First slide

Heat engine

Question

N moles of a monoatomic gas is carried round the reversible rectangular cycle ABCDA as shown in the diagram. The temperature at A is T_o. The thermodynamic efficiency of the cycle is :

Difficult

A

15%
B

50%
C

20%
D

25%

Solution

$η = \frac{W}{Q_{1}} = \frac{work done by gas}{Heat supplied} W = Area = P_{0} V_{0} = {nRT}_{0} and Q_{1} = Q_{AB} + Q_{BC} = \frac{3}{2} {nRT}_{o} + \frac{5}{2} nR (2 T_{0}) = \frac{13}{2} {nRT}_{0} \Rightarrow % η = \frac{{nRT}_{0}}{\frac{13}{2} {nRT}_{0}} \times 100 = 15.3 %$

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