To find the coefficient of performance (COP) of a refrigerator that works on a reversed Carnot cycle, we need to use the formula:

COP = QH / W

Where:
- COP is the coefficient of performance
- QH is the heat absorbed from the high-temperature reservoir
- W is the work done by the refrigerator

In this case, the refrigerator produces a temperature of -40°C, which is equivalent to 233K. Since the Carnot cycle operates between two temperature reservoirs, we need to find the temperature of the high-temperature reservoir.

Given that the work done per TR (temperature ratio) is 700 kJ per ten minutes, we can convert this to SI units by dividing it by 600 (to convert minutes to seconds):

W = 700 kJ / 600 = 1.17 kJ/s

To find the temperature of the high-temperature reservoir, we use the equation:

TR = TH / TL

Where:
- TH is the temperature of the high-temperature reservoir
- TL is the temperature of the low-temperature reservoir

In this case, TL is -40°C (233K). Rearranging the equation, we can solve for TH:

TH = TR * TL = 1 * 233K = 233K

Now, we can calculate the COP using the formula mentioned earlier:

COP = QH / W = (QH / QL) * (QL / W)

Since the Carnot cycle is reversible, the heat transferred from the high-temperature reservoir is equal to the heat transferred to the low-temperature reservoir:

QH = QL

Therefore:

COP = QH / W = (QL / W) = 1 / (W / QL)

Since the work done per TR is given, we can rewrite the equation as:

COP = 1 / (W / (TR * QL)) = 1 / (1.17 kJ/s / (1 * QL))

Since the COP is a ratio, the units cancel out, and we are left with:

COP = 1 / (1.17 / QL)

Since the COP is a positive value, the higher the value of QL, the lower the value of the COP. Therefore, the minimum value of the COP occurs when QL is maximum. In this case, the maximum value of QL occurs at TL, which is -40°C (233K).

Plugging in the values, we get:

COP = 1 / (1.17 / 233) = 1 / 0.005 = 200

Therefore, the value of the COP is 200.

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