Thermodynamics C Question 10
Question 10 - 2024 (31 Jan Shift 2)
If 5 moles of an ideal gas expands from $10 \mathrm{~L}$ to a volume of $100 \mathrm{~L}$ at $300 \mathrm{~K}$ under isothermal and reversible condition then work, $\mathrm{w}$, is $-x \mathrm{~J}$. The value of $x$ is _________.
(Given $\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ )
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Answer (28721)
Solution
It is isothermal reversible expansion, so work done negative
$$ \begin{aligned} & \mathrm{W}=-2.303 \mathrm{nRT} \log \left(\frac{\mathrm{V}{2}}{\mathrm{~V}{1}}\right) \ & =-2.303 \times 5 \times 8.314 \times 300 \log \left(\frac{100}{10}\right) \ & =-28720.713 \mathrm{~J} \ & \equiv-28721 \mathrm{~J} \end{aligned} $$
