This is the boss. No calculator — today $c_p = 4.0\ \mathrm{kJ/(kg \cdot K)}$ for water, the round number every operator keeps for mental work, and both streams are pinned to the SAME capacity rate. That last choice is a gift with a lesson inside it: with equal capacity rates in counterflow, the two streams' temperature profiles run parallel down the shell, both terminal differences come out identical, and the log mean quietly equals that difference. No logarithm, no chart, no calculator.

One exchanger, one long problem, and every answer feeds the next: the duty, then the cold outlet it produces, then the driving difference, then the surface it all costs. Write each line down as you go — one early slip rolls the whole way to the fabrication drawing.

Then the bonus mark asks the question a purchasing department always asks: could we buy the cheaper shell instead? Answer it with the physics, not with the price. 5★ under par here is the chapter crown. Clock in.