## Heat Loss or Gain During a Change of State for a Gas

The heat received by the gas during a process which changes the state of the gas is
$\oint_C dU + p dV$
.
$U$
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
$C$
.

If the curve
$C$
is described clockwise then the area is taken as positive and the gas experiences a net gain of heat energy.