Three Carnot engines operate between temperature reservoirs as follows: Engine A: Th = 1,100 K, Tc = 800 K; Engine B: Th = 1,100 K, Tc = 700 K; Engine C: Th = 550 K, Tc = 400 K. Which two engines have the same thermal efficiency?Select one:a.No two have the same thermal efficiency.b.B and Cc.A and Cd.A and Be.A and B and C
Question
Three Carnot engines operate between temperature reservoirs as follows: Engine A: Th = 1,100 K, Tc = 800 K; Engine B: Th = 1,100 K, Tc = 700 K; Engine C: Th = 550 K, Tc = 400 K. Which two engines have the same thermal efficiency?Select one:a.No two have the same thermal efficiency.b.B and Cc.A and Cd.A and Be.A and B and C
Solution
The thermal efficiency of a Carnot engine is given by the formula:
Efficiency = 1 - (Tc/Th)
where Th is the temperature of the hot reservoir and Tc is the temperature of the cold reservoir.
Let's calculate the efficiency for each engine:
Engine A: Efficiency = 1 - (800/1100) = 0.2727 or 27.27% Engine B: Efficiency = 1 - (700/1100) = 0.3636 or 36.36% Engine C: Efficiency = 1 - (400/550) = 0.2727 or 27.27%
So, engines A and C have the same thermal efficiency. Therefore, the correct answer is c. A and C.
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