Minimum capacity rate ratio of a heat exchanger

[theBEAST]

Homework Statement

Here is the question:

I am confused about the solution. In the solution they found that the minimum capacity rate ratio R = C_min/C_max was zero. This is because of the term I circled in the red which I do not understand why it goes towards infinity.

Here is the solution:

Could someone please explain why that term goes to infinity?

 

[haruspex]

Not a subject I know anything about, but it seems to me that c_h represents the specific heat of the condensing steam. Where the steam is condensing but not changing in temperature, specific heat = ΔQ/Δθ = ΔQ/0. That said, I'm sure some of the steam would be hotter than its condensate.

 

[Chestermiller]

That said, I'm sure some of the steam would be hotter than its condensate.

The problem statement (and the way they solve the problem) implies that not all the steam condenses. So the inlet and outlet temperatures on the steam side are supposed to be taken as 125 C. Regarding the line involving the red encircled portion, I have no idea what the max and min on (mc) or the parameter R are supposed to be used for. Anyway, the rest of the development makes perfect sense.

Chet