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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 (p2,V2) to (p1,V1) against constant pressure
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B
The work done on 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.
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C
The change in internal energy of the gas (i) zero, if it is expanded reversibly with T1=T2, and (ii) negative, if it is expanded reversibly under adiabatic conditions with T1T2
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D
If the expansion is carried out freely, it is simultaneosly both isothermal as well as adiabatic
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Solution

## The correct options are A The work done on the gas is maximum when it is compressed irreversibly from (p2,V2) to (p1,V1) against constant pressure B The work done on 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. C The change in internal energy of the gas (i) zero, if it is expanded reversibly with T1=T2, and (ii) negative, if it is expanded reversibly under adiabatic conditions with T1≠T2 D If the expansion is carried out freely, it is simultaneosly both isothermal as well as adiabatic(A)(B)(C) (i) ΔU=nCvΔT=0 (isothermal hence ΔT=0) (ii) ΔU=q+w=−ve(q=0,w<0) ΔU=nCvΔT⇒ΔT<0 (D)q=0 (adibatic), w=0 (free expansion) ΔU=0⇒ΔT=0(isothermal)

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