# Mixing water with steam, find equilibrim

• sallychan
In summary, when 100 g of steam at 100 °C is mixed with 500 g of water at 25 °C, the steam will condense into the water until they reach equilibrium at a final temperature. This happens because the water is colder than the steam, allowing for heat exchange through direct contact condensation. The final temperature will be somewhere between 25 °C and 100 °C, depending on the amount of steam that condenses into the water.
sallychan

## Homework Statement

100 g of steam at 100 °C is mixed with 500 g of water at 25 °C. What is the final temperature of the mixture?

Q= mL

Q= mcΔT

## The Attempt at a Solution

Heat given by to water = heat loss at condensation
= mLv
= (0.1) (2.26 E 6)
= 226000 J

Maximum possible heat water can take = mc ΔT
= (0.5) (4186)(100-25)
= 156975 J

Because water does not take up all the latent heat from steam, only some of the steam condensate.

I wonder is my conclusion right? Or will latent heat given by steam actually boils water?

Thanks!

Last edited:
Your conclusions are correct. Congratulations for having the intuition that 100degC is the maximum temperature possible.

But how am I going to find the final temperature if all water is boiled?

Think about a 500g pot of water with a tube going to the bottom. Through that tube you inject the 100g steam. What will you see after the water reaches 100C?

insightful said:
Think about a 500g pot of water with a tube going to the bottom. Through that tube you inject the 100g steam. What will you see after the water reaches 100C?
Theoretically, when water reaches 100C, they become steam?

Picture a bubble of 100C steam entering below the surface of 100C water. What happens to that bubble?

insightful said:
Picture a bubble of 100C steam entering below the surface of 100C water. What happens to that bubble?
I think the bubbles will float on the surface of the water... just guessing

Good guess! So the bubbles come off the surface carrying the same amount of water that came into the pot with the steam. How much of the water (liquid) phase leaves the pot?

insightful said:
Good guess! So the bubbles come off the surface carrying the same amount of water that came into the pot with the steam. How much of the water (liquid) phase leaves the pot?
Oh so you are saying that the steam will condensate? If that is the case, the total amount of water will become 500g + 100g = 600 g.
But how does that happen? Isn't it water does not remove enough latent heat from the steam?

Well, no. For the steam to condense, the water must be colder than the steam. Think about it for a while.

insightful said:
Well, no. For the steam to condense, the water must be colder than the steam. Think about it for a while.
Oh right. I understand.
But can you explain a bit more on the heat exchange of condensation? I really want to fully understand it.
Thanks a lot!

Your problem is called direct contact condensation. As you have realized, the hot steam will condense into the cold water until there is no temperature difference. You have reached equilibrium between the steam and the water at that point. That's really all there is to it.

insightful said:
Your problem is called direct contact condensation. As you have realized, the hot steam will condense into the cold water until there is no temperature difference. You have reached equilibrium between the steam and the water at that point. That's really all there is to it.
So the steam will always condense when in contact with water in lower temperature?

You got it.

insightful said:
You got it.
Okay Thank you very much!

## What happens when you mix water with steam?

When you mix water with steam, the steam will condense into liquid water. This process releases a significant amount of energy, which can be harnessed for various purposes.

## What is the equilibrium point between water and steam?

The equilibrium point between water and steam is the point at which the amount of water and steam in a system remains constant. This is also known as the saturation point.

## How does pressure affect the equilibrium between water and steam?

The pressure of a system affects the equilibrium between water and steam. At higher pressures, the equilibrium point will shift towards more steam, while at lower pressures, the equilibrium point will shift towards more liquid water.

## Can you reverse the process of mixing water and steam to separate them?

Yes, the process of mixing water and steam can be reversed through a process called vaporization. This involves heating the mixture to its boiling point, causing the steam to evaporate and separate from the water.

## What are some practical uses of mixing water with steam?

Mixing water with steam has several practical uses, including power generation, heating systems, and industrial processes such as sterilization and cooking. The energy released during the condensation process can also be used for propulsion in steam engines.

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