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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To calculate the efficiency of a Carnot heat engine, we can use the formula:
Efficiency = 1 - (T2 / T1)
where T1 and T2 are the temperatures of the hot and cold reservoirs, respectively.
Given T1 = 800 K and T2 = 300 K, we can calculate the efficiency:
Efficiency = 1 - (300 K / 800 K)
= 1 - 0.375
= 0.625
So, the efficiency of the Carnot heat engine is 0.625, or 62.5%.
To calculate the amount of heat absorbed from the hot reservoir, we can use the formula:
Q_hot = W / Efficiency
where Q_hot is the heat absorbed from the hot reservoir and W is the work done by the heat engine.
Given that the heat engine does 4000 J of work (W = 4000 J) and the efficiency is 0.625, we can calculate the amount of heat absorbed:
Q_hot = 4000 J / 0.625
= 6400 J
So, the Carnot heat engine absorbs 6400 J of heat from the hot reservoir.
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