- #1
Silent
- 4
- 0
Homework Statement
You are required to calculate the efficiency of an ice-making machine that takes in water at a temperature of 16°C and produces ice cubes at a temperature of -6°C. Water is taken in at the rate of 1kg every 5 minutes and the input power to the machine is 300W. The Specific Heat Capacity of water is 4200J/kg, the specific Heat Capacity of Ice is 2100J/kg and the specific Latent Heat of Fusion is 335kJ/kg.
Homework Equations
Q = mcΔt
Q = mLF
The Attempt at a Solution
Input energy:
Q5mins = (300)(300) = 90 x 103J
Energy to cool ice from 16°C to 0°C:
Q = (1)(4200)(16) = 67.2 x 103J
Energy to change water to ice:
Q = (1)(335 x 103) = 335 x 103J
Energy to cool ice from 0°C to -6°C:
Q = (1)(2100)(6) = 12.6 x 103J
Total energy required to make the ice:
QT = 67.2 x 103J + 335 x 103J + 12.6 x 103J = 414.8 x 103J
We haven't done any efficiency calculations at all, so I'm not sure of the process. I know (or think I do), the energy supplied by the ice cube maker and the energy required to make the ice cubes, but I'm not sure how to combine the two. My instinct is to divide one by the other, but that gives a very low efficiency rating of ~21%. All the stuff I've found on the intarwebs refers to the Carnot Cycle, is that relevant here?
Thank you to anyone that responds.