Finite Changes in Many Dimensions

If one changes both T and V by small amounts, i.e.,

$$T \rightarrow T+\Delta T$$

and

$$V \rightarrow V+\Delta V$$

one has

$$\Delta p = p(T+\Delta T, V+\Delta V) - p(T,V) = \left (\frac... ...elta T +\left (\frac{\partial P}{\partial V}\right )_T\Delta V$$

to first order ².