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Problem 1 - Olympiad

Two Carnot engines operate in series between hot and cold reservoirs at temperatures of 500 K and 200 K. The first engine operates between 500 K and T, and the second between T and 200 K. If both engines deliver equal work, find the intermediate temperature T.

Correct: B

For equal work output, the work of each engine is proportional to their temperature differences. Using Carnot efficiency: $\frac{T - 200}{T} = \frac{500 - T}{500}$. Cross-multiplying gives $500(T - 200) = T(500 - T)$, which simplifies to $T^2 - 700T + 100000 = 0$. Solving the quadratic gives $T = 350$ K.