Q. An ideal gas at $27℃$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. If $\gamma = \frac{5}{3}$, then the rise in temperature is
A) $450\ K$
B) $375\ K$
C) $225\ K$
D) $405\ K$
Explanation
(b) $\frac{T_{2}}{T_{1}} = \left( \frac{V_{1}}{V_{2}} \right)^{\gamma - 1} \Rightarrow T_{2} = 300\left( \frac{27}{8} \right)^{\frac{5}{3} - 1} = 300\left( \frac{27}{8} \right)^{\frac{2}{3}}$
$= 300\left\{ \left( \frac{27}{8} \right)^{1/3} \right\}^{2} = 300\left( \frac{3}{2} \right)^{2} = 675K$
$\Rightarrow \mathrm{\Delta}T = 675 - 300 = 375K$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.