A Level H2 Physics Thermal Physics Quiz

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]