IB Physics HL B 4 12 Hl Heat Engine Efficiency Questions

Practise IB Physics HL B.4.12 by calculating heat-engine efficiency, energy rejected and Carnot limits from cycle data.

Exam points

Calculate heat-engine efficiency from net work and heat input, or from the energy magnitudes using η = W/QH = 1 − QC/QH over a complete cycle.
Calculate Carnot efficiency from hot- and cold-reservoir temperatures in kelvin, and compare an actual engine's efficiency with that theoretical limit when the question supplies both.
Use the efficiency and cycle energy balance to determine missing work, heat input or rejected heat, and explain why a real heat engine must reject energy and cannot be 100% efficient.

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Study B.4.12 (HL)—Heat engine efficiency conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 2]

This question is in two parts. Part 1 is about simple harmonic motion (SHM). Part 2 is about gas in an engine.

Part 1 Simple harmonic motion (SHM)
An object is placed on a frictionless surface. The object is attached by a spring fixed at one end and oscillates at the end of the spring with simple harmonic motion (SHM).

Figure for Question IB Physics HL B 4 12 Hl Heat Engine Efficiency Questions question 1 — IB Physics HL

The tension F in the spring is given by F=k x where x is the extension of the spring and k is a constant.

The shaded area WXYZ is 610 J . The total thermal energy transferred out of the gas in one cycle is 1.3 kJ .

Determine the efficiency of cycle WXYZ.

efficiency $=\frac{610}{1300}$ ;
0.47 or 47 %;

Marking guidance:

Award [2] for a bald correct answer.
Award [1] for $\frac{610}{(610+1300)}=0.32$ .
Award [0] for any fraction that would exceed 1 even if later fudged.
Award [0] for efficiency $=\frac{T_{C}-T_{H}}{T_{H}}=38 \%$ , question does not imply that this is a Carnot cycle.

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IB Physics HL B 4 12 Hl Heat Engine Efficiency Questions question 1