MHT CET Medical202624 April 2026Morning ShiftPhysicsThermodynamicsActual
A mono-atomic ideal gas, initially at temperature T₁ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T₂ by releasing the piston suddenly. L₁ and L₂ are the lengths of gas columns before and after the expansion, respectively. The value of T₁ T₂ is [ = 5 3 ]
Options
- A( L₁ L₂ )^ 2 3
- B( L₂ L₁ )^ 2 3
- C( L₁ L₂ )^ 5 3
- D( L₂ L₁ )^ 5 3
Correct answer
B. ( L₂ L₁ )^ 2 3
Step-by-step solution
For a reversible adiabatic process, the relationship between temperature and volume is given by TV^ - 1 = constant . Applying this to the initial and final states of the gas: T₁ V₁^ - 1 = T₂ V₂^ - 1 T₁ T₂ = ( V₂ V₁ )^ - 1 Let A be the cross-sectional area of the cylinder. The volume of the gas column of length L is V = AL . Substituting V₁ = AL₁ and V₂ = AL₂ : T₁ T₂ = ( AL₂ AL₁ )^ - 1 = ( L₂ L₁ )^ - 1 Given that the gas is mono-atomic, = 5 3 . - 1 = 5 3 - 1 = 2 3 Substituting this value into the equation: T₁ T₂ = (