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

Explanation

`TV^(gamma-1)=` constant
Volume of a cylinder =V=AL
`(T_(1))/(T_(2))=((V_(2))/(V_(1)))^(gamma-1)=((AL_(2))/(AL_(1)))^(gamma-1)`