A monoatomic ideal gas, initially at temperature T1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If l1 and l2 are the lengths of the gas column, before and after the expansion respectively, then the value of ${{{T_1}} \over {{T_2}}}$ will be :

Question

A monoatomic ideal gas, initially at temperature T₁ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T₂ by releasing the piston suddenly. If l₁ and l₂ are the lengths of the gas column, before and after the expansion respectively, then the value of ${{{T_1}} \over {{T_2}}}$ will be :

${\left( {{{{l_1}} \over {{l_2}}}} \right)^{{2 \over 3}}}$

${\left( {{{{l_2}} \over {{l_1}}}} \right)^{{2 \over 3}}}$

${{{l_2}} \over {{l_1}}}$

${{{l_1}} \over {{l_2}}}$

Solution

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