Question

An ideal gas at ${27}^{o}C$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. The rise in temperature is (Take $\gamma =5/3$)

• A. $475K$
• B. $150K$
• C. $275K$
• D. $375K$

Answer 1

The correct option is D $375K$

In an adiabatic process,
$T{V}^{\gamma -1}=$constant
$\frac{T_1}{T_2}={\left(\frac{V_2}{V_1}\right)}^{\gamma -1}$
$\frac{300}{T_2}={\left(\frac{\frac{8}{27}V}{V}\right)}^{\frac{5}{3}-1}={\left(\frac{8}{27}\right)}^{\frac{2}{3}}=\frac{4}{9}$
$T_2=300\times \frac{9}{4}=675K$
$\therefore$Rise in temperature$=675-300=375K$
Option D.