11.2.6 Reversed heat engines

Concept Overview:

Reversed heat engines operate by having work done on them to move heat from a colder region to a warmer one. This requires external energy because, under normal circumstances, heat flows naturally from warmer to colder regions.

Key Terms:

• Coefficient of Performance (COP): Unlike efficiency, COP can be greater than 1. COP measures how effectively the engine transfers heat for each unit of work done.

Types of Reversed Heat Engines and COP Calculations:

1. Refrigerator: COP (denoted as $\text{COP}_{\text{ref}})$ is the ratio of heat removed from the cold region $( Q_C )$ to the work done $( W )$:

$$\text{COP}_{\text{ref}} = \frac{Q_C}{W} = \frac{Q_C}{Q_H - Q_C} = \frac{T_C}{T_H - T_C}$$

• Where $T_C$ and $T_H$ are the temperatures of the cold and hot regions, respectively.

2. Heat Pump: COP (denoted as $\text{COP}_{\text{hp}}$ is the ratio of heat added to the warm region ($Q_H )$ to the work done $( W )$:

$$\text{COP}{\text{hp}} = \frac{Q_H}{W} = \frac{Q_H}{Q_H - Q_C} = \frac{T_H}{T_H - T_C}$$

Note: Calculations assume maximum theoretical efficiency, using the absolute temperatures of the regions.

Explanation of COP:

• If a system has a COP of 5, this means that 5 joules of heat energy are transferred for every 1 joule of work done.
• COP depends on whether the system functions as a refrigerator or a heat pump, which impacts the formula and interpretation.

Practical Applications:

1. Dual Functionality: Heat pumps can act both as refrigerators and heating systems, making them versatile. They are more energy-efficient compared to conventional electric heaters since they can transfer more than 1 joule of heat energy per joule of work done.
2. Cost Efficiency: In heating mode, heat pumps are more cost-effective because they deliver more heat energy than the electrical energy they consume, unlike traditional heaters that convert electrical energy directly to heat.

Important Considerations:

• Specification of Heat Flow: When discussing energy transfer in reversed heat engines, always clarify which region (hot or cold) the heat is being moved into, as this defines whether it's working as a refrigerator or a heat pump. For example:

  • "Input energy" could refer to the work done on the engine or the energy transferred into either the hot or cold region.