Question

An ideal gas at ${27}^{\circ }$C is compressed adiabatically to $\frac{8}{27}$ of its originalvolume. If $\gamma =\frac{5}{3}$, then the rise in temperature is

• A. 450 K
• B. 375 K
• C. 225 K
• D. 405 K

Answer 1

The correct option is B 375 K

$\frac{T_2}{T_1}={\left(\frac{V_1}{V_2}\right)}^{\gamma -1}\Rightarrow T_2=300{\left(\frac{27}{8}\right)}^{\frac{5}{3}-1}=300{\left(\frac{27}{8}\right)}^{\frac{2}{3}}$
$=300{\left\{{\left(\frac{27}{8}\right)}^{1/3}\right\}}^2=800{\left(\frac{3}{2}\right)}^2=675K$
$\Rightarrow △T=657-300=375K$