A monoatomic ideal gas, initially at temperature $T_1 $ is enclosed in a cylindes fitted witha frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2 $ by releasing the piston suddenly If $L_1$ and $L_2$ the lengths of the gas colum be fore and afters expansion respectively, then $ { T_1 \over T_2} $ is given by
TV = [an adiabatic process] $T_1 V_1 = T_2 V_2 $ $ {T_1 \over T_2 } = \left( { V_2 \over V_1 } \right) $