Consider the following heat engine involving one mole of ideal monatomic gas. The gas begins at temperature T 0 , pressure P 0 , and volume V 0 , and undergoes four reversible steps. 1. The gas

Question

Consider the following heat engine involving one mole of ideal monatomic gas. The gas begins at temperature $T_{0}$ , pressure $P_{0}$ , and volume $V_{0}$ , and undergoes four reversible steps.

1. The gas is expanded at constant pressure until its temperature rises to $(1 + β) T_{0}$ .
2. The gas is expanded at constant temperature until its pressure falls to $\frac{P _{0}}{α}$ .
3. The gas is contracted at constant pressure until its temperature falls back to $T_{0}$ .
4. The gas is contracted at constant temperature until its pressure rises back to $P_{0}$ .

TestHub · Accepted Answer

The two isobaric works cancel; net work comes from the two isothermal steps:

$W = β P_{0} V_{0} ln α$

C is correct.

Heat absorbed in isobaric heating:

$Q_{1} = \frac{5}{2} β P_{0} V_{0}$

Heat absorbed in isothermal expansion:

$Q_{2} = (1 + β) P_{0} V_{0} ln α$

A omits part of the heat supplied. B gives the wrong rejected heat.

Efficiency:

$η = \frac{W}{Q _{1} + Q _{2}} = \frac{β l n α}{( 1 + β ) l n α + \frac{5 β}{2}}$

D is correct.

Correct options: C, D.

Physics - Heat & Thermo Question with Solution | TestHub

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