Question

A monatomic gas initially at $18{}^{\circ }$C is compressed adiabatically to $\frac{1}{8}$ of its original volume. The temperature after compression will be

• A. $180{}^{\circ }$C
• B. $144{}^{\circ }$C
• C. $891{}^{\circ }$C
• D. $887{}^{\circ }$C

Answer 1

The correct option is C $891{}^{\circ }$C

For an adiabatic process,
$T_1{V_1}^{\gamma -1}=T_2{V_2}^{\gamma -1}$
For monoatomic gas, $\gamma =\frac{5}{3}$
Given,
$T_1=18+273=291K$, $V_2=\frac{V_1}{8}$
$291\times V_1^{\frac{5}{3}-1}=T_2{\left(\frac{V_1}{8}\right)}^{\frac{5}{3}-1}$
$T_2=291\times 8^{2/3}$
$T_2=291\times 4$
$T_2=1164K=891{}^{\circ }$C