An ideal gas is expand from `(p_(1),V_(1),T_(1))` to `(p_(2),V_(2),T_(2))` under different conditions. The correct statement(s) among the following is (are):

Options

A. 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
B. The change in internal energy of the gas is (i) zero, if it is expanded 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 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)`

Answer

A, C, D

Explanation

(a)
Area under curve in reversible isothermal is more. So, more work will be done by gas.
(b) `T_(1)=T_(2)impliesDeltaU=nC_(v)DeltaT=0`
In reversible adiabatic expansion, `T_(2)ltT_(1)`
`therefore DeltaT=-ve therefore DeltaU=-ve`
(c ) In free expansion, `P_(ext)=0 therefore W=0`
If carried out isothermally `(DeltaU=0)implies q=0` (Adiabatic), From 1 law
If carried out adiabatically `(q=0)implies DeltaU=0` (Isothermal), From 1 law
(d)
During irreversible compression, maximum work is done on the gas (corresponding to shaded area)