Question #249455

0.23 kg of air has an initial pressure of 1.7 MN/m2 and a temperature of 2000C. It is expanded to a pressure of 0.34MN/m2 according to the law PV1.35 = constant. determine the work transfer during the expansion. take R= 0.29 kj/kg K


1
Expert's answer
2021-10-14T23:42:01-0400

For any polytropic process;

PVn=CPV^{n}=C

W=P1V1P2V2n1=mR(T1T2)n1W=\frac{P_1V_1-P_2V_2}{n-1}=\frac{mR(T_1-T_2)}{n-1}

We first find T2;

PV1.35=CPV^{1.35}=C

VTPV \propto\frac{T}{P}

P(TP)1.35=CP(\frac{T}{P})^{1.35}=C

P11.35T1.35=CP^{1-1.35}T^{1.35}=C

T1.35P0.35T^{1.35}\propto P^{0.35}

(T2T1)1.35=(P2P1)0.35(\frac{T_2}{T_1})^{1.35}=(\frac{P_2}{P_1})^{0.35}

T2=T1(P2P1)0.351.35T_2=T_1(\frac{P_2}{P_1})^{\frac{0.35}{1.35}}

=473(0.340.17)0.351.35=473(\frac{0.34}{0.17})^{\frac{0.35}{1.35}}

=566.116K

W=mR(T1T2)n1W=\frac{mR(T_1-T_2)}{n-1}

W=0.230.29(566.116473)1.351W=\frac{0.23*0.29(566.116-473)}{1.35-1}

W=12.745kJW=12.745kJ


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