Question

An ideal gas is expanded from (p₁, V₁, T₁) to (p₂, V₂, T₂) under different conditions. The correct statement(s) among the following is(are) 

(A) The work done on the gas is maximum when it is compressed irreversibly from (p_2, V₂) to (p₁, V₁) against constant pressure p₁ 

(B) If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic 

(C) The work done by the gas is less when it is expanded reversibly from V₁ to V₂ under adiabatic conditions as compared to that when expanded reversibly from V₁ to V₂ under isothermal conditions 

(D) The change in internal energy of the gas is (i) zero, if it is expanded reversibly with T₁ = T₂, and (ii) positive, if it is expanded reversibly under adiabatic conditions with T₁ ≠ T₂

Answer 1

(A, B, C) (A) During adiabatic expansion, the final temperature is less than the initial temperature. Therefore the final volume in adiabatic expansion will also be less than the final volume in isothermal expansion. This can be graphically shown as  

The magnitude of work done by the gas is equal to the area under the curve. As seen from the figure the area under curve in reversible isothermal is more. Hence, the magnitude of work done is lesser in adiabatic reversible expansion as compared to the corresponding work in isothermal expansion.