Chemistry - Thermodynamics - II Question with Solution | TestHub

Path: $\mathrm{A}\to \mathrm{B}$ isothermal expansion ($V_0\to 3V_0$, $P_0\to P_0$/3); $\mathrm{B}\to \mathrm{C}$ isobaric compression at $P_0/3$ (T falls to $T_0/3$); $\mathrm{C}\to \mathrm{A}$ isochoric heating back to $T_0$.

(A) The isotherm is a hyperbola $\mathrm{A}\to \mathrm{B}$, then a horizontal line $\mathrm{B}\to \mathrm{C}$ and a vertical line $\mathrm{C}\to \mathrm{A}$, as drawn: true.

(B) W(A→B) = $P_0{V}_0$ ln3 = 1.1 $P_0{V}_0$. W(B→C) = -$(P_0/3)(2V_0)$ = -0.667 $P_0{V}_0$. Net W = 0.433 $P_0{V}_0$. Cycle ΔU = 0, so Q = W = 0.43 $P_0{V}_0$: true.

(C) Net work is done by the gas (W is positive): false.

(D) The temperature changes in between ($T_0/3$ at C), so internal energy is not the same throughout: false.

Answer: (A), (B).