The coefficient of performance $K=H/P$ is a dimensionless quantity. Its value is independent of the units used for $H$ and $P$, as long as the same units, such as watts, are used for both quantities. However, it is common practice to express $H$ in Btu/h and $P$ in watts. When these mixed units are used, the ratio $H/P$ is called the energy efficiency ratio ($EER$). If a room air conditioner has $K=3.0$, what is its $EER$?

Verified step by step guidance

1. Understand that the coefficient of performance (K) is defined as the ratio of heat output (H) to power input (P), both measured in the same units, typically watts. Here, K = 3.0.
2. Recognize that the energy efficiency ratio (EER) is a similar concept to K, but it uses mixed units: H is measured in Btu/h and P in watts.
3. To convert the coefficient of performance (K) to the energy efficiency ratio (EER), you need to account for the unit conversion between Btu/h and watts. The conversion factor is 1 watt = 3.412 Btu/h.
4. Express the relationship between K and EER using the conversion factor: EER = K * 3.412.
5. Substitute the given value of K (3.0) into the equation to find the EER: EER = 3.0 * 3.412. This will give you the EER in Btu/h per watt.

Key Concepts

Coefficient of Performance (COP)

The Coefficient of Performance (COP) is a measure of the efficiency of a heat pump or air conditioning system, defined as the ratio of useful heating or cooling provided (H) to the work or energy input (P). It is dimensionless and indicates how effectively a system converts energy input into heating or cooling output.

Energy Efficiency Ratio (EER)

The Energy Efficiency Ratio (EER) is a metric used to evaluate the efficiency of cooling devices, calculated as the ratio of cooling capacity (H) in British thermal units per hour (Btu/h) to the electrical power input (P) in watts. EER provides a standardized way to compare the energy efficiency of air conditioners using mixed units.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another set, ensuring consistency in calculations. In the context of EER, converting between Btu/h and watts is crucial for accurate efficiency assessment, as it involves understanding the relationship between different energy units and maintaining dimensional consistency.