Answer to Question #249455 in Mechanical Engineering for russman

Question

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 PV^1.35 = constant. determine the work transfer during the expansion. take R= 0.29 kj/kg K

Answer 1

For any polytropic process;

$PV^{n}=C$

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

We first find T₂;

$PV^{1.35}=C$

$V \propto\frac{T}{P}$

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

$P^{1-1.35}T^{1.35}=C$

$T^{1.35}\propto P^{0.35}$

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

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

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

=566.116K

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

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

$W=12.745kJ$