Value of (∂Z/∂P)ₜ for Gas... | JEE Main 2021 | Gaseous State

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JEE MAIN 2021

26-02-2021 S1

Question

A certain gas obeys $\mathrm{P}\left(\mathrm{V}_{\mathrm{m}}-\mathrm{b}\right)=\mathrm{RT}$. The value of $\left(\frac{\partial \mathrm{Z}}{\partial \mathrm{P}}\right)_{\mathrm{T}}$ is $\frac{\mathrm{xb}}{\mathrm{RT}}$. The value of x is $\_\_\_\_$ . (Integer answer) (Z: compressibility factor)

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Solution

$\begin{aligned} & \mathrm{Z}+1+\frac{\mathrm{Pb}}{\mathrm{RT}} \\ & \left(\frac{\partial \mathrm{Z}}{\partial \mathrm{P}}\right)_{\mathrm{T}}=0+\frac{\mathrm{b}}{\mathrm{RT}} \times 1\end{aligned}$

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