Question

An ideal gas is expanded from $\left(p_1,V_1,T_1\right)$ to $(p_2,V_2,T_2)$ under different conditions. The incorrect statement among the following is?

• A. The word 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 and adiabatic
• D. The work done on the gas is maximum when it is compressed irreversibly from $\left(p_2,V_2\right)$ to $\left(p_1,V_1\right)$ against constant pressure $p_1$

Answer 1

Answer: (B)

Area under curve in reversible isothermal is more. So, more work will be done by gas.
$T_1=T_2$
$\Delta U=n{C}_V\Delta T=0$
In reversible adiabatic expansion, $T_2<T_1$
So $\Delta T=-ve$ , $\Delta U=-ve$
In free expansion, $P_{ext}=0$
So $W=0$
If carried out isothermally $\left(\Delta U=0\right)$
$q=0$ (adiabatic); from I law
If carried out adiabatically $\left(q=0\right)$
$\Delta U=0$ (isothermal); From I law

During irreversible compression, maximum work is done on the gas (corresponding to shaded area).