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

Here `TV^(gamma-1)=`constant
As `gamma=5//3` , hence `TV^(2//3)=`constant
Now `T_(1)L_(1)^(2//3)=T_(2)L_(2)^(2//3)` , `(because V prop L)`
Hence `(T_(1))/(T_(2))=((L_(2))/(L_(1)))^(2//3)`