Air in a piston-cylinder device is compressed from 25°C and 100 kPa to 500 kPa during a polytropic process for which Pv^1.3 = constant. The air temperature after compression is A)33°C B)156°C C)1207°C D)115°C E)182°C

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Quizplus · Accepted Answer

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R=0.287 "kJ/kg.K"
P1=100 "kPa"
T1=25+271 "K"
P2=500 "kPa"
"PV^1.3 = constant gives V1/V2=(P2/P1)^(1/1.3). 
Substituting into P1V1/T1=P2V2/T2 gives (P1/T1)*(P2/P1)^(1/1.3)=P2/T2 "
(P1/T1)*(P2/P1)^(1/1.3)=P2/T2
T2_C=T2-273 "C"
"Some Wrong Solutions with Common Mistakes:"
(P1/(T1-273))*(P2/P1)^(1/1.3)=P2/W1_T2 "Usinf C instead of K"
P1/T1=P2/(W2_T2+273) "Assuming V=constant and using K"
P1/(T1-273)=P2/(W3_T2) "Assuming V=constant, and using C"
(P1/T1)*(P2/P1)^(1.3)=P2/W4_T2 "Using the exponent 1.3 instead of 1/1.3"

Air in a Piston-Cylinder Device Is Compressed from 25°C and 100