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At what cold-reservoir temperature (in ∘C) would a Carnot engine with a hot-reservoir temperature of 420 ∘C have an efficiency of 60 % ?

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Final answer:

The cold reservoir at 168°C temperature the Carnot engine has an efficiency of 60%.

Step-by-step explanation:

To find the cold-reservoir temperature at which a Carnot engine with a hot-reservoir temperature of 420°C has an efficiency of 60%, we can use the formula for the efficiency of a Carnot engine:

Efficiency = 1 - (Tc/Th)
Where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.

Given that the efficiency is 60% and the hot-reservoir temperature is 420°C, we can rearrange the formula to solve for Tc:

Tc = Th * (1 - Efficiency)

Substituting the values, we have:

Tc = 420°C * (1 - 0.60)

Tc = 420°C * 0.40

Tc = 168°C

Therefore, the cold-reservoir temperature at which the Carnot engine has an efficiency of 60% is 168°C.

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