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 byA. `(L_1/L_2)^(2//3)`B. `L_1/L_2`C. `L_2/L_1`D. `(L_2/L_1)^(2//3)`

A monoatomic ideal gas, initially at temperature `T_1,` is enclosed in

1.	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 byA. `(L_1/L_2)^(2//3)`B. `L_1/L_2`C. `L_2/L_1`D. `(L_2/L_1)^(2//3)`
Answer» Correct Answer - D<br>Here `TV^(gamma-1)=`constant<br> As `gamma=5//3` , hence `TV^(2//3)=`constant<br> Now `T_(1)L_(1)^(2//3)=T_(2)L_(2)^(2//3)` , `(because V prop L)`<br> Hence `(T_(1))/(T_(2))=((L_(2))/(L_(1)))^(2//3)`

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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 byA. `(L_1/L_2)^(2//3)`B. `L_1/L_2`C. `L_2/L_1`D. `(L_2/L_1)^(2//3)`
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