# Heat exchange in an isolated system

• Ian Baughman
In summary, the problem involves mixing equal amounts of ice at 0°C and steam at 100°C in a container with no heat exchange with the surroundings. The equilibrium temperature of the system is unknown, and the fractions of weights of ice, water, and steam are also unknown. The solution process involves calculating the heat required to melt the ice and condense the steam, and then considering the change in mass of the resulting water and steam. Ultimately, the goal is to determine the heat required to melt all the ice and raise the temperature of the water produced to 100°C.
Ian Baughman

## Homework Statement

In a container of negligible mass, equal amounts (in weight) of ice at 0°C and steam at 100°C are mixed at atmospheric pressure. Assuming no heat exchange with the surroundings, what is the temperature when the system reaches equilibrium? What are the fractions of weights of ice, water, and steam?

Q = mCΔT
Q = mLf
Q = mLv

## The Attempt at a Solution

1) First I began by calling the mass M.
2) Then I calculated the heat required to melt the ice since it is already at 0°C:
Q = MLf = M(3.34×105)​
3) Then I did the same but for the steam at 100°C:
Q = MLv = M(2.256×106)​
4) You can see it requires more heat loss to condense the steam versus melt the ice so now we have a solution consisting of just water and steam.
5) This is where I run into trouble. I know we have all the ice (mass M) now in the form of water plus some of the steam that was condensed to water. I assume that the equilibrium temperature is under 100°C therefore the solution would be 100% water but I don't know how to show that or find the equilibrium temperature.

How much heat would it take to melt all the ice and then raise the temperature of the water produced to 100 C?

Chestermiller said:
How much heat would it take to melt all the ice and then raise the temperature of the water produced to 100 C?
That's what I was thinking but since some of the steam has condensed to water I thought I would need to consider the change in mass for both the water and steam.

You do, in a way. Condensing of the steam at 100 C produces more water, and reduces the amount of steam.

## 1. What is a "isolated system" in the context of heat exchange?

An isolated system is a closed system that does not exchange matter or energy with its surroundings. This means that no heat, work, or mass can enter or leave the system, and the total energy of the system remains constant.

## 2. How does heat exchange occur in an isolated system?

In an isolated system, heat exchange occurs through the transfer of thermal energy between objects within the system. This can happen through conduction, convection, or radiation.

## 3. What factors affect heat exchange in an isolated system?

The rate of heat exchange in an isolated system is influenced by several factors, including the temperature difference between objects, the thermal conductivity of the materials, and the surface area available for heat transfer.

## 4. What is the relationship between heat exchange and entropy in an isolated system?

In an isolated system, heat exchange can lead to changes in the system's entropy. As heat flows from hotter objects to colder objects, the entropy of the colder objects increases while the entropy of the hotter objects decreases, leading to an overall increase in the system's entropy.

## 5. Can heat exchange ever be completely prevented in an isolated system?

In theory, it is possible to prevent all heat exchange in an isolated system by ensuring that all objects within the system are at the same temperature. However, in practice, this is nearly impossible to achieve as there will always be some degree of temperature difference and therefore some rate of heat exchange.

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