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IB Physics HL B 4 13 Hl Carnot Efficiency Limit Questions

Practise IB Physics HL B.4.13 by calculating the Carnot limit and comparing real-engine efficiency with it.

Syllabus
First assessment 2025
Course
Physics HL
Level
HL

Exam points

  • Calculate Carnot efficiency with ηC = 1 − TC/TH, converting reservoir temperatures to kelvin and obtaining the hot/cold temperature ratio from supplied data when needed.
  • Determine how the Carnot limit changes when a reservoir temperature changes while the other remains fixed, including qualitative or multiple-choice comparisons.
  • Compare an actual or claimed engine efficiency with the Carnot limit and explain, using the second law and real energy losses, why the limit cannot be reached by a real engine.

Learn this topic

Study B.4.13 (HL)—Carnot efficiency limit conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Physics HL B 4 13 Hl Carnot Efficiency Limit Questions question 1

[Maximum number: 2]

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.

Figure for Question IB Physics HL B 4 13 Hl Carnot Efficiency Limit Questions question 1 — IB Physics HL

The following data are available:

pA=5.00×105 PaVA=2.00×10−3 m3TA=602 KpB=3.00×104 PapC=4.60×103 Pa\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}

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.

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