Thermodynamics and Thermochemistry 1 Question 23
26. A piston filled with 0.04 mole of an ideal gas expands reversibly from $50.0 \mathrm{~mL}$ to $375 \mathrm{~mL}$ at a constant temperature of $37.0^{\circ} \mathrm{C}$. As it does so, it absorbs $208 \mathrm{~J}$ of heat. The values of $q$ and $W$ for the process will be
$(R=8.314 \mathrm{~J} / \mathrm{mol} \mathrm{K}, \ln 7.5=2.01)$
(2013 Main)
(a) $q=+208 \mathrm{~J}, W=-208 \mathrm{~J}$
(b) $q=-208 \mathrm{~J}, W=-208 \mathrm{~J}$
(c) $q=-208 \mathrm{~J}, W=+208 \mathrm{~J}$
(d) $q=+208 \mathrm{~J}, W=+208 \mathrm{~J}$
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Solution:
- The process is isothermal expansion, hence
$$ \begin{aligned} q & =-W \ \Delta E & =0 \ W & =-2.303 n R T \log \frac{V_{2}}{V_{1}} \ & =-2.303 \times 0.04 \times 8.314 \times 310 \times \log \frac{335}{50} \ & =-208 \mathrm{~J} \ q & =+208 \mathrm{~J} \ W & =-208 \mathrm{~J} \quad \text { (expansion work) } \end{aligned} $$
