A machine is used as both Refrigeration Unit and Heat pump. For the same limits of temperatures, if the ratio of Coefficient of Performance of Heat Pump to Coefficient of Performance of Refrigeration Unit is 1.2, then the Coefficient of Performance of Refrigeration Unit is:
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To solve these quickly, remember that the Heat Pump is always 1 better than the Refrigerator. If the ratio is 1.2, it means that 0.2 of the Refrigerator's COP equals 1. $\frac{1}{0.2} = 5$.
1. The COP Relationship: The basic relationship between the COP of a Heat Pump ($COP_{HP}$) and the COP of a Refrigerator ($COP_{R}$) is:
$$COP_{HP} = COP_{R} + 1$$
2. Setting up the Equation: The question states that the ratio of $COP_{HP}$ to $COP_{R}$ is 1.2.
$$\frac{COP_{HP}}{COP_{R}} = 1.2 \implies COP_{HP} = 1.2 \times COP_{R}$$
3. Substitution and Calculation: Substitute the value of $COP_{HP}$ into the primary relationship:
$$1.2 \times COP_{R} = COP_{R} + 1$$
Subtract $COP_{R}$ from both sides:
$$0.2 \times COP_{R} = 1$$
Divide by 0.2:
$$COP_{R} = \frac{1}{0.2} = 5$$
Therefore, the Coefficient of Performance for the refrigeration unit is