A thermo-dynamical system is changed from state `(P_(1),V_(1))` to `(P_(2),V_(2))` by two different process. The quantity which will remain same will be

Options

A. The work done on the gas is maximum when it is compressed irreversibly from `(p_(2),V_(2))` to `(p_(1),V_(1))` against constant pressure `p_(1)`.
B. The change in internal energy of the gas is (i) zero, if it explained reversibly with `T_(1) = T_(2)`, and (ii) positive, if it is expanded reversibly under adiabatic conditions with `T_(1) ne T_(2)`.
C. If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic
D. The work done by the gas is less when it is expanded reversibly from `V_(1)` to `V_(2)` under adiabatic conditions as compared to that when expanded reversibly from `V_(1)` to `V_(2)` under isothermal conditions.

Answer

acd

Explanation

`underset(p_(1),V_(1),T_(1))("statement-1") overset("Expansion") to underset(P_(2),V_(2),T_(2))("statement-2")`
`rArr` Work done in reversible compression process is smaller than the work done in irreversible compression process.
`rArr DeltaU =0` for reversible isothermal expression.
`DeltaU lt 0` for reversible adiabatic expansion.
`rArr` For free expansion q=0, w=0 and `DeltaU=0`, hence it is simultaneously both isothermal `(DeltaU=0)` as well as adiabatic (q=0)
`rArr` Work done in reversible adiabatic expansion is less than the work done in reversible isothermal expansion as shown in figure.