How much ice melts in water?

  • #1

Homework Statement


Ice at 0°C is added to a 1 kg of lemonade cooling it from 20°C to 0°C. How much ice melts? (The heat capacity of lemonade equals that of water.)


Homework Equations


Q = mcΔT


The Attempt at a Solution


Found the heat in of the lemonade to the ice... = 83.38 kJ and don't know where to go from there. c of water is 4.169.
 

Answers and Replies

  • #2
gneill
Mentor
20,925
2,867

Homework Statement


Ice at 0°C is added to a 1 kg of lemonade cooling it from 20°C to 0°C. How much ice melts? (The heat capacity of lemonade equals that of water.)


Homework Equations


Q = mcΔT


The Attempt at a Solution


Found the heat in of the lemonade to the ice... = 83.38 kJ and don't know where to go from there. c of water is 4.169.

What happens to the ice that melts? What's involved?
 
  • #3
A phase change occurs, but the problem does not give the mass of the ice.
 
  • #4
gneill
Mentor
20,925
2,867
A phase change occurs, but the problem does not give the mass of the ice.

Right. Because it's the mass of ice that melts that you're looking for.... Write out the formula that pertains to that phase change. Which of the variables do you you have values for?
 
  • #6
gneill: Ok, so the formula that pertains to that phase is ΔQ = Lm. I know that L is the latent heat of fusion for water so it is 333 kJ/kg. Would the change in heat be the 3.38 kJ?

Chestermiller: I found the change in heat for the lemonade form 20-0 °C to be 83.38 kJ.
 
  • #8
gneill
Mentor
20,925
2,867
gneill: Ok, so the formula that pertains to that phase is ΔQ = Lm. I know that L is the latent heat of fusion for water so it is 333 kJ/kg. Would the change in heat be the 3.38 kJ?

Chestermiller: I found the change in heat for the lemonade form 20-0 °C to be 83.38 kJ.

Yes. You calculated the heat that needed to be extracted from the lemonade in order to cool it to 0C, and that heat had to go somewhere. Clearly it went to melt some of the ice, providing the heat of fusion for the process.
 
  • #9
21,261
4,720
So if the heat removed from the lemonade was 83.38 kJ, and the amount of heat required to melt 1 kg of ice is 333 kJ/kg, how many kg of ice have to melt?

Chet
 
  • #10
Right, so I got 83.38 kJ/(333 kJl/kg) = .25 kg. So .25 kg. Is this right?
 
  • #12
Great! Thank you Chestermiller and gneill!
 

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