + 273)}{2.0 \times 10^5} = \frac{0.5 \times 8.31 \times 300}{2.0 \times 10^5} = 6.23 \times 10^{-3}\text{ m}^3$. [3]
17. $c_{\text{rms}} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3 \times 8.31 \times 373}{4.0 \times 10^{-3}}} = \sqrt{\frac{9302.79}{0.004}} = \sqrt{2325697.5} \approx 1525\text{ m/s}$. [3]
18. $P_1V_1 = P_2V_2 \implies V_2 = \frac{P_1V_1}{1.25P_1} = \frac{V_1}{1.25} = 0.8V_1$. [2] Decrease is $1 - 0.8 = 0.2$ or $20\%$. [1]
19. Molecules collide with walls, changing momentum from $+mv$ to $-mv$. [1] Change in momentum $\Delta p = 2mv$. [1] Force is the rate of change of momentum $F = \frac{\Delta p}{\Delta t}$. [1] Pressure is this force divided by the area of the wall $P = \frac{F}{A}$. [1]
20. (a) Pressure increases (doubles). [1] (b) Remains constant. [1] (c) Average kinetic energy is directly proportional to absolute temperature. [1] Since the process is isothermal, $T$ is constant, so average KE is constant. [1]