Question

Two moles of a perfect gas undergo the following process:

(a) A reversible isobaric expansion from ($1$ atm to $20L$) to ($1$ atm to $40L$)

(b) A reversible isochoric change of state from ($1$ atm to $40L$) to ($0.5$ atm to $40L$)

(c) A reversible isothermal compression from ($0.5$ atm to $40L$) to ($1$ atm to $20L$)

(i) Sketch with labels each of the process on the same P-V diagram.

(ii) Calculate the total work $\left(w\right)$ and the total change $\left(q\right)$ involved in the above process

(iii) What will be the value of $\Delta U,\Delta H,\Delta S$ for the overall process?

Answer 1

$AB$-Isobaric process
$BC$-Isochoric process
$CA$-Isothermal process
Total work $=w_{AB}+w_{BC}+w_{CA}=-P\times \Delta V+2.303nRT\log \left(\frac{V_2}{V_1}\right)$

$=-1\times 20\times 101.3+0+2.303\times 2\times 8.314\times T\log \frac{40}{20}...\left(i\right)$

$PV=nRT$ (At $A$)

$1\times 20=2\times 0.0821\times T$

$T=121.8K$

From eq.(i)

Total work$=-2026+2.303\times 2\times 8.314\times 121.8\log 2=-622.06J$

In cyclic process:
$\Delta U=0,\Delta H=0,\Delta S=0$