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

[www123]

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!

 

[cepheid]

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.

 

[www123]

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..

 

[D H]

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!

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.

 

[www123]

Thanks for replies!

 

[Naty1]

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

 

[russ_watters]

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.

 

[russ_watters]

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.

 

[cepheid]

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.

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."

 

[phhasek]

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