Final answer:
The question is related to thermodynamics within Physics, covering topics such as the coefficient of performance for heat pumps, heat transfer, cost analysis of heating methods, and engine efficiency. Calculations will be based on specified temperatures, energy values, and theoretic principles like Carnot efficiency.
Step-by-step explanation:
The subject of this question is Physics, specifically focusing on thermodynamics and heat exchange mechanisms. The question pertains to determining various thermodynamic properties such as the coefficient of performance of a heat pump, heat transfer amounts, cost comparisons with other heating methods, and efficiency of an engine.
Coefficient of Performance and Heat Transfer
The coefficient of performance (COP) for a heat pump is a measure of its efficiency, and in an ideal scenario with a hot reservoir temperature of 50.0°C and a cold reservoir temperature of -20.0°C, it can be calculated using the Carnot efficiency formula. Additionally, the amount of heat transfer into the warm environment when work is done on the system and the comparative costs of different heating methods can be determined based on the given energy values.
Engine Efficiency and Work
Calculating the thermodynamic efficiency of an engine involves determining the ratio of work output to heat input, and the given scenario provides sufficient details to perform this calculation. Likewise, the amount of heat absorbed from a high-temperature bath and the work performed by the engine can also be established.