A certain gas obeys \(\mathrm{P(V_m - b) = RT}\). The value of \(\left(\dfrac{\partial Z}{\partial P}\right)_T\) is \(\dfrac{xb}{RT}\). The value of x is _________. (Integer answer) (Z : compressibility factor)
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Correct Answer: 1
Solution and Explanation
\(Z = \dfrac{PV_m}{RT} = 1 + \dfrac{bP}{RT}\).
\(\left(\dfrac{\partial Z}{\partial P}\right)_T = \dfrac{b}{RT}\), compared with \(\dfrac{xb}{RT}\) gives x = 1.
Answer: 1
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