Thermodynamics And Thermochemistry
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Thermodynamics and Thermochemistry - Result Question 26
26. A piston filled with $0.04$ mole of an ideal gas expands reversibly from $50.0$ $ mL$ to $375$ $ mL$ at a constant temperature of $37.0^{\circ} C$. As it does so, it absorbs $208$ $ J$ of heat. The values of $q$ and $W$ for the process will be
$(R=8.314$ $ J / mol$ $ K, \ln 7.5=2.01)$
(2013 Main)
(a) $q=+208 $ $J$ $, W=-208 $ $J$
(b) $q=-208 $ $J$ $, W=-208 $ $J$
(c) $q=-208 $ $J$ $, W=+208 $ $J$
(d) $q=+208 $ $J$ $, W=+208 $ $J$
Show Answer
Answer:
Correct Answer: 26. (a)
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 J \\ q & =+208 J \\ W & =-208 J \quad \text { (expansion work) } \end{aligned} $
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