Question

One mole of a monoatomic gas is subjected to the following cyclic process:
(a) Calculate $T_1$ and $T_2$.
(b) Calculate $\Delta U,q$ and $w$ in calories in each step of cyclic process.

Answer 1

(a) At $A$:
$PV=nRT$
$20\times 1=1\times 0.0821\times T_1$
$T_1=243.6K$
At $B$:
$PV=nRT$
$20\times 10=1\times 0.0821\times T_2$
$T_2=243.05K$
(b) Path $AB$: Isobaric process ($\Delta U=0,q=w$)
$w=P\Delta U=10\times 9=180litre-atm$
$=\frac{180\times 101.3}{4.185}cal$
$=4356.9cal$ (work in compression is positive)
Path $BC$: Isochoric process
$w=0$
$q_V=\Delta U=n{C}_V\Delta T=1\times \frac{3}{2}R\times (2436-243.6)$
$=\frac{3}{2}\times 2\times 2192.4=6577.2cal$
It is cooling process : $q_V=-6577.2cal$
Path $CA$: It is isothermal compression $\Delta U_0$
$q=w=2.303nRT\log \frac{V_2}{V_1}=2.303\times 1\times 2\times \log \frac{10}{1}=1122.02cal$