What is reversible heat flow, and how is it related to entropy? What is the difference between reversible and irreversible heat flow?
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"#
#q_"irr"/T + q_"lost"/T = q_"rev"/T #
The righthand side is equal to
#DeltaS = (q_"irr")/T + (q_"lost")/T#
If we write
#DeltaS >= q/T#,
we would then have that the equals sign represents
#color(blue)(DeltaS > q_"irr"/T)#
#color(blue)(DeltaS = q_"rev"/T)#