Answer :
Final answer:
The efficiency of a heat engine like the one described, with specific heat transfers to and from the environment, is calculated using a formula from thermodynamics. Efficiency depends on the amount of heat transferred into the engine and the amount released into the environment.
Explanation:
The efficiency of a heat engine is calculated using the formula: efficiency = 1 - Qc/Qh, where Qc is the heat transferred to the cold reservoir, and Qh is the heat absorbed from the hot reservoir. In the first provided information, a cyclical heat engine moves 75.0 kJ to the environment (Qc) for every 95.0 kJ of heat transfer into the engine (Qh). Using the efficiency formula, the calculation would be efficiency = 1 - (75.0/95.0), which simplifies to an efficiency of approximately 21%.
Efficiency of heat engines can significantly vary depending on the initial and final temperatures of the reservoirs, as demonstrated by Carnot's theorem. This theorem tells us that no engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.
The efficiency of a Carnot engine is particularly relevant because it sets the maximum possible efficiency any heat engine can achieve under given conditions, which depends on the temperatures of the hot and cold reservoirs (Th and Tc respectively).
