Final answer:
The maximum power that could be generated by a heat engine with a heat source at 2000 K and a sink at 300 K is 425 kW, assuming Carnot's efficiency. The waste heat rejected to the sink at 300 K is 200 kW.
Step-by-step explanation:
Heat Engine Efficiency and Work
The subject of your question involves thermodynamics, specifically the efficiency and work output of heat engines.
(a) To determine the maximum power that could be generated by the engine for the same heat input, we use the Carnot efficiency, which is the theoretical maximum efficiency of a heat engine operating between two temperatures. The efficiency (η) is given by:
η = 1 - (Tₜ / Tₛ)
Where Tₛ is the absolute temperature of the hot source, and Tₜ is the absolute temperature of the cold sink. For a source at 2000 K and a sink at 300 K, the maximum efficiency would be:
η = 1 - (300 K / 2000 K)
η = 0.85 or 85%
The power output at maximum efficiency (Pₘ) is then:
Pₘ = efficiency × heat input rate
Pₘ = 0.85 × 500 kW
Pₘ = 425 kW
(b) The waste heat rejected to the medium at 300 K can be determined by subtracting the net output from the engine from the heat input:
Qₜ = Qₛ - W = 500 kW - 300 kW
Qₜ = 200 kW
This waste heat to the medium at 300 K is 200 kW.