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^(t-1)` = constant
As `gamma = 5/3`, hence `TI^(2//3)` = constant
Now, `T_(1)L_(1)^(2//3) = T_(2)L_(2)^(2//3) (therefore V prop L)`,
Hence, `T_(1)/T_(2) = (L_(2)/L_(1))^(2//3)`