Coefficient of Performance (COP) Formula: Explained with Examples

📚 Quick Study Guide

• 🧊 The Coefficient of Performance (COP) measures the efficiency of a heat pump or refrigeration system.
• 🌡️ COP is defined as the ratio of useful heating or cooling provided to the work required.
• 🔢 For heating: $COP_{heating} = \frac{Q_{hot}}{W_{in}}$, where $Q_{hot}$ is the heat delivered to the hot reservoir and $W_{in}$ is the work input.
• ❄️ For cooling: $COP_{cooling} = \frac{Q_{cold}}{W_{in}}$, where $Q_{cold}$ is the heat removed from the cold reservoir and $W_{in}$ is the work input.
• 💡 A higher COP indicates greater efficiency.

Practice Quiz

1. Which of the following best describes the Coefficient of Performance (COP)?
   1. (A) The amount of work done by a system.
   2. (B) The ratio of useful heating or cooling to the work required.
   3. (C) The temperature difference between two reservoirs.
   4. (D) The rate of heat transfer in a system.
2. What does a higher COP value indicate?
   1. (A) Lower efficiency.
   2. (B) Greater efficiency.
   3. (C) No change in efficiency.
   4. (D) Higher work input required.
3. For a heating system, the COP is calculated as:
   1. (A) $\frac{W_{in}}{Q_{hot}}$
   2. (B) $\frac{Q_{cold}}{W_{in}}$
   3. (C) $\frac{Q_{hot}}{W_{in}}$
   4. (D) $\frac{Q_{hot}}{Q_{cold}}$
4. A refrigerator removes 120 J of heat from the cold reservoir with a work input of 40 J. What is its COP?
   1. (A) 0.33
   2. (B) 3
   3. (C) 4800
   4. (D) 160
5. Which of the following factors can affect the COP of a heat pump?
   1. (A) Temperature difference between the reservoirs.
   2. (B) Type of refrigerant used.
   3. (C) System design.
   4. (D) All of the above.
6. For a cooling system, $Q_{cold}$ represents:
   1. (A) Heat delivered to the hot reservoir.
   2. (B) Work input.
   3. (C) Heat removed from the cold reservoir.
   4. (D) Total energy of the system.
7. A heat pump has a COP of 3.5 and delivers 700 J of heat. How much work input is required?
   1. (A) 2450 J
   2. (B) 200 J
   3. (C) 0.005 J
   4. (D) 703.5 J