air enters a compressor at 167 kPa and 290 K and exits at a

air enters a compressor at 167 kPa and 290 K and exits at a temperature of 504.1K. determine the power (kW) for the compressor if the inlet volumetric flow rate is 0.194 m^3/s and the heat transfer through the shell of the compressor to the surroundings is 1.64 kW. use the ideal gas tables ( variable specific heat)

Solution

Using ideal gas relations

density   = P / RT    = 167 * 1000 / (287 * 290)    = 2 kg/m^3

mass flow rate = denisty * volume flow rate = 2 * 0.194 = 0.39 kg/s

from Energy balance equation

Q - W   = m * (h2 - h1)

h1 = Cp * T1 = 1.005 * 290 = 291.45 kJ/kg K

h2 = Cp * T2 = 1.03 * 504.1 = 519.223 kJ/kg K

-1.64 - W = 0.39 * (   519.223 - 291.45)

W   = -90.47147 kW

power required = 90.47147 kW