Specific heat capacity - heating ice/water

[slaw155]

Homework Statement

A pot on a stove burner contains 10kg of water and an unknown mass of ice at equilibrium at 0degC at time = 0min. During the first 50mins, the mixture remains at 0degC. From 50 to 60mins the temperature increases to 2degC. What is the initial mass of ice? Ignore the heat capacity of the pot. Take specific heat capacity of water to be 4186J/kg/degC and latent heat of water fusion to be 3.3x10^5 J/kg.

Homework Equations

q=mcT and q=mL

The Attempt at a Solution

I tried equating the two 'q' in the above equations with 'm' in mcT being mass of ice added to mass of water, and T there being 2. However this gives me an answer different to the book. Is my approach wrong or am I missing something?

 

[NascentOxygen]

What is your approach to solving this?

 

[slaw155]

What is your approach to solving this?

I went (mass of ice + mass of water) x c x 2 = mass of ice x L. This gives mass of ice in the range of 0.3kg whereas the textbook answer is about 1.4kg.

 

[haruspex]

I went (mass of ice + mass of water) x c x 2 = mass of ice x L. This gives mass of ice in the range of 0.3kg whereas the textbook answer is about 1.4kg.

What about the time taken in each stage?

 

[slaw155]

What about the time taken in each stage?

How would we take into account the time of each stage? Melting takes 50mins and the heating to raise temp by 2degC takes 10mins.

 

[NascentOxygen]

How would we take into account the time of each stage? Melting takes 50mins and the heating to raise temp by 2degC takes 10mins.

The heat source is adding heat to the pot's contents at a constant rate.

 

[slaw155]

Forgot to quote

 

[slaw155]

The heat source is adding heat to the pot's contents at a constant rate.

Thanks