How much heat is required to melt 2.4kg of ice at 0 degrees Celsius?

So here's what I did:
Q=mct
= 4200x2.4x(100-0) I assumed the ice was at 100 but I'm pretty sure you're not allowed to do that.

Q=mlf
1008000=2.4Lf

So I ended up getting the wrong answer, I'd appreciate help!

Oh I'm dumb, I don't know why I would assume ice is at 100. But even if you assume it's at 0 my method still doesn't work

Heat of fusion of water (water to ice transition) is

3,340,000 Joules/kilogram
so
2.4 * 3,340,000 Joules

The mixture stays at 0 degrees centigrade until the ice is all melted. That is how ice works in your cold drink.

To calculate the amount of heat required to melt the ice, you need to use the specific heat capacity and latent heat of fusion of water.

The specific heat capacity (c) is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius per unit mass. For water, the specific heat capacity is approximately 4200 J/kg°C.

The latent heat of fusion (Lf) is the amount of heat energy required to change a substance from solid to liquid state without any change in temperature. For water, the latent heat of fusion is approximately 333,500 J/kg.

To find the total heat required to melt the ice, you need to consider two stages:

1. Heating the ice from 0°C to its melting point:
In this stage, you can use the formula Q = mcΔT, where Q is the amount of heat energy, m is the mass of the ice, ΔT is the change in temperature, and c is the specific heat capacity of water.

So, for this stage:
Q1 = (2.4 kg) × (4200 J/kg°C) × (0 - 0)
= 0 J (no change in temperature)

2. Melting the ice at its melting point:
In this stage, you can use the formula Q = mLf, where Q is the amount of heat energy, m is the mass of the ice, and Lf is the latent heat of fusion of water.

So, for this stage:
Q2 = (2.4 kg) × (333,500 J/kg)
= 800,400 J

Now, to find the total heat required, you need to add the heat required in both stages:
Q_total = Q1 + Q2
= 0 J + 800,400 J
= 800,400 J

Therefore, the amount of heat required to melt 2.4 kg of ice at 0 degrees Celsius is 800,400 Joules (J).