How much water to melt ice at 0 degC with water at 5 degC ?

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In summary: Therefore, the problem is asking for the minimum amount of water needed to reach this temperature of 0°C when all the ice has melted.In summary, the amount of water needed to melt ice at 0 degC with water at 5 degC is 16 kg, based on the heat required to melt 1kg of ice and the heat provided by water at 5 degC. The assumption is that the final temperature will be 0°C when all the ice has melted.
  • #1
www123
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how much water to melt ice at 0 degC with water at 5 degC ?

If heat required to melt 1kg of ice is equal to: 334 kJ

and water at 5 degC provides: 4.2KJ/kg/degC * 5degC = 21 kJ/kg,

then the amount of water needed to melt ice is qual to:
334 kJ / 21 kJ/kg = 16 kg

Is this correct?

Thanks for your replies!
 
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  • #2


If you stick a chunk of ice at 0 deg. in a bunch of water at 5 deg, won't they come into thermal equilibrium at some temperature in between those two extremes? I.e. the water will cool and ice will heat. So, I guess what I'm trying to say is that I don't know if the assumption that the temperature change of the liquid water will be 5 deg C is true. It will probably be less than that.
 
  • #3


I assumed that the needed heat is equal to 334 kJ, because this would give me a phase change, but no temperature rise of the ice (or melted water from the ice).. i.e. I want to calculate the minimum amount of water needed to melt the ice and not more that would result in a temperature rise.. so, temperature of thermal equilibrium should be 0 degC (I assume no heat losses to the surroundings during melting).. if I had more water than the minimum amount, then you are right, but I want water usage, so the minimum amount..
 
  • #4


www123 said:
If heat required to melt 1kg of ice is equal to: 334 kJ

and water at 5 degC provides: 4.2KJ/kg/degC * 5degC = 21 kJ/kg,

then the amount of water needed to melt ice is qual to:
334 kJ / 21 kJ/kg = 16 kg

Is this correct?

Thanks for your replies!
Correct!
cepheid said:
If you stick a chunk of ice at 0 deg. in a bunch of water at 5 deg, won't they come into thermal equilibrium at some temperature in between those two extremes?
Incorrect. You are ignoring water's (rather high) heat of fusion, which is the entire point of the problem.
 
  • #5


Thanks for replies!
 
  • #6


The above is correct only if the ice is at zero degrees centigrade before adding the warmer water...
 
  • #7


cepheid said:
If you stick a chunk of ice at 0 deg. in a bunch of water at 5 deg, won't they come into thermal equilibrium at some temperature in between those two extremes? I.e. the water will cool and ice will heat. So, I guess what I'm trying to say is that I don't know if the assumption that the temperature change of the liquid water will be 5 deg C is true. It will probably be less than that.
Ice doesn't get warmer than 0C. So either the water cools to 0C and only some of the ice melts or the ice completely melts and then they reach an equilibrium somewhere between 0 and 5C. And what the problem is asking is what amount of water is required for that equilibrium temp with all the ice melted to be 0C.
 
  • #8


Naty1 said:
The above is correct only if the ice is at zero degrees centigrade before adding the warmer water...
...which is stated in the title of the thread.
 
  • #9


russ_watters said:
Ice doesn't get warmer than 0C. So either the water cools to 0C and only some of the ice melts or the ice completely melts and then they reach an equilibrium somewhere between 0 and 5C.

Yeah, yeah, I meant after the ice completely melted, I was just being sloppy.

russ_watters said:
And what the problem is asking is what amount of water is required for that equilibrium temp with all the ice melted to be 0C.

Where does it say in the problem that the final temp should be zero C? You are just assuming that the problem is asking for "just enough water to provide just enough energy to melt all the ice but not heat it any further."
 
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  • #10


cepheid said:
Yeah, yeah, I meant after the ice completely melted, I was just being sloppy.



Where does it say in the problem that the final temp should be zero C? You are just assuming that the problem is asking for "just enough water to provide just enough energy to melt all the ice but not heat it any further."

Because exactly when all of the ice has melted, the temperature will be be 0°C
 

1. How much water is needed to melt ice at 0 degC with water at 5 degC?

The amount of water needed to melt ice at 0 degC with water at 5 degC depends on the mass of the ice and the specific heat capacity of water. The equation Q = m * c * ΔT can be used, where Q is the amount of heat energy required to melt the ice, m is the mass of the ice, c is the specific heat capacity of water, and ΔT is the temperature difference between the ice and water.

2. What is the specific heat capacity of water?

The specific heat capacity of water is the amount of heat energy required to raise the temperature of 1 gram of water by 1 degree Celsius. It is approximately 4.186 joules per gram per degree Celsius.

3. Can the temperature of the water affect the amount of water needed to melt ice?

Yes, the temperature of the water can affect the amount of water needed to melt ice. Warmer water will require less energy to reach 0 degC, while colder water will require more energy. This means that less water will be needed to melt the ice if the initial water temperature is higher.

4. Is it possible to melt ice at 0 degC with water at a temperature higher than 5 degC?

Yes, it is possible to melt ice at 0 degC with water at a temperature higher than 5 degC. The amount of water needed will depend on the initial temperature of the water and the amount of ice that needs to be melted.

5. What other factors can affect the amount of water needed to melt ice?

In addition to the mass of the ice and the specific heat capacity of water, other factors that can affect the amount of water needed to melt ice include the atmospheric pressure, the purity of the water, and the efficiency of the heating method used.

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