An intercooler is used to cool the air temperature between stages of a two$-$stage compressor. The air

enters the first stage with a temperature of $300K$ and a pressure of $100$kPa. The inlet pressure of the

intercooler is $300$kPa and the air is cooled to $300K$ when entering into the second stage compressor.

The design exit pressure of the compressor is $1,200$kPa. Assume all processed are isentropic$,$ determine

$(1)$ the exit temperature of the compressor, $(2)$ the inlet temperature of the intercooler, $(3)$ the total

compressor work per unit mass, $(4)$ the amount of the heat removed from the intercooler.

$($Note: you should solve this problem three different ways:

$($a$)$ Assume a constant specific heat $C_p$ for each of the processes by using the average temperature

of the device to estimate $C_p($use standard thermodynamic tables$).$

$($b$)$ Use the relative pressure concept to take into account of the temperature dependence of $C_p.$

Compare $($b$)$ to $($a$)$ and discuss.

Assume both compressors operate at an isentropic efficiency of $0\mathrm{.}8,$ rework part $($b$).$