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How to know heat flows out or in from $pV$ diagram?

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If the process is adiabatic, there is no heat exchange. If not, the heat has to flow in or out.

Let's say, we are looking at a PV diagram of some gas with a known adiabatic index, $\gamma$. All adiabatic curves of this gas will be described by the following equation: $PV^\gamma=constant$.

If at any particular point of the diagram the volume is increasing and the pressure gradient is greater than the pressure gradient of an adiabatic curve at that point, the heat flows in. Otherwise, the heat flows out.

Similarly, if at any particular point of the diagram the volume is decreasing and the pressure gradient is greater than the pressure gradient of an adiabatic curve at that point, the heat flows out. Otherwise, the heat flows in.

If the volume is constant (isochoric process), it could be approximated as either slight expansion or slight compression - the result would be the same: if the pressure increases, the heat flows in, if the pressure decreases, the heat flows out.

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