Question

A diatomic gas initially at ${18}^{o}C$ is compressed adiabatically to one eightth of its original volume. The temperature after compression will be

• A. ${18}^{o}C$
• B. ${887}^{o}C$
• C. ${327}^{o}C$
• D. None of these

Answer 1

Answer: (D)

None of these

$T_1={18}^{o}C=(273+18)=291K$
and $V_2=V_1/8$

We know that $T{V}^{\gamma -1}$ = constant
or, $T_2{V}_2^{\gamma -1}=T_1{V}_1^{\gamma -1}$
$T_2=T_1{\left(\frac{V_1}{V_2}\right)}^{\gamma -1}=291\times (8{)}^{1.4-1}=668.5K={395.5}^{o}C$