Question

A fixed amount of dry air at temperature of ${27}^{o}C$ is compressed to $\frac{1}{9}th$ of original volume. Its final temperature is $(\gamma =1.5)$

• A. ${627}^{o}C$
• B. ${600}^{o}C$
• C. ${158}^{o}C$
• D. ${527}^{o}C$

Answer 1

The correct option is A ${627}^{o}C$

In an adiabatic process,
$T{V}^{\gamma -1}=$constant
$T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$
$T_2=T_1\times \frac{V_1^{\gamma -1}}{V_2^{\gamma -1}}=300\times {\left(\frac{1}{1/9}\right)}^{1.5-1}=300\left(3\right)=900K={627}^{o}C$
Option A.