# How Do You Calculate the Final Temperature in a Mixed Water and Ice System?

• jdstokes
In summary, this conversation is discussing a problem involving an insulated container with water and ice at different temperatures. The goal is to find the final temperature of the system after the ice and water reach equilibrium. In order to calculate the final temperature, the phases present at equilibrium need to be known. The specific heat of water and ice, as well as the heat of fusion of ice, are necessary to determine the phases present and the final temperature. Calculations involving the heat transfers and specific heats of water and ice can determine whether all the ice melts or not, and if so, the final temperature of the system.
jdstokes
I'm a conceptual difficulty with this simple problem

In an insulated container, 0.800 kg of water at 40.0 degrees centigrade is mixed with 0.500 kg of ice at -15.0 degrees centigrade. Find the final temperature $T_\mathrm{f}$ of the system. The freezing point of water is 0 degrees centigrade.

I need to know the phases present at equilibrium in order to calculate the final temperature, but these are not given.

Just out of curiosity, how do you determine the final temp. if you know the phases present at equilibrium?

You set the sum of the heat transfers equal to zero and solve the resulting equation for the final temperature $T_\mathrm{f}$.

Last edited:
jd.stokes,

Do you know the specific heat of water and ice and the heat of fusion of ice? I think with those, you can find out whether all the ice melts or not. Without them, I don't think you can.

Edit: Ok, I Googled: heat of fusion of ice. One nice site gave me all three values. Unfortunately it looks like there's plenty of enthalpy in the water to melt all the ice, and then some. So it's not just T = 0 But it's not hard.

Last edited:
Certainly you need to know the specific heat of water and ice (it seems odd that the problem would tell you an obvious point (that the melting point of ice is 0) but not tell you the specific heats and heat of fusion (also called "heat of melting"):

What heat does the water give up in going from 40 degrees to 0?
What heat is required to bring the ice from -15 degrees to 0?
(You get those from the specific heats of water and ice.)

If the heat the water gave up was greater than the heat required to raise the temperature of the ice to 0, then at least some of the ice is melted.

How much heat is required to melt all the ice?
(You need the heat of fusion for that.)

If that is more than the heat left after raising the temperature of the ice, then some ice remains. The final temperature would be 0 C.

If that is less than the heat left after raising the termperature of the ice, then all the ice melts and the amount of heat still left now raises the temperature of the total 1.3 kg of water.

## What is simple thermal physics?

Simple thermal physics is the study of the behavior of heat and energy in systems. It involves understanding the transfer of heat and the changes in temperature within a system.

## What are some common problems in simple thermal physics?

Some common problems in simple thermal physics include calculating the final temperature of a system after two objects with different temperatures are brought into thermal contact, determining the amount of heat required to change the temperature of a substance, and finding the efficiency of a heat engine.

## What are the basic principles of simple thermal physics?

The basic principles of simple thermal physics include the first and second laws of thermodynamics, the concept of thermal equilibrium, and the relationship between temperature and heat energy.

## How is simple thermal physics used in real life?

Simple thermal physics is used in many practical applications, such as designing heating and cooling systems for buildings, understanding the efficiency of engines and power plants, and developing insulation materials for better energy conservation.

## What are some common misconceptions about simple thermal physics?

One common misconception about simple thermal physics is that heat and temperature are the same thing. Heat is a form of energy while temperature is a measure of the average kinetic energy of particles in a system. Another misconception is that heat always flows from hot to cold, when in reality it can flow in either direction depending on the difference in temperature between two objects.

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