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

`T_1V_1^(gamma-1)=T_2V_2^(gamma-1)`
`(T_1)/(T_2)=((V_2)/(V_1))^(gamma-1)=((AL_2)/(AL_1))^((7)/(5)-1)=((L_2)/(L_1))^((2)/(3))`