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 $T_1/T_2$ is given by
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 $T_1/T_2$ is given by
- A
${\left( {\frac{{{L_1}}}{{{L_2}}}} \right)^{\frac{2}{3}}}$
- B
$\left( {\frac{{{L_1}}}{{{L_2}}}} \right)$
- C
$\left( {\frac{{{L_2}}}{{{L_1}}}} \right)$
- D
${\left( {\frac{{{L_2}}}{{{L_1}}}} \right)^{\frac{2}{3}}}$
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