A monoatomic ideal gas, initially at temperature `T_1,` is enclosed in a cylinder fitted with a friction less 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

Options

A. `((L_(1))/(L_(2)))^(2//3)`
B. `(L_(1))/(L_(2))`
C. `(L_(2))/(L_(1))`
D. `((L_(2))/(L_(1)))^(2//3)`

Answer

D