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. (a)`((L_(1))/(L_(2)))^(2//3)`
B. (b)`((L_(1))/(L_(2)))`
C. (c)`((L_(2))/(L_(1)))`
D. (d)`((L_(2))/(L_(1)))^(2//3)`

Answer

D

Explanation

`T_(1)V_(1)^(gamma-1) = T_(2)V_(2)^(gamma-1) "but" V= AL` So `(T_(1))/(T_(2)) = ((V_(2))/(V_(1)))^(5//3-1) = ((L_(2))/(L_(1)))^(2//3)`