# Water and Ice heat transfer equilibrium

• merbear
In summary, the content of the glass after equilibrium has been reached is a combination of water and ice at a certain temperature. The mass of water and ice can be determined by setting up a series of equations, including the equation Q=mL for the latent heat of fusion. However, it is important to first determine if there is enough heat in the water to melt all of the ice, and then continue with the appropriate case to solve for the unknowns.
merbear

## Homework Statement

A 300 cm3 glass is filled with 120 g of ice at 0°C and 210 g of water at 25°C.

(a) Characterize the content of the glass after equilibrium has been reached. Neglect heat transfer to and from the environment.

Find:
mass of water?
mass of ice?
equilibrium temperature?

## Homework Equations

Q=mL

delta Q1 + delta Q2 + delta Q3 = 0

delta q= 0 (for the system)

## The Attempt at a Solution

I don't know how to solve for the latent heat of fusion, so I tried to set up a series of equations from which I would be able to substitute to solve for the unknowns. I ended up with too many variables and not able to isolate them to solve for values. Since the latent heat of fusion is the heat flow necessary to bring about a phase change, I assumed that Q=mL would be a necessary equation, but I can't figure out how to implement the equation to get values. Any help on starting this problem would be appreciated!

Thank-you!

First find out whether there is enough heat in the water to melt all of the ice.

Heat reqd to melt ice = m1*L. Heat given up by water to come down to 0 C = m2*c*(25 -0).

Case 1.
If the whole ice cannot melt, find how much would melt. The resulting temp is obvious.

Case 2.
If the whole ice does melt, then the water from the ice is at 0 C will heat up to temp t, say. Then it becomes a straight forward heat exchange problem.

## 1. What is the principle of heat transfer between water and ice?

The principle of heat transfer between water and ice is based on the second law of thermodynamics, which states that heat always flows from a higher temperature to a lower temperature until equilibrium is reached. In the case of water and ice, heat is transferred from the warmer water to the colder ice until both reach the same temperature.

## 2. How does the temperature of water and ice change during heat transfer?

During heat transfer, the temperature of the water decreases while the temperature of the ice increases. This is due to the fact that heat is being transferred from the water to the ice, causing the water to lose heat and the ice to gain heat.

## 3. What factors affect the rate of heat transfer between water and ice?

The rate of heat transfer between water and ice is affected by several factors, including the temperature difference between the water and the ice, the surface area and volume of the water and ice, and the thermal conductivity of the materials.

## 4. Can heat transfer between water and ice be reversed?

Yes, heat transfer between water and ice can be reversed. If the temperature of the surrounding environment is lowered, the heat will flow from the ice back to the water, causing the ice to cool and the water to warm until they reach equilibrium again.

## 5. How is the heat transfer between water and ice used in everyday life?

The principle of heat transfer between water and ice is used in many everyday applications, such as refrigerators and air conditioners. These devices use the transfer of heat from the inside to the outside to cool the air or keep food and drinks cold. It is also used in cooking, as heat is transferred from the stove to the pot of water, causing it to boil and cook the food inside.

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