Question

An air compressor with compression ratio of $5\left(r_p\right)$ is used to compress air having inlet temperature of 300 K. If the temperature of air at exit is 500 K. The change in temperature of air at exit for unit increase in percentage polytropic efficiency is _____ K. $({\gamma }_{air}=1.4)$

(Assume constant inlet temperature and pressure ratio).

• A. -2.75

Answer 1

The correct option is A -2.75
Given, $r_p=5;T_1=300k;T_2=500k$

$\frac{T_2}{T_1}=(r_P{)}^{\frac{\gamma -1}{\gamma {\eta }_p}}{\eta }_P=\text{polytropic eff.}=90.0$

${\eta }_P=91$

$\frac{T_2^{\prime }}{T_1}=5^{\frac{0.4}{1.4{\eta }_p}}=T_2^{\prime }=497.25k$

Change in temperature $=T_2^{\prime }=T_1$

$=-2.75K$

= 2.75 K decreases