A Carnot heat engine operates between two reservoirs at temperatures T1 = 800 K and T2 = 300 K. Calculate its efficiency and the amount of heat it absorbs from the hot reservoir when it does 4000 J of work.
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The efficiency of a Carnot heat engine is given by the equation:
Efficiency = (T1 - T2) / T1
where T1 is the temperature of the hot reservoir and T2 is the temperature of the cold reservoir.
In this case, T1 = 800 K and T2 = 300 K, so the efficiency is:
Efficiency = (800 - 300) / 800
= 500 / 800
= 0.625
The amount of heat absorbed from the hot reservoir is given by the equation:
Heat absorbed = Work done / Efficiency
In this case, the work done is 4000 J. Therefore, the heat absorbed is:
Heat absorbed = 4000 J / 0.625
= 6400 J
So, the Carnot heat engine absorbs 6400 J of heat from the hot reservoir.
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