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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 by the gas is less when it is expanded reversibly from V1 to V2under adiabatic conditions as compared to that when expanded reversibly from V1 to V2under isothermal conditions.
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B
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 T1T2
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C
If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic
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D
The work done on the gas is maximum when it is compressed irrversibly from (p2, V2) to (p1, V1) against constant pressure p1
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Solution

## The correct option is D The work done on the gas is maximum when it is compressed irrversibly from (p2, V2) to (p1, V1) against constant pressure p1(a) Maximum work is done on the system when compression occur irreversibly and minimum work is done is reversible compression. (b) AB is isothermal and AC is adiabatic path. Work done is area under the curve. Hence, less work is obtained in adiabatic process than in isothermal (c) It is incorrect. In adiabatic expansion cooling is observed, hence ΔU=nCvΔT<0 (d) q = 0 (adiabatic), W = 0 (Free expansion) Hence, ΔU=0, ΔT=0 (Isothermal)

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