\[\oint_C dU + p dV\]
. \[U\]
is a function of \[p\]
and \[V\]
. We can define the state of a gas using these two coordinates, so a point \[(p,V)\]
determine \[U\]
uniquely.If
\[C\]
is a closed curve \[\oint_C dU =0\]
and the gas gains heat energy equal to \[\oint_C p dV\]
This is the area enclosed by the curve
\[C\]
.
\[C\]
is described clockwise then the area is taken as positive and the gas experiences a net gain of heat energy.