Question

An ideal gas at ${27}^{o}C$ is compared adiabatically to $\frac{8}{27}$ its original volume [$T{V}^{\gamma -1}=$constant] and $\gamma =\frac{5}{3}$, then the rise in temperature will be:

• A. ${480}^{o}C$
• B. ${450}^{o}C$
• C. ${375}^{o}C$
• D. ${225}^{o}C$

Answer 1

Answer: (C)

${375}^{o}C$

Applying the formula For adiabatic Process

$T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$
$\frac{T_1}{T_2}={\left(\frac{V_2}{V_1}\right)}^{\gamma -1}$
$⟹\left(\frac{27+273}{T_2}\right)={\left(\frac{8}{27}\right)}^{\gamma -1}={\left(\frac{8}{27}\right)}^{5/3-1}$
or, $\frac{300}{T_2}={\left(\frac{2}{3}\right)}^{\frac{2}{3}\times 3}=\frac{4}{9}$
$T_2=\frac{9\times 300}{4}={675}^{o}K$
$t^{o}C=675-273={402}^{o}C$
Rise in temperature $=402-27={375}^{o}C$