Question

Como resolver essa derivada parcial?

Answer 1

$PV=knT\\\\\\ V=\dfrac{knT}{P}\\\\ \dfrac{\delta V}{\delta T}=\dfrac{kn}{P}\\\\\\ T=\dfrac{PV}{kn}\\\\ \dfrac{\delta T}{\delta P}=\dfrac{V}{kn}\\\\\ P=\dfrac{knT}{V}\\\\ \dfrac{\delta P}{\delta V}=-\dfrac{knT}{V^2}\\\\\\\dfrac{\delta V}{\delta T}\cdot\dfrac{\delta T}{\delta P}\cdot \dfrac{\delta P}{\delta V}=\dfrac{kn}{P}\cdot\dfrac{V}{kn}\cdot\left(-\dfrac{knT}{V^2}\right)=-\dfrac{knT}{PV}=-\dfrac{knT}{knT}=-1$