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A monoatomic ideal gas, initially at temperature \( T_{1} \), is enclosed in a cylinder fitted with a frictionless piston. The
\( \mathrm{P} \) 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
W of the gas column before and after expansion respectively, then \( T_{1} / T_{2} \) is given by
[IIT-JEE (Screening) 2000]
(a) \( \left(\frac{L_{1}}{L_{2}}\right)^{2 / 3} \)
(b) \( \cdot \frac{L_{1}}{L_{2}} \)
(c) \( \frac{L_{2}}{L_{1}} \)
(d) \( \left(\frac{L_{2}}{L_{1}}\right)^{2 / 3} \)
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