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.

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