The p V diagram in the figure shows a cycle of a heat engine that uses 0.250 mol

Question

The pV diagram in the figure shows a cycle of a heat engine that uses 0.250 mole of an ideal gas having ?=1.40. The curved part ab of the cycle is adiabatic.

Part A

Find the pressure of the gas at point a. (SOLVED)

Pa = 12.3 atm

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Part B

How much heat enters this gas per cycle?

Qin = J

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Part C

Where does the entering of heat happen?

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Part D

How much heat leaves this gas in a cycle?

Q leav = J

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Part E

Where does the leaving of heat of this gas occur?

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Part F

How much work does this engine do in a cycle?

A = J

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Part G

What is the thermal efficiency of the engine?

e = %

Explanation / Answer

b. Heat Qin = constant pressure process

Tb=Pb*Vb/nR = 151987.5*0.009/8.314*0.250

Tb = 658.11 K

Tc=146.247 K

Qbc=nCp(Tc-Tb)=-3723.53 J

Cp=3.5R,Cv=2.5R , ( as =1.4 implies diatomic gas)

Qca = nCv(Tc-Ta)

Ta/Tb = (Va/Vb)1-

Ta=1201.11 K

Qca=0.250*2.5R*(1201.11-146.247)

Qin =5481.34 J

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c. at c-a
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D. Q=U+W

for cycles U=0;Q=W=5481.34 J+(-3723.53 J) = 1757.8J

e. heat leaves in b--c

f efficiency e = W/Qin

e = 1757.8J/5481.34 J

e = 0.3206 or 32.06%

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