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Yet this holds good only subject to the condition that the temperature is not varied; it has been seen above that for the more general variation neither δH nor δU is an exact differential, and no line of separation can be drawn between thermal and mechanical energies.

These are in fact the various relations ensuring that the right-hand side is an exact differential, and are of the type of reciprocal relations such as dμr/dϕ = dT/dmr.

But what the exact differential should be has been a matter of dispute.