Answer to Question #267525 in Molecular Physics | Thermodynamics for MaTMaT

Question

Air flows steadily through an engine at a constant temperature of 400k. Find the work per kilogram if the exit pressure is one-third the inlet pressure and the inlet pressure is 207 KPa. Assume that the kinetic energy and potential energy variation are negligible.

Answer 1

Solution;

Given;

$T_1=T_2=400K$

$P_1=27kPa$

$P_2=\frac{P_1}{3}=\frac{207}{3}=69kPa$

Work done per kilogram;

$m=1kg$

Temperature is constant,hence the process is isothermal;

$W=mRTln(\frac{P_1}{P_2})$

$R=287J/kg.K$

$W=1×287×400×ln\frac{207}{69}$

$W=126120.6907J$

$W=126.12kJ$