JEE MAIN - Chemistry (2024 - 31st January Evening Shift - No. 28)
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 R = 8.314 J K$$^{-1}$$ mol$$^{-1}$$)
Answer
28721
Explanation
It is isothermal reversible expansion, so work done negative
$$\begin{aligned} & \mathrm{W}=-2.303 \mathrm{nRT} \log \left(\frac{\mathrm{V}_2}{\mathrm{~V}_1}\right) \\ & =-2.303 \times 5 \times 8.314 \times 300 \log \left(\frac{100}{10}\right) \\ & =-28720.713 \mathrm{~J} \\ & \equiv-28721 \mathrm{~J} \end{aligned}$$
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