Refrigerator A works between `-10^@C` and `27^@C`, while refrigerator B works between `-27^@C` and `17^@C`, both removing heat equal to 2000J from the freezer. Which of the two is the better refrigerator?

Explanation

To determine which refrigerator is better, we need to calculate the Coefficient of Performance (COP) for both refrigerators A and B. The COP is defined as the ratio of the heat removed from the cold reservoir (the freezer) to the work input required to remove that heat.

### Step-by-step Solution:

1. **Identify the temperatures for both refrigerators:**
- For Refrigerator A:
- Freezer temperature (T2) = -10°C = 263 K (convert to Kelvin by adding 273)
- Surrounding temperature (T1) = 27°C = 300 K (convert to Kelvin by adding 273)
- For Refrigerator B:
- Freezer temperature (T2) = -27°C = 246 K (convert to Kelvin by adding 273)
- Surrounding temperature (T1) = 17°C = 290 K (convert to Kelvin by adding 273)

2. **Calculate the Coefficient of Performance (COP) for Refrigerator A:**
\[ \text{COP}_A = \frac{T_2}{T_1 - T_2} = \frac{263}{300 - 263} = \frac{263}{37} \approx 7.11 \]

3. **Calculate the Coefficient of Performance (COP) for Refrigerator B:**
\[ \text{COP}_B = \frac{T_2}{T_1 - T_2} = \frac{246}{290 - 246} = \frac{246}{44} \approx 5.59 \]

4. **Compare the COP values:**
- COP for Refrigerator A ≈ 7.11
- COP for Refrigerator B ≈ 5.59

5. **Determine which refrigerator is better:**
Since Refrigerator A has a higher COP than Refrigerator B, it means that Refrigerator A is more efficient at removing heat from the freezer for the same amount of work input. Therefore, Refrigerator A is the better refrigerator.

### Final Conclusion:
Refrigerator A is better than Refrigerator B because it has a higher Coefficient of Performance (COP).

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