If we look at fundamental thermodynamic equation we see that $$dU=\left(\frac{\partial U}{\partial S}\right)dS+\left(\frac{\partial U}{\partial V}\right)dV.$$ We call $\left(\dfrac{\partial U}{\partial S}\right)$ as temperature. But we call $\left(\dfrac{\partial U}{\partial V}\right)$ as negative pressure of the gas. Why is $\left(\dfrac{\partial U}{\partial V}\right)$ negative? Is there any good way to resolve if intensive/extensive variables have "negative" relation?
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2$\begingroup$ Short answer: If you have gas in an adiabatic container and you compress it, you're doing work on it and its energy increases: since $dV < 0$, $\partial U / \partial V < 0$. $\endgroup$– JavierCommented Sep 18, 2015 at 10:44
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