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

##### 1 Answer
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:

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

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