A monoatomic 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. Of `L_(1) and L_(2)` are the lengths of the gas column before and after 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