partial differentiation

**kingsolomonsgrave** · December 13th 2012, 09:01 PM

I have no idea what's going on here, perhaps tell me what topic heading this would fall under so I can look it over?

**MarkFL** · December 13th 2012, 09:42 PM

We are given:

$PV=mRT$

hence:

$P=\frac{mRT}{V}\,\therefore\,\frac{\delta P}{\delta V}=-\frac{mRT}{V^2}$

$V=\frac{mRT}{P}\,\therefore\,\frac{\delta V}{\delta T}=\frac{mR}{P}$

$T=\frac{PV}{mR}\,\therefore\,\frac{\delta T}{\delta P}=\frac{V}{mR}$

and so:

$\frac{\delta P}{\delta V}\frac{\delta V}{\delta T}\frac{\delta T}{\delta P}=\left(-\frac{mRT}{V^2} \right)\left(\frac{mR}{P} \right)\left(\frac{V}{mR} \right)=-\frac{mRT}{PV}=-\frac{PV}{PV}=-1$

**kingsolomonsgrave** · December 13th 2012, 10:10 PM

thanks! how did you know which partials to take? can we just go right to left so partial derivatives: P/V then V/T then T/P ?

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