Final answer:
The first law efficiency or thermal efficiency of the heat engine is 40%, and the second law efficiency also known as Carnot efficiency is approximately 70%.
Step-by-step explanation:
The student's question concerns the calculation of the first and second law efficiencies of a heat engine that operates between two thermal reservoirs at different temperatures. Initially, the heat engine receives 5 MJ of heat at 995 K and performs 2 MJ of work, ejecting the rest of the heat to the surroundings at 25°C (which translates to 298 K).
The first law efficiency is also known as the thermal efficiency and is calculated using the formula:
- First law efficiency (η) = Work output / Heat input
Therefore, η = (2 MJ) / (5 MJ) = 0.4 or 40%.
The second law efficiency, also known as the Carnot efficiency, is determined by the temperatures of the hot and cold reservoirs and is given by:
- Second law efficiency (ηCarnot) = 1 - (Tc / Th)
Where Tc and Th are absolute temperatures of the cold and hot reservoirs respectively. Thus, ηCarnot = 1 - (298 K / 995 K) ≈ 0.70 or 70%.
The first and second law efficiencies are 40% and approximately 70%, respectively.