Heat Loss or Gain During a Change of State for a Gas
\[\oint_C dU + p dV\].
\[U\]is a function of
\[V\]. We can define the state of a gas using these two coordinates, so a point
\[C\]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
If the curve
\[C\]is described clockwise then the area is taken as positive and the gas experiences a net gain of heat energy.