The figure ( Figure 1 ) shows the cycle for a heat engine that uses a gas having

Question

The figure (Figure 1) shows the cycle for a heat engine that uses a gas having ? =1.25. The initial temperature is T1 =300K, and this engine operates at 10 cycles per second.

What is the engine's thermal efficiency?

I know that the Power output of the engine is 550W.

knight_Figure_19_54.jpg

The figure (Figure 1) shows the cycle for a heat engine that uses a gas having ? =1.25. The initial temperature is T1 =300K, and this engine operates at 10 cycles per second. What is the engine's thermal efficiency?

Explanation / Answer

Here Pout=550W

n=number of moles taken

Here Pout=((PdV)2-3 +nRT ln(V2/V1))*no. of cycles per second

therefore,

(3*101325*400*10^-6+n*8.314*300*ln(200/600))*10=550

or,n=0.0243

Again in the path from 2-3 it intakes heat

here clearly from PV=nRT we get T3=3*T2=900 K

Here ? =1.25

or,Cp=1.25 Cv

or Cv=0.8Cp

Again Cp-Cv=R

or,0.2Cp=8.314

or,Cp=41.57

dQin/dt=dQ2-3/dt = (nCpdT)*number of cycles per second = (0.0243*41.57*600)*10=6060.906 W

Efficiency =Pout/Qin =550/6060.906 =0.0907 =9.07 %

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