The gas law for a fixed mass m of an ideal gas at absolute temperature T, pressure P, and volume V is PV = mRT, where R is the gas constant. Find the partial derivatives ?P/?V = ?V/?T = ?T/?P = ?P/?V ?V/?T ?T/?P = (an integer)
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Step 1: Given gas law equation PV = mRT, where R is the gas constant. Show more…
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The gas law for a fixed mass $m$ of an ideal gas at absolute temperature $T,$ pressure $P,$ and volume $V$ is $P V=m R T,$ where $R$ is the gas constant. Show that $$ \frac{\partial P}{\partial V} \frac{\partial V}{\partial T} \frac{\partial T}{\partial P}=-1 $$
Partial Derivatives
(a) The gas law for a fixed mass $m$ of an ideal gas at absolute temperature $T,$ pressure $P,$ and volume $V$ is $P V=m R T,$ where $R$ is the gas constant. Show that $$\frac{\partial P}{\partial V} \frac{\partial V}{\partial T} \frac{\partial T}{\partial P}=-1$$ (b) For the ideal gas of part (a), show that $$T \frac{\partial P}{\partial T} \frac{\partial V}{\partial T}=m R$$
PARTIAL DERIVATIVES
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