Question

4.58 Air enters a compressor operating at steady state with a pressure of 14.7 lbf/in^2, a temperature of 808 F, and a volumetric flow rate of 18 ft /s. The air exits the compressor at a pressure of 90 lbf/in^2 Heat transfer from the compressor to its surroundings occurs at a rate of 9.7 Btu per lb of air flowing. The compressor power input is 90 hp. Neglecting kinetic and potential energy effects and modeling air as an ideal gas, determine the exit temperature, in F.

Answer 1

As per the data provided we will model air as an ideal gas and for an ideal gas the vale of Heat capacity ( Cp) remains constant

Cp of air = 1 KJ/Kg K

Consider the data at the inlet of compressor

P1 = 14.7 lbf/in2 = 1.013 bar

T = 808 F = 704.261K

Voumetric flow rate = 18 ft/s = 5.486 m/s

By ideal gas law

P V = n R T

1.0139 * 5.486 = n*8.314*10^-5 *704.26

n = 94.9965 mol/s

Now

Heat transfer through the compressor = 9.7 Btu/lb = 22.56 KJ/Kg

Net power output = 90 hp = 67.113 KW

Now we will do a simple enthalpy balance, ignoring the kinetic and potential energy

Heat absorbed by the air during compression - Rate of heat transfer through the compressor = Compressor Power

m*Cp*dT - m*22.56 = 67.113

m*1*(T-704.261) - m*22.56 = 67.113

94.9965*(T-704.261) - 94.9965*22.56 = 67.113

Solving the above equation for T we get, T =727.527 K