To calculate the rate of irreversibility for the refrigerator, we need to determine the rate of heat transfer from the cold space and the rate of heat transfer to the kitchen, and then compare them.
The rate of heat transfer from the cold space can be determined using the formula:
Q_cold = Power_input - Power_output
where Power_input is the power input to the refrigerator and Power_output is the power output from the refrigerator. In this case, the power input is given as 750 W. The power output can be calculated using the formula:
Power_output = Rate_of_cooling + Rate_of_irreversibility
Given that the refrigerator removes 1.5 kW from the cold space, we convert it to watts:
Rate_of_cooling = 1.5 kW = 1500 W
Substituting these values, we can calculate the power output:
Power_output = 1500 W + Rate_of_irreversibility
Now we can substitute the power input and power output values into the first equation to find the rate of heat transfer from the cold space:
Q_cold = 750 W - (1500 W + Rate_of_irreversibility)
Since the refrigerator rejects heat to the kitchen at 25 degrees, the rate of heat transfer to the kitchen can be calculated using the formula:
Q_kitchen = Rate_of_cooling + Rate_of_irreversibility
Substituting the known values:
Q_kitchen = 1500 W + Rate_of_irreversibility
To find the rate of irreversibility, we set Q_cold equal to Q_kitchen and solve for Rate_of_irreversibility:
750 W - (1500 W + Rate_of_irreversibility) = 1500 W + Rate_of_irreversibility
Simplifying the equation:
750 W - 1500 W - Rate_of_irreversibility = 1500 W + Rate_of_irreversibility
-750 W = 3000 W + 2 * Rate_of_irreversibility
-375 W = 1500 W + Rate_of_irreversibility
Rate_of_irreversibility = -1875 W
The rate of irreversibility for the refrigerator is -1875 watts, indicating that it is losing 1875 watts of useful energy. The negative sign signifies that the irreversibility represents a loss of useful work.