A Level H2 Physics Thermal Physics Quiz

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A-Level Physics H2 Quiz - Thermal Physics

Name: ___________________________
Class: ___________________________
Date: ___________________________
Score: _______ / 40

Duration: 60 minutes
Total Marks: 40

Instructions:

• Answer all 20 questions.
• Section A: Short structured questions (1–10). Section B: Data and calculation (11–15). Section C: Extended response (16–20).
• Show all working where calculation is required.
• Use $K = {}^\circ C + 273.15$ for temperature conversion unless stated.

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Section A: Short Structured Questions (1–10) [12 marks]

1. State the thermodynamic temperature of $27.0\,^\circ\mathrm{C}$ in kelvin. [1]

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2. Write the equation of state for an ideal gas in terms of number of molecules $N$, using Boltzmann constant $k$. [1]

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3. State one key assumption of the kinetic theory of gases about the volume occupied by gas molecules. [1]

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4. Define internal energy of a thermodynamic system. [1]

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5. State the zeroth law of thermodynamics in one sentence. [1]

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6. Write the first law of thermodynamics using the sign convention where $W$ is work done on the system. [1]

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7. A gas expands at constant pressure $p$. Write the expression for work done by the gas for volume change $\Delta V$. [1]

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8. Define specific heat capacity of a substance. [1]

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9. State the unit of specific latent heat. [1]

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10. The mean translational kinetic energy of a gas molecule is $\frac{3}{2}kT$. State what the symbol $T$ represents. [1]

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Section B: Data and Calculation (11–15) [15 marks]

11. A sealed flask contains $2.50 \times 10^{23}$ molecules of helium at $300\,\mathrm{K}$. Calculate the pressure if the volume is $0.0200\,\mathrm{m^3}$. ($k = 1.38 \times 10^{-23}\,\mathrm{J\,K^{-1}}$) [3]

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12. An ideal gas at $1.01 \times 10^5\,\mathrm{Pa}$ and $0.0500\,\mathrm{m^3}$ is compressed to $0.0200\,\mathrm{m^3}$ at constant temperature. Calculate the final pressure. [3]

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13. A $1.20\,\mathrm{kg}$ block of copper ($c = 390\,\mathrm{J\,kg^{-1}\,K^{-1}}$) cools from $80.0\,^\circ\mathrm{C}$ to $20.0\,^\circ\mathrm{C}$. Calculate the heat lost. [3]

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14. $0.0100\,\mathrm{kg}$ of ice at $0\,^\circ\mathrm{C}$ is converted to water at $0\,^\circ\mathrm{C}$. Specific latent heat of fusion $= 3.34 \times 10^5\,\mathrm{J\,kg^{-1}}$. Calculate the energy required. [3]

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15. A gas is compressed. Work done on the gas is $+240\,\mathrm{J}$ and it loses $90\,\mathrm{J}$ as heat. Using $\Delta U = Q + W$, calculate $\Delta U$. [3]

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Section C: Extended Response (16–20) [13 marks]

16. (a) State the basic assumptions of the kinetic theory of gases. [3]
(b) Explain how the pressure of a gas arises from molecular motion. [2]

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17. Derive the relation $pV = \frac{1}{3}Nm\langle c^2\rangle$ from kinetic theory, stating any assumption used. [5]

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18. A student heats $0.200\,\mathrm{kg}$ of water from $20.0\,^\circ\mathrm{C}$ to $100.0\,^\circ\mathrm{C}$ using a $500\,\mathrm{W}$ heater.
(a) Calculate the energy needed. ($c_{\text{water}} = 4180\,\mathrm{J\,kg^{-1}\,K^{-1}}$) [2]
(b) Calculate the minimum time required. [2]

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19. An ideal gas undergoes a cycle. In step 1, $400\,\mathrm{J}$ of heat enters and gas does $150\,\mathrm{J}$ of work. In step 2, $100\,\mathrm{J}$ of heat leaves and $200\,\mathrm{J}$ of work is done on the gas. Calculate the net change in internal energy over the cycle. [3]

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20. The pressure-volume graph below shows a gas process.

Image pending generation: graph for Q20.

(a) Calculate work done by the gas from A to B. [2]
(b) State the total work done over the full cycle A→B→C→D→A. [1]

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

Total Marks: 40
Duration: 60 minutes

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Section A: Short Structured Questions (1–10)

1. [1 mark]
$T = 27.0 + 273.15 = 300.15\,\mathrm{K}$ (accept $300\,\mathrm{K}$).
Teaching: Thermodynamic (kelvin) temperature is Celsius + 273.15.

2. [1 mark]
$pV = NkT$
Teaching: $N$ = number of molecules, $k$ = Boltzmann constant.

