# Homework Help: Highschool Question on Thermal Equilibrium

1. Jul 11, 2012

### chris1

Hi guys,
I'm having a bit of trouble with following thermal equilibrium question...

1. The problem statement, all variables and given/known data

Create an equation representing energy transfers of thermal energy equilibrium, that will enable one to determine the latent heat of fusion for ice.

One conducts an experiment mixing ice and water in a jug, recording the changes in mass and temperature:

The mass of the ice used ( m$_{i}$ ) = 0.10kg

The initial temperature of the ice ( T$_{i}$ ) = -15°C

The initial mass of the water ( m$_{w}$ ) = 0.45kg

The initial temperature of the water ( T$_{w}$ ) = 23°C

Final Temperature of mixture ( T$_{f}$ ) = 16°C

Specific heat capacity of water ( c$_{w}$ ) = 4.2 kJ kg$^{-1}$°C$^{-1}$

Specific heat capacity of ice ( c$_{i}$ ) = 2.1 kJ kg$^{-1}$°C$^{-1}$

So one must set up an equation of thermal equilibrium, that will allow for the value for the latent heat of fusion of ice (l) can be determined.

2. Relevant equations
c = $\frac{Q}{mΔT}$

For changes of state:
Q = ml

3. The attempt at a solution

Here is my attempt of working it out:

(m$_{i}$ * c$_{i}$ * 15°C) + (m$_{i}$ * l) + (m$_{i+w}$ * c$_{w}$ * 16°C) = (m$_{i+w}$ * c$_{w}$ * 7°C)

I know my solution isn't correct due to cancelling of terms but I dont know what to do to fix it. The answer isn't in the text book either.

Thanks for the feedback guys

Last edited: Jul 11, 2012
2. Jul 11, 2012

### mukundpa

heat absorbed by ice and the water due to fusion of ice will be

(mi * ci * 15°C) + (mi * l) + (mi * cw * 16°C)

and heat given up by initially hot water will be

(mw * cw * 7°C)

3. Jul 11, 2012

### chris1

So would that mean:

(mi * ci * 15°C) + (mi * l) + (mi * cw * 16°C) = (mw * cw * 7°C)

But wouldn't the mass on the right side of the equation be constantly changing as the ice melts, or is that irrelevant ?

4. Jul 11, 2012

### Staff: Mentor

Imagine that the material comprising the original mass of the ice, and the mass comprising the original mass of the water are kept separate from one another by a thin invisible membrane. Both masses are allowed to thermally equilibrate with one another. Afterwards the membrane is removed.