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.
Guide On Rating System
Vote
The efficiency of a Carnot heat engine is given by the equation:
Efficiency = 1 - (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 = 1 - (300 / 800) = 1 - 0.375 = 0.625 or 62.5%
The amount of heat absorbed from the hot reservoir is equal to the work done by the engine plus the heat rejected to the cold reservoir:
Q_hot = W + Q_cold
Since the engine does 4000 J of work, the heat absorbed from the hot reservoir is:
Q_hot = 4000 J + Q_cold
Given that the efficiency is 62.5% or 0.625, we can rearrange the equation for efficiency to solve for Q_cold:
Q_cold = (1 - Efficiency) * Q_hot
Q_cold = (1 - 0.625) * Q_hot
Q_cold = 0.375 * Q_hot
Plugging in the value of Q_hot, we get:
Q_cold = 0.375 * 4000 J
Q_cold = 1500 J
Therefore, the amount of heat absorbed from the hot reservoir is 1500 J.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99