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

For further reading, see additional explanation here.

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:

#DeltaS = (q_"rev")/T#

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

#q_"irr" + q_"lost" = q_"rev"#

That is, #q_"irr" < q_"rev"#. Let's then divide by #T#:

#q_"irr"/T + q_"lost"/T = q_"rev"/T #

The righthand side is equal to #DeltaS#:

#DeltaS = (q_"irr")/T + (q_"lost")/T#

If we write

#DeltaS >= q/T#,

we would then have that the equals sign represents #q_"rev"#, and the greater-than sign represents #q_"irr"#. i.e. we have:

#color(blue)(DeltaS > q_"irr"/T)#

#color(blue)(DeltaS = q_"rev"/T)#