IB Physics HL B 4 Thermodynamics Questions

Practise IB Physics HL B.4 by reading p–V cycles, tracking heat, work and internal energy, then using entropy and reservoir temperatures to assess heat-engine limits.

Exam points

Use Q = ΔU + W with consistent signs to find heat, work and ΔU for a closed system.
Read p–V paths to identify isobaric, isothermal or adiabatic processes and calculate work and gas states.
Calculate ΔS using ΔQ/T or kB ln Ω and assess gas, surroundings and isolated-system changes.
Interpret cyclic-engine p–V diagrams to find net work and assess process limits and irreversibility.
Calculate heat-engine efficiency from work, heat or reservoir temperatures and compare it with the Carnot limit.

Covered syllabus points

B.4.1 (HL)—First law of thermodynamics B.4.2 (HL)—Gas work B.4.3 (HL)—Internal energy change B.4.4 (HL)—Entropy and disorder B.4.5 (HL)—Entropy equations B.4.6 (HL)—Second law of thermodynamics B.4.7 (HL)—Irreversibility B.4.8 (HL)—Local entropy decrease B.4.9 (HL)—Gas processes B.4.10 (HL)—Adiabatic ideal gas B.4.11 (HL)—Heat engine cycles B.4.12 (HL)—Heat engine efficiency B.4.13 (HL)—Carnot efficiency limit

[Maximum number: 8]

This question is in two parts

(a)

A gas undergoes a thermodynamic cycle. The P-V diagram for the cycle is shown below.

In the changes of state B to C and D to A , the gas behaves as an ideal gas and the changes in state are adiabatic.

[ 1 ]

(i)

State what is meant by an adiabatic change of state.

[ 1 ]

(b)

With reference to the first law of thermodynamics, explain for the change of state A to B, why energy is transferred from the surroundings to the gas.

[ 4 ]

(c)

Estimate the total work done in the cycle.

[ 3 ]

[Maximum number: 10]

The p V diagram shows a heat engine cycle consisting of adiabatic, isothermal and isovolumetric parts. The working substance of the engine is an ideal gas.

The following data are available:

\begin{aligned} & p_{\mathrm{A}}=5.00 \times 10^{5} \mathrm{~Pa} \\ & V_{\mathrm{A}}=2.00 \times 10^{-3} \mathrm{~m}^{3} \\ & T_{\mathrm{A}}=602 \mathrm{~K} \\ & p_{\mathrm{B}}=3.00 \times 10^{4} \mathrm{~Pa} \\ & p_{\mathrm{C}}=4.60 \times 10^{3} \mathrm{~Pa} \end{aligned}

(a)

Suggest why AC is the adiabatic part of the cycle.

[ 2 ]

(b)

Show that the volume at C is $3.33 \times 10^{-2} \mathrm{~m}^{3}$ .

[ 2 ]

Alternative 1:
Use the adiabatic formula $p_A V_A^{5/3}=p_C V_C^{5/3}$ , so $V_C=\left(\frac{p_A}{p_C}\right)^{3/5}V_A$ .
$V_C=\left(\frac{5.00\times10^5}{4.60\times10^3}\right)^{3/5}\times2.00\times10^{-3}=3.333\times10^{-2}\ \mathrm{m^3}$ .

Alternative 2:
$V_C=V_B$ and $p_AV_A=p_BV_B$ .
$V_C=\frac{5\times10^5\times2\times10^{-3}}{3\times10^4}$ .

Alternative 3:
$V_C=V_B$ and $n=0.2\ \mathrm{mol}$ .
$V_C=\frac{0.2\times8.31\times602}{3\times10^4}$ .

For MP2, working or answer to at least 4 significant figures must be seen.

(c)

Suggest, for the change $A \Rightarrow B$ , whether the entropy of the gas is increasing, decreasing or constant.

[ 2 ]

Increasing because thermal energy/heat is being provided to the gas « and temperature is constant, $\Delta S=\frac{\Delta Q}{T} \gg$

(d)

Calculate the thermal energy (heat) taken out of the gas from B to C.

[ 2 ]

Alternative 1:
$Q=\Delta U=\frac{3}{2}V_C\Delta P$ .
$Q=\frac{3}{2}\times3.33\times10^{-2}\times(3.00\times10^4-4.60\times10^3)=1268.7\approx1270\ \mathrm{J}$ .

Alternative 2:
$Rn=\frac{5\times10^5\times2\times10^{-3}}{602}=1.66$ OR $T_C=\frac{4.6\times10^3\times3.33\times10^{-2}}{1.66}=92.2\ \mathrm{K}$ .
$\Delta U=\frac{3}{2}\times1.661\times(602-92.21)=1270\ \mathrm{J}$ .

Award [2] for BCA. Accept negative values.
Award MP1 if $T_C=92$ is taken from (e).

(e)

The highest and lowest temperatures of the gas during the cycle are 602 K and 92 K .

The efficiency of this engine is about 0.6 . Outline how these data are consistent with the second law of thermodynamics.

[ 2 ]

$e_{\mathrm{C}}=1-\frac{92}{602}=0.847$

this engine has $e<e_{\mathrm{c}}$ as it should

Marking guidance:

Award [0] if no calculation shown.

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (b)

Question (c)

Question 2

Question (a)

Question (b)

Question (c)

Question (d)

Question (e)