3. [1 mark]
The volume of the gas molecules themselves is negligible compared with the volume of the container.
(Other valid: molecules are point particles / no intermolecular forces except during collisions.)

4. [1 mark]
Internal energy is the sum of the microscopic kinetic and potential energies of the molecules in the system.

5. [1 mark]
If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

6. [1 mark]
$\Delta U = Q + W$ (with $W$ = work done on system).

7. [1 mark]
Work done by gas = $p\Delta V$ (positive for expansion).

8. [1 mark]
Specific heat capacity is the energy required per unit mass to raise the temperature by 1 K (or $1\,^\circ\mathrm{C}$).

9. [1 mark]
$\mathrm{J\,kg^{-1}}$ (joules per kilogram).

10. [1 mark]
$T$ is the thermodynamic (absolute) temperature in kelvin.

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Section B: Data and Calculation (11–15)

11. [3 marks]
$pV = NkT \Rightarrow p = \frac{NkT}{V}$
$= \frac{(2.50\times10^{23})(1.38\times10^{-23})(300)}{0.0200}$
$= \frac{1035}{0.0200} = 5.18\times10^{4}\,\mathrm{Pa}$
Mark breakdown: formula (1), substitution (1), answer + unit (1).

12. [3 marks]
Isothermal: $p_1V_1 = p_2V_2$
$p_2 = \frac{p_1V_1}{V_2} = \frac{(1.01\times10^5)(0.0500)}{0.0200} = 2.525\times10^5\,\mathrm{Pa}$
Marks: method (1), substitution (1), answer (1).

13. [3 marks]
$Q = mc\Delta\theta = 1.20 \times 390 \times (80.0-20.0)$
$= 1.20 \times 390 \times 60.0 = 2.81\times10^4\,\mathrm{J}$
Marks: formula (1), substitution (1), answer (1).

14. [3 marks]
$Q = ml = 0.0100 \times 3.34\times10^5 = 3.34\times10^3\,\mathrm{J}$
Marks: formula (1), substitution (1), answer (1).

15. [3 marks]
$Q = -90\,\mathrm{J}$ (lost), $W = +240\,\mathrm{J}$
$\Delta U = Q + W = -90 + 240 = +150\,\mathrm{J}$
Marks: sign of Q (1), sum (1), answer (1).

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Section C: Extended Response (16–20)

16. [5 marks total]
(a) [3] Assumptions:

• Large number of identical molecules in random motion.
• Volume of molecules negligible.
• No intermolecular forces except elastic collisions.
• Collisions with walls and each other are perfectly elastic.
• Duration of collision negligible; obey Newton’s laws.
  (Any 3 clear points = 3 marks)
  (b) [2] Pressure arises from repeated elastic collisions of molecules with container walls, delivering momentum change per unit time per unit area.

17. [5 marks]
Derivation:

• Consider molecule mass $m$, speed $c_x$ normal to wall of cube side $L$.
• Momentum change per collision = $2mc_x$.
• Time between collisions = $2L/c_x$.
• Force on wall = $\frac{2mc_x}{2L/c_x} = \frac{mc_x^2}{L}$.
• Pressure from one molecule: $p = \frac{mc_x^2}{L^3} = \frac{mc_x^2}{V}$.
• For $N$ molecules, average $\langle c_x^2\rangle = \frac{1}{3}\langle c^2\rangle$.
• $pV = \frac{1}{3}Nm\langle c^2\rangle$.
  Marks: setup (1), momentum (1), averaging (1), sum (1), final (1).

18. [4 marks]
(a) [2] $Q = mc\Delta\theta = 0.200 \times 4180 \times 80.0 = 6.69\times10^4\,\mathrm{J}$.
(b) [2] $t = Q/P = 6.69\times10^4 / 500 = 134\,\mathrm{s}$.
Marks: each part formula+answer.

19. [3 marks]
Step1: $\Delta U_1 = +400 - 150 = +250\,\mathrm{J}$ (work by gas = negative W on).
Step2: $\Delta U_2 = -100 + 200 = +100\,\mathrm{J}$.
Net = $250 + 100 = +350\,\mathrm{J}$.
Marks: each step (1+1), total (1).

20. [3 marks]
(a) [2] A→B isobaric expansion: $W = p\Delta V = (1.0\times10^5)(0.030-0.010) = 2.0\times10^3\,\mathrm{J}$.
(b) [1] Total cycle work = area enclosed = rectangle = $(3.0-1.0)\times10^5 \times (0.030-0.010) = 4.0\times10^3\,\mathrm{J}$ done by gas.
Image must show labelled A,B,C,D and path; answer uses those values.