# Mixing water with steam, find equilibrim

1. May 16, 2015

### sallychan

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

Q= mL

Q= mcΔT

3. 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: May 16, 2015
2. May 16, 2015

### insightful

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

3. May 16, 2015

### sallychan

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

4. May 16, 2015

### insightful

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?

5. May 16, 2015

### sallychan

Theoretically, when water reaches 100C, they become steam?

6. May 16, 2015

### insightful

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

7. May 16, 2015

### sallychan

I think the bubbles will float on the surface of the water..... just guessing

8. May 16, 2015

### insightful

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?

9. May 16, 2015

### sallychan

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?

10. May 16, 2015

### insightful

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

11. May 16, 2015

### sallychan

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!

12. May 16, 2015

### insightful

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.

13. May 16, 2015

### sallychan

So the steam will always condense when in contact with water in lower temperature?

14. May 16, 2015

### insightful

You got it.

15. May 16, 2015

### sallychan

Okay Thank you very much!!!!