Question

A gas is expanded from volume $V_1$ to volume $V_2$ in three processes, shown in the figure. If $U_A,U_B$ and $U_C$ and $U_D$ represent the internal energies of the gas in state A, B, C and D respectively, the which of the following is not correct.

• A. $U_B-U_A>0$
• B. $U_C-U_A=0$
• C. $U_D-U_A<0$
• D. $U_B=U_C=U_D$

Answer 1

The correct option is D $U_B=U_C=U_D$

The correct answer is option(D).

Process(1): Isobaric

$\Delta w=P\left(\Delta V\right)$ and $PV=nRT$

$⟹P\Delta V=nR\Delta T⟹\Delta T=\frac{\Delta w}{nR}⟹\Delta u=\frac{nR}{(r-1)}.\Delta T=\frac{nR}{(r-1)}.\frac{\Delta w}{nR}=\frac{\Delta w}{r-1}$

Process (2): Isothermal: $\Delta T=0$ and $\Delta u=0$

Process (3): Adoiabatic: $\Delta Q=0$ and $\Delta w=-\Delta u$

$\frac{nR}{r-1}\Delta T=\Delta w⟹\Delta T=\frac{\Delta w(r-1)}{nR}$