Question

A monoatomic ideal gas, initially at temperature $T_1$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature. $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion respectively, then $\frac{T_1}{T_2}$ is given by

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}\Rightarrow \frac{T_1}{T_2}={\left(\frac{V_2}{V_1}\right)}^{\gamma -1}={\left(\frac{L_{2}A}{L_{1}A}\right)}^{\frac{5}{3}-1}={\left(\frac{L_2}{L_1}\right)}^{\frac{2}{3}}$