A monoatomic 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 lengths of the gas column. before and after expansion respectively, then (T_(1))/(T_(2)) is given by

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 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 lengths of the gas column. before and after expansion respectively, then (T_(1))/(T_(2)) is given by
Answer» Solution :For monoatomic gas `gamma = 5//3` For ADIABATIC process, `TV^(gamma-1)` = constant `:. T_(1)(L_(1)A)^(2//3) = T_(2)(L_(2)A)^(2//3)` `:. (T_(1))/(T_(2)) = ((L_(2))/(L_(1)))^(2//3)`.