Find amount of water at 20 degrees to melt 100 g ice

[vtl]

This an extra voluntary question on a physics assignment I've already handed in. But I still want to try and figure it out so here goes:

Homework Statement

This is what I'm told: "You take 100 g ice cubes from the freezer. The ice cubes' temperature is -18°C." The specific heat capacity of ice is 2,0 kJ/kg*K.

And then asked: "How big an amount of water at 20°C is required to melt the ice cubes from the freezer?"

Homework Equations

Q_water = cmΔT
Q_ice = mL

c_water*m_water*∆T_water+m_ice*L_melt+c_water*m_ice*∆T_ice=0

The Attempt at a Solution

I assume I need to find L, because in the examples in the book the L's used are for materials at either 0°C or 100°C, which I've isolated:

-L_melt=(c_water*m_water*∆T_water)/(-m_is )+(c_water*m_ice*∆T_ice)/(-m_ice )

The problem is that I also don't know m_water because that's what the problem asks me to find. Will any amount of 20°C hot water melt the ice cubes eventually or something?

 

[haruspex]

You don't mention the water temperature in the problem statement. That's needed. You mention 20C later - is that given, or a number out of the air?

in the examples in the book the L's used are for materials at either 0°C or 100°C

What temperature do you think the ice will be at just before it melts?

 

[vtl]

That's because there are three questions attached to the problem statement. 20 degrees is the temperature of the water you use to melt the ice.

0 and 100 degrees is not related to the temperature of the ice, but of the water used to melt the ice.Edit: forgot to mention the 20 degrees when I translated the problem.

 

[haruspex]

0 and 100 degrees is not related to the temperature of the ice, but of the water used to melt the ice.

Then I don't understand what that has to do with L. You wrote

in the examples in the book the L's used are for materials at either 0°C or 100°C

L stands for latent heat, right? The latent heat of fusion of ice is nothing to do with the temperature of the water used to melt it. It's a constant which you can just plug in.