Total heat rejected by compressor = Heat rejected by compression + Heat rejected by intercooler
Heat rejected by compression :
Q = (y - n)/(y - 1) • W
Q = (y - n)/(y - 1) • R(T2 - T1)/(n - 1) ... (i)
Heat rejected by intercooler :
Q = Cp(T2 - T1) ... (ii)
Sum of (i) and (ii) :
Q = (i) + (ii)
Q = (y - n)/(y - 1) • R(T2 - T1)/(n - 1) + Cp(T2 - T1) ... (iii)
Remember that :
R = Cp - Cv
y = Cp/Cv
So :
R = yCv - Cv
R = Cv(y - 1) ... (iv)
Now, subtitute (iv) to (iii) :
Q = (y - n)/(y - 1) • Cv(y - 1)(T2 - T1)/(n - 1) + Cp(T2 - T1)
Q = (y - n)/(n - 1) • Cv(T2 - T1) + Cp(T2 - T1)
Q = [Cp + Cv • (y - n)/(n - 1)] • (T2 - T1)
Hope this help