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(See Steps) The so-called Vanderwaals equation relates the pressure p, temperature T, and volume V of a given gas and is given by (p+(a N^2)/(V^2))(V-N

Question: The so-called Vanderwaals equation relates the pressure $p$, temperature $T$, and volume $V$ of a given gas and is given by

\[\left(p+\frac{a N^{2}}{V^{2}}\right)(V-N b)=N R T\]

where $N$ is the amount of the gas present (expressed in number of moles), $a$ and $b$ are constants related to the intermolecular interactions and the size of the molecules respectively, and $R$ is the fundamental gas constant. Express $p$ as a function of $V, T$ and $N$ and calculate $\frac{\partial p}{\partial V}(V, T, N)$ and $\frac{\partial p}{\partial T}(V, T, N)$.

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(See Steps) The so-called Vanderwaals equation relates the pressure p, temperature T, and volume V of a given gas and is given by (p+(a N^2)/(V^2))(V-N

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