Question

Calculate the heat involved in a reaction for the isothermal expansion of one mole of a ideal gas at ${27}^o$ C from a volume of 50 L to 100 L.

• A. $Q$ = 159 J
• B. $Q$ = 2294 J
• C. $Q$ = 1729 J
• D. $Q$ = 2197 J

Answer 1

The correct option is C $Q$ = 1729 J

Since the process is isothermal.
$\Delta U=0$
W = $-2.303nRTlog\frac{V_2}{V_1}$
where $V_2$ and $V_1$ is the final and initial volume respectively.
n = moles of ideal gas
W = $-2.303\times 8.314\times 300log\frac{100}{50}$
W = $-1729J$
From the first law,
$\Delta U=Q+W$
$Q=-W$ = 1729 J