How Can Hot Water Turn Ice to Water?

[Kyoma]

Homework Statement

Question 1: Hot water at 100 degrees is added to 5 g of ice at 0 degrees. What is the minimum mass of hot water needed to melt all the ice? (Specific latent heat of fusion of ice = 336Jg^-1, specific heat capacity of water is 4.2Jg^-1K^-1)

2. The attempt at a solution

Question 1:
mc$$\Delta$$$$\theta$$ = m(latent fusion)
m$$\Delta\theta$$ = 400
And then I have a doubt: How can the hot water's temperature decrease from 100 degrees to 0 degrees? ($$\Delta\theta$$ = 100 - 0)

 

[Onamor]

$$\Delta\theta$$

what does this mean?

 

[Kyoma]

Change in temperature.

 

[Jobrag]

Think about it this way.
What is the starting temperature of my hot water? 100
What is the final temperature of my "hot" water? 0
What is the change in temperature? 100-0
Delta T is 100

 

[Astronuc]

The questions asks for "the minimum mass of hot water to melt ice". So all of the heat must go into the ice to melt it. The melting temperature of water/ice is 0°C.