# How much ice melts in water?

## 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.)

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.

gneill
Mentor

## 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.)

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?

A phase change occurs, but the problem does not give the mass of the ice.

gneill
Mentor
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?

Chestermiller
Mentor
How much heat is removed from from the lemonade when it cooled from 20C to 0 C?

Chet

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.

Sorry, i meant the 83.38 kJ

gneill
Mentor
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.

• 1 person
Chestermiller
Mentor
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

Right, so I got 83.38 kJ/(333 kJl/kg) = .25 kg. So .25 kg. Is this right?

Chestermiller
Mentor
Yes.

• 1 person
Great! Thank you Chestermiller and gneill!