# What is reversible heat flow, and how is it related to entropy? What is the difference between reversible and irreversible heat flow?

Apr 6, 2017

Heat flow can either be reversible or irreversible; all that means is that it is either perfectly conservative or we missed a spot and the heat is lost somewhere.

Reversible heat flow is the process of transferring heat infinitesimally slowly in such a way that no heat is lost, i.e. it is the MAXIMUM heat flow that can occur. That is the kind of heat flow described here:

$\Delta S = \frac{{q}_{\text{rev}}}{T}$

Irreversible heat flow is basically inefficient heat flow plus the heat that was inadvertently missed or lost:

${q}_{\text{irr" + q_"lost" = q_"rev}}$

That is, ${q}_{\text{irr" < q_"rev}}$. Let's then divide by $T$:

${q}_{\text{irr"/T + q_"lost"/T = q_"rev}} / T$

The righthand side is equal to $\Delta S$:

$\Delta S = \frac{{q}_{\text{irr")/T + (q_"lost}}}{T}$

If we write

$\Delta S \ge \frac{q}{T}$,

we would then have that the equals sign represents ${q}_{\text{rev}}$, and the greater-than sign represents ${q}_{\text{irr}}$. i.e. we have:

$\textcolor{b l u e}{\Delta S > {q}_{\text{irr}} / T}$

$\textcolor{b l u e}{\Delta S = {q}_{\text{rev}} / T}$