A refrigerator is to maintain eatables kept inside at 9°C. If room temperature is 36° C, calculate the coefficient of performance.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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**Problem Statement:**

A refrigerator is to maintain eatables kept inside at 9°C. If the room temperature is 36°C, calculate the coefficient of performance.

---

**Solution:**

To solve this problem, we need to determine the Coefficient of Performance (COP) for the refrigerator. The COP of a refrigerator is given by the formula:

\[ \text{COP} = \frac{T_{\text{low}}}{T_{\text{high}} - T_{\text{low}}} \]

where:
- \( T_{\text{low}} \) is the temperature inside the refrigerator in Kelvin.
- \( T_{\text{high}} \) is the temperature outside (room temperature) in Kelvin.

First, we convert the given temperatures from Celsius to Kelvin by adding 273 to each temperature in Celsius.

\[ T_{\text{low}} = 9°C + 273 = 282 \, \text{K} \]
\[ T_{\text{high}} = 36°C + 273 = 309 \, \text{K} \]

Now substitute the values into the COP formula:

\[ \text{COP} = \frac{282 \, \text{K}}{309 \, \text{K} - 282 \, \text{K}} = \frac{282}{27} \approx 10.44 \]

Therefore, the coefficient of performance (COP) of the refrigerator is approximately 10.44.
Transcribed Image Text:**Problem Statement:** A refrigerator is to maintain eatables kept inside at 9°C. If the room temperature is 36°C, calculate the coefficient of performance. --- **Solution:** To solve this problem, we need to determine the Coefficient of Performance (COP) for the refrigerator. The COP of a refrigerator is given by the formula: \[ \text{COP} = \frac{T_{\text{low}}}{T_{\text{high}} - T_{\text{low}}} \] where: - \( T_{\text{low}} \) is the temperature inside the refrigerator in Kelvin. - \( T_{\text{high}} \) is the temperature outside (room temperature) in Kelvin. First, we convert the given temperatures from Celsius to Kelvin by adding 273 to each temperature in Celsius. \[ T_{\text{low}} = 9°C + 273 = 282 \, \text{K} \] \[ T_{\text{high}} = 36°C + 273 = 309 \, \text{K} \] Now substitute the values into the COP formula: \[ \text{COP} = \frac{282 \, \text{K}}{309 \, \text{K} - 282 \, \text{K}} = \frac{282}{27} \approx 10.44 \] Therefore, the coefficient of performance (COP) of the refrigerator is approximately 10.44.
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