First slide

Heat engine

Question

A Carnot engine uses first an ideal monoatomic gas $(γ = \frac{5}{3})$ and then an ideal diatomic gas $(γ = \frac{7}{5})$ as its working substance. The source and sink temperature are 411°C and 69°C respectively and the engine and the engine extracts 1000 J of heat from the source in each cycle, then :

Easy

A

efficiencies of the engine in the two cases are in the ratio 21:25
B

area enclosed by the P-V diagram in only the first case is 500J
C

area enclosed by the P-V diagram in both cases is 500 J
D

heat rejected to the sink in the first case is 600 J while that in the second case is 713 J.

Solution

$η = 1 - \frac{T_{2}}{T_{1}} = \frac{W}{Q_{1}} Here T_{1}, T_{2} and Q_{1} are same for both So W will be same . W = Q_{1} (1 - \frac{T_{2}}{T_{1}}) = 1000 (1 - \frac{342}{684}) = 500 J$

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