Why Heat Exchangers are preferred to work in Constant Pressure Process than Constant Volume Process?
Mostly, all problems are solved in Constant Pressure Process
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I'm assuming that you want to know why we use the heat capacity at constant pressure, $c_p$, instead of at constant volume, $c_v$, in analyzing heat exchangers.
The main reason is that the pressure drop through most heat exchangers will be minimal, so a constant-pressure assumption works well. This is especially true for liquids, whose thermodynamic properties are not very sensitive to changes in pressure. You will of course need to verify and justify this assumption for any heat exchanger analysis that you do.