A monatomic ideal 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. 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

(d) Here `TV^(gamma-1)=constant`
As `gamma=5/3, hence TV^(2//3)=constant`
Now `T_1L_1^(2//3)=T_2L_2^(2//3) (:' VpropL)`
Hence, `(T_1)/(T_2)=((L_2)/(L_1))^(2//3)`