Question

Finding the equilibrium temperature of a mixture: An isolated thermal system consists of a copper container filled with a quantity of liquid water and a quantity of ice. What is the fully thermalized state of the system (the final temperature, how much water, and how much ice) provided that initially there is 1.0kg of ice at−100◦C, 10.0kg of water at 1◦C, and the copper container has the mass of 15.0kg and is initially at 10◦C? The heat capacities of ice, water, and copper are 2050, 4186, and 385 J/◦C, and the latent heat of ice is 3.33×105J/kg.

Answer 1

DATA:

Solution:

The energy transfered is defined as:

Where;

is the specific heat. (J/kg.ºC)

mass of the substance (kg)

Now, starting with the mixture Water-Ice-copper. We can define:

Here,

and

Replacing equation (3),(4) into equation (2) we have:

Applying equation (1) into equation (5) we have

Isolating we have:

Replacing values given in DATA:

Solving we obtain:

This result means that mass of water (in the fully thermalized state) is frozen. Therefore the mass of ice is:

and the mass of "water" is