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 rotational kinetic energy using Ek = ½Iω².
Relate rotational kinetic energy to moment of inertia and angular speed, including energy transfers, using complete evidence.

[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