# 11.5.3 Isochoric

Isochoric literally means constant volume. On the P-V diagram, an isochoric cooling is represented by a downward vertical line: vertical because volume is constant, downward because it must move from a higher isotherm to a lower isotherm.

Since cooling implies a decrease in temperature,$\displaystyle \Delta U<0$ . And since the volume does not change, $\displaystyle {{W}_{{ON}}}=0$ .

Applying the first law of thermodynamics,

$\displaystyle \displaystyle \overset{{-ve}}{\mathop{{\Delta U}}}\,=Q+{{\overset{0}{\mathop{W}}\,}_{{ON}}}$

it is also clear that Q is negative, i.e. heat is lost to the surrounding during an isochoric cooling.

A simple practical example of an isochoric cooling is to immerse a canister (with rigid walls) of gas in an ice bath.