To calculate the rate of irreversibility in the refrigerator, we can use the concept of the Coefficient of Performance (COP) for a refrigerator. The COP is defined as the ratio of the heat removed from the cold space (Qc) to the work input (W) to the system. It is given by:
COP_refrigerator = Qc / W
We are given the power input (W) to the refrigerator as 750 W, and the heat removed from the cold space (Qc) is 1.5 kW (1 kW = 1000 W). We need to convert the heat removed to watts before using it in the COP equation.
1.5 kW = 1.5 * 1000 W = 1500 W
Now, we can calculate the COP of the refrigerator:
COP_refrigerator = 1500 W / 750 W = 2
Next, we can calculate the Carnot COP (COP_Carnot) for the refrigerator, which represents the maximum possible COP for a refrigerator operating between two temperature reservoirs (Tc and Th, where Th is the higher temperature):
COP_Carnot = Th / (Th - Tc)
where: Th = Temperature of the kitchen (in Kelvin) = 25°C + 273.15 = 298.15 K Tc = Temperature of the cold space (in Kelvin) = -10°C + 273.15 = 263.15 K
COP_Carnot = 298.15 K / (298.15 K - 263.15 K) ≈ 1.53
Finally, the rate of irreversibility (I) can be calculated using the following formula:
I = Qc * (1 - (COP_refrigerator / COP_Carnot))
I = 1500 W * (1 - (2 / 1.53)) ≈ 1500 W * (1 - 1.307) ≈ 1500 W * (-0.307) ≈ -460.5 W
The rate of irreversibility is approximately -460.5 Watts. The negative sign indicates that this irreversibility represents a loss of power from the system.