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A monatomic ideal gas, initially at temp...

A monatomic 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 length of the gas column before expansion respectively, then `(T_1)/(T_2)` is given by

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