Physics II / Cyclic Processes and the Carnot Cycle
Practice question · Numerical answer

A Carnot engine has a hot reservoir at 600 K and an efficiency of 25 %. Compute the cold reservoir temperature in K.

Hints
  1. Rearrange the Carnot formula for the cold temperature.
  2. If efficiency is 0.25 then Tc/Th is 0.75, so Tc = 0.75 x 600.
Show the answer

450 (answers within ±5 count)

Why

η=1Tc/Th\eta = 1 - T_c/T_h gives Tc=Th(1η)=600×0.75=450T_c = T_h(1 - \eta) = 600 \times 0.75 = 450 K. Note how modest an efficiency a 150 K temperature drop buys.

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