Question

For an isothermal irreversible expansion of $1$ mole of a perfect gas, identify the correct relation where symbols have their usual meaning

• A. $△U=0$
• B. $△H=0$
• C. $q=RT(1-\frac{P_2}{P_1})$
• D. $w=RTln\left(\frac{P_2}{P_1}\right)$

Answer 1

Answer: (A), (B), (C)

$q=RT(1-\frac{P_2}{P_1})$

(a)We know that,
$△U=n{C}_v△T$
$(\because △T=0;△U=0)\left(b\right)△H=n{C}_p△T(\because △T=0;△H=0)\left(c\right)\text{According to 1st law of thermodynamics}△U=q+w=0\therefore q=-ww=-{\int }_{V_1}^{V_2}{P}_{ext}dv{P}_{ext}=P_{2}w=-P_2(V_2-V_1)w=-P_2[\frac{RT}{P_2}-\frac{RT}{P_1}]=-RT[1-\frac{P_2}{P_1}]\therefore q=RT[1-\frac{P_2}{P_1}]$