Final answer:
To estimate the power required by the compressor motor, we can use the equation for the coefficient of performance (COP) of a refrigerator. Given the COP of 3.5 and the amount of ice produced, we can calculate the power required. We can also find the amount of heat transferred from the system per minute. Heat transferred per minute = (10×10³ kg × 334,000 J/kg) / 1,440 minutes.
Step-by-step explanation:
To estimate the power required by the compressor motor of an ice plant, we can use the equation for the coefficient of performance (COP) of a refrigerator: COP = Qc / W, where Qc is the heat transferred from the cold reservoir and W is the work done by the compressor motor. Rearranging the equation, we have W = Qc / COP. Given that the COP is 3.5, we can substitute the values to calculate the power required by the compressor motor.
First, we need to find Qc. Since ice is being produced, the heat transferred from the system is equal to the latent heat of fusion of water, which is 334,000 J/kg. The amount of ice produced is 10×10³ kg, so the total heat transferred is Qc = 10×10³ kg × 334,000 J/kg.
Next, we can calculate the power required: W = Qc / COP = (10×10³ kg × 334,000 J/kg) / 3.5.
But since the problem asks for the power required per day, we need to convert it to minutes. Assuming a day has 24 hours, we have 24 hours × 60 minutes = 1,440 minutes. So, the power required by the compressor motor is (10×10³ kg × 334,000 J/kg) / 3.5 / 1,440 minutes.
Now, if we consider the transmission efficiency of 85%, we need to multiply the power required by the compressor motor by the reciprocal of the transmission efficiency: Power required = (10×10³ kg × 334,000 J/kg) / 3.5 / 1,440 minutes / 0.85.
To find the amount of heat transferred from the system per minute, we need to divide the total heat transferred by the number of minutes in a day: Heat transferred per minute = (10×10³ kg × 334,000 J/kg) / 1,440 minutes.