A monoatomic ideal gas, initially at temperature T₁ is enclosed in a cylinder fitted with frictionless piston. The gas is allowed to expand adiabatically to a temperature T ₂ by releasing the piston suddenly. L₁ and L₂ are the lengths of the gas columns before and after the expansion respectively. The ratio T₂ / T₁ is

Step-by-step solution

For an adiabatic process aligned & T ₁ ~V ₁^ -1 = T ₂ ~V ₂^ -1 & ~T ₂ ~T ₁ = ( V ₁ ~V ₂ )^ -1 aligned For a monoatomic gas, = 5 3 array ll & -1= 5 3 -1= 2 3 & Volume = Area Length, & V ₁= AL ₁ and V ₂= AL ₂ & ~T ₂ ~T ₁ = [ AL ₁ AL ]₂ ]^ 2 / 3 = [ L ₁ ~L ₂ ]^ 2 / 3 & ~T ₂ ~T ₁ = ( L ₁ ~L ₂ )^ 2 3 array