# Must irreversible heat transfer be quasistatic?

Suppose there is an isolated system composed of two subsystems $A$ and $B$ in thermal contact with each other, but mechanically and diffusively insulated from each other.

The system starts off with a finite temperature difference between $A$ and $B$ (let $A$ have the higher temperature). $A$ then transfers heat to $B$. Can this transfer be quasistatic? If it was to be quasistatic, then $-\delta Q > T_A dS_A$ and $\delta Q > T_B dS_B$ would have to be strict. Then the discrepancies would need to be accounted for by assigning non-zero values to $\delta W$, $dV_A$, and/or $dV_B$ such that the equations $$-\delta Q -\delta W = T_A dS_A -P_A dV_A$$ and $$\delta Q +\delta W = T_B dS_B -P_B dV_B$$ hold. Is this possible to do?

• Does a counterflow heat exchanger approximate what you are thinking about? Irreversible heat transfer can be anything you want, so I am assuming you are asking about reversible heat transfer? Am I completely misunderstanding the question? – CuriousOne Jun 18 '15 at 6:53
• Well the question is about an isolated system. In a counterflow heat exchanger matter is continually flowing in and out of the system, so it's not what I'm talking about. Also the question is about whether heat transfer can be quasistatic; I know that it is irreversible if it is through a finite temperature difference. – Joshua Meyers Jun 18 '15 at 14:12
• You can connect the output of a counterflow heat exchanger with its input and make it into a closed system that keeps moving the heat from one fluid to the other forth and back. The whole is still isolated. The counterflow heat exchanger is quasistatic and reversible. – CuriousOne Jun 18 '15 at 17:25