To solve this problem, we can use the Carnot efficiency formula and the first law of thermodynamics.
The Carnot efficiency (η) of a heat engine operating between two reservoirs at temperatures T1 and T2 (where T1 is the higher temperature and T2 is the lower temperature) is given by:
η = 1 - (T2 / T1)
Given that the temperatures of the reservoirs are T1 = 500 K and T2 = 300 K, we can calculate the efficiency:
η = 1 - (300 / 500) = 1 - 0.6 = 0.4 = 40%
The efficiency of the Carnot engine is 40%.
The work produced per cycle (W) by the engine is given as 200 J.
According to the first law of thermodynamics, the work produced by the engine (W) is equal to the difference between the heat absorbed (Q1) and the heat released (Q2) during a cycle:
W = Q1 - Q2
Since the Carnot engine is reversible, the heat absorbed (Q1) is equal to the heat released (Q2). Therefore, we can rewrite the equation as:
W = Q - Q 200 J = Q - Q 200 J = 0
Thus, the heat absorbed (Q) by the engine is also 200 J.
In summary:
- The heat absorbed by the engine (Q) is 200 J.
- The efficiency of the engine (η) is 40% or 0.4.