Calculating Max Ice Production Rate Given kW Input and Temperature Conditions

[eku_girl83]

Here's my problem:
For each kW of power input to an icemaker at steady state, determine the maximum rate that ice can be produced in kg/h, from liquid water at 0 C. Assume that 333 kJ/kg of energy must be removed by heat transfer to freeze water at 0 C, and that the surroundings are at 20 C.

I know that W = 1 kw, Tc = 0C=273 K, Th = 20C=293 K.
Since the device operates at steady state, W = Qh - Qc.
I also know that W/Qh is less than or equal to (1- Tc/Th)

Could someone give me a hint on where to start with this one? What is the 333 kJ/kg?

Thanks!

 

[CartoonKid]

The answer is $$14.76kgh^{-1}$$, is it?

My working is as follow:
$$Q_c=mL_f=m(333\times10^3)$$
$$\frac{Q_c}{Q_h}=\frac{T_c}{T_h}$$
$$\Rightarrow Q_h=m(357.4\times10^3)$$
$$W=Q_h-Q_c=m(24.4\times10^3)$$
$$1\times10^3=\frac{m(24.4\times10^3)}{t}$$
$$\frac{m}{t}=40.98\times10^{-3}kgs^{-1}=147.54kgh^{-1}$$

 

[wais]

To calculate the maximum rate of ice production, we can use the following formula:

Maximum ice production rate = (W/Qh) * 3600

Where:
W = power input in kW
Qh = heat transfer rate in kW
3600 = conversion factor from seconds to hours

To find Qh, we can use the formula:

Qh = W * (1 - Tc/Th)

Where:
Tc = temperature of the water being frozen (0°C = 273 K)
Th = temperature of the surroundings (20°C = 293 K)

Now, we need to find the heat transfer rate (Qh) in kW. To do this, we need to know the amount of energy required to freeze 1 kg of water at 0°C. This is given as 333 kJ/kg. This means that for every 1 kg of water frozen, 333 kJ of energy is removed.

To find Qh, we need to convert 333 kJ/kg to kW. We can do this by dividing by the conversion factor of 3600 seconds (since 1 hour = 3600 seconds).

So, Qh = (333 kJ/kg) / (3600 seconds) = 0.0925 kW

Now, we can plug in the values into the formula for maximum ice production rate:

Maximum ice production rate = (W/Qh) * 3600 = (1 kW / 0.0925 kW) * 3600 = 38756.76 kg/h

Therefore, for every 1 kW of power input, the maximum rate of ice production from liquid water at 0°C is 38756.76 kg/h.