The efficiency of a machine is in general defined as the ratio between useful (released) energy and the input energy. Therefore, the exact formulas for efficiency depend on the purpose of the machine. What's the difference in the maximal efficiency of a heat pump and a heat engine? Both the engine and the pump have the cold reservoir set at T_c=10∘C and the hot reservoir at T_h=70∘C.
To determine the maximal efficiency of a heat pump and a heat engine, we can use the Carnot efficiency formula, which applies to both types of machines.
The Carnot efficiency formula is given by:
Efficiency = 1 - (Tc / Th)
Where:
- Efficiency is the maximal efficiency of the machine
- Tc is the temperature of the cold reservoir
- Th is the temperature of the hot reservoir
For the heat pump, the cold reservoir temperature (Tc) is set at 10°C, and the hot reservoir temperature (Th) is set at 70°C. Plugging these values into the Carnot efficiency formula, we can calculate the efficiency.
Heat pump efficiency = 1 - (10 / 70)
= 1 - 0.1429
= 0.8571, or 85.71%
For the heat engine, the calculation is the same since the formula applies to both types of machines. So, the maximal efficiency of the heat engine would also be 85.71%.
Therefore, the difference in the maximal efficiency of a heat pump and a heat engine, in this case, is zero. Both have a maximal efficiency of 85.71%.