Finding the final temperature of mixed ice and steam

In summary, the ice needs 21344J to reach 100 degrees, steam releases 416J when it becomes 100 degrees, and steam needs 15g to condense to release the rest of the energy needed to bring the ice up to 100 degrees.
  • #1
kiro484
21
0

Homework Statement


Suppose that 20.0g of steam at 110°C is mixed with 25.0g of ice at -40°C What will the final temperature be?

Ice - Specific heat capacity 2.10 J/g°C
Water - Specific heat capacity 4.19 J/g°C
Water - Latent heat of fusion 334 J/g
Water - Latent heat of vaporization 2268 J/g
Steam - Specific heat capacity 2.08 J/g°C


Homework Equations


Q=mcΔt
Q=mH

The Attempt at a Solution


Heat loss (steam) = Heat gain (ice)
mcΔt+mH+mcΔt = mcΔt+mH+mcΔt
(20g)(2.08J/g°C)(10°C)+(20g)(2268J/g)+(20g)(4.19J/g°C)(100-t) = (25g)(2.1T/g°C)(40°C)+(25g)(334J/g)+(25g)(4.19J/g°C)(t-0)
416J+45360J+83.8J/°C(100-t) = 2100J+8350J+104.75J/°C(t-0)
Combining like terms
45776J+83.8J/°C(100-t) = 10450J + 104.75J/°C(t-0)
35326J+83.8J/°C(100-t) = 104.75J/°C(t-0)
35326J+8380J/°C-83.8J/°Ct = 104.75J/°Ct
35326J+8380J/°C = 188.55J/°Ct
187.356139(1/°C)+44.444444444444444444444444444444 = t
231.8005834°C = t
232°C = t

Any help would be greatly appreciated, thanks in advance.
 
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  • #2
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  • #3
It ends in 2 different states. But I don't know how to show any of the work needed to show this. Am I supposed to say that only (for example, not the actual values) that only 15g of steam condenses? What about the other 5g? Does it stay at 110 degrees? It can't do that because then you have 2 different temperatures. This is what I don't understand, and I've asked many times hoping more people will be able to help me.
 
  • #4
I wrote in your other thread that
The ice can not condense all steam. Steam and water coexist at the boiling point of water.
Do you understand what it means? ehild
 
  • #5
Ok so that means they both have to be at 100 degrees. All the steam cooling to that temperature releases 416J of heat. The ice needs 21344J to reach 100 degrees. Where would the rest of this energy come from? Some of the steam condensing? How much of the steam would be needed to provide that heat?
 
  • #6
kiro484 said:
Ok so that means they both have to be at 100 degrees. All the steam cooling to that temperature releases 416J of heat. The ice needs 21344J to reach 100 degrees. Where would the rest of this energy come from? Some of the steam condensing? How much of the steam would be needed to provide that heat?

It is some steam condensing. So use t=100 in your equation, but when multiplying the latent heat of evaporation with the mass x instead of 20 g.

ehild
 
  • #7
Could I do this? This is using the values of ice needing 21344J to reach 100 degrees and steam releasing 416J when becoming 100 degrees.
21344-416=20928J needed to get all the ice to 100 degrees.
Q=mH
m=Q/H
m=20928J/2268J/g
m=9.22751323g
So that is the mass of steam needed to condense to release the rest of the energy needed to bring the ice up to 100 degrees.
 
Last edited:
  • #8
kiro484 said:
Could I do this? This is using the values of ice needing 21344J to reach 100 degrees and steam releasing 416J when becoming 100 degrees.
21344-416=20928J needed to get all the ice to 100 degrees.
Q=mH
m=Q/H
m=20928J/2268J/g
m=9.22751323g
So that is the mass of steam needed to condense to release the rest of the energy needed to bring the ice up to 100 degrees.

Yes, you can do it.

Do not use so many digits in the end result. ehild
 
  • #9
Yeah you have to round off to the amount of significant digits of the original values given in the question, correct?
 
  • #10
kiro484 said:
Yeah you have to round off to the amount of significant digits of the original values given in the question, correct?

Yes. To three digits.

ehild
 
  • #11
Ok thank you so so much for all the help. Sorry for creating a billion threads trying to find more help, yours is all I needed.
 

What is the formula for finding the final temperature of mixed ice and steam?

The formula for finding the final temperature of mixed ice and steam is Tf = (mi * Ti + ms * Ts) / (mi + ms), where Tf is the final temperature, mi is the mass of ice, Ti is the initial temperature of ice, ms is the mass of steam, and Ts is the initial temperature of steam.

How do you determine the initial temperatures of ice and steam in the formula?

The initial temperatures of ice and steam can be determined through experimentation or by using a thermometer. The initial temperature of ice will typically be 0 degrees Celsius, while the initial temperature of steam will depend on the pressure and volume of the steam.

Can the formula be used for any amount of ice and steam?

Yes, the formula can be used for any amount of ice and steam as long as the units are consistent (e.g. mass in grams, temperature in degrees Celsius).

Why is it important to use the mass of ice and steam in the formula?

The mass of ice and steam is important because it determines the amount of heat energy that is needed to raise the temperature of the mixture. This information is crucial in finding the final temperature of the mixture.

Are there any other factors to consider when finding the final temperature of mixed ice and steam?

Yes, there are other factors that can affect the final temperature such as the rate of heat transfer, the specific heat capacities of ice and steam, and any external factors that may influence the temperature of the mixture. These factors should be taken into account when conducting the experiment or calculation.

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