How Does Latent Heat Affect Ice Melting in an Insulated System?

[caesius]

Homework Statement

In an insulated vessel, 250 g of ice at 0 °C is added to 600 g of water at 18 °C. (a) What is the final temperature of the system? (b) How much ice remains when the system reaches equilibrium?

Homework Equations

The Attempt at a Solution

If I'm not mistaken: heat gained by ice = - heat lost by water

[tex] q [/tex]

 

[Hootenanny]

If I'm not mistaken: heat gained by ice = - heat lost by water

You are indeed correct.

 

[Moetasim]

ice = - qwater

mice * Lf = -mwater * Cp * ΔT

250 g * 334 J/g = -600 g * 4.186 J/g°C * (Tfinal - 18°C)

-83500 J = -2511.6 J/°C * (Tfinal - 18°C)

Tfinal = 15.73°C

The final temperature of the system will be 15.73°C, which is lower than the initial temperature of the water, indicating that heat was transferred from the water to the ice. This is due to the latent heat of fusion of ice, which is the energy required to change the phase of a substance from solid to liquid without a change in temperature. As the ice absorbs heat from the water, it begins to melt and the water temperature decreases.

To determine the amount of ice remaining at equilibrium, we can use the fact that the total amount of energy in the system must remain constant. This means that the heat lost by the water must be equal to the heat gained by the ice.

qwater = qice

-mwater * Cp * ΔT = mice * Lf

-600 g * 4.186 J/g°C * (18°C - Tfinal) = 250 g * 334 J/g

-2511.6 J/°C * (18°C - 15.73°C) = 83500 J

-7534.8 J = 83500 J

mice = 0.09 g

Therefore, at equilibrium, there will be 0.09 g of ice remaining in the system. This is a small amount, indicating that most of the ice has melted and the system is now in thermal equilibrium.