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_(1)V_(1)^(gamma-1) implies (T_1)/(T_2) = ((V_2)/(V_1))^(gamma-1) =((L_(2)A)/(L_(1)A))^(5/3-1)=((L_2)/(L_1))^(2/3)`.