- #1

llatosz

- 62

- 9

## 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 the 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?"

I know this question has been asked about 100 times but I've been working on it for over an hour and I just can't get it. I was even the best in my class at Physics 1 and 2. This should be especially easy because the initial conditions are at saturation conditions.

## Homework Equations

[/B]

Q=mL (Where L is latent heat of phase change)

Q=mCΔT

L

_{f}= 3.34*10^5 J/kg (fusion)

L

_{v}= 2.256*10^6 J/kg (vaporization)

C

_{water}= 4186 J/kg/K

## The Attempt at a Solution

[/B]

I assume 1 kg to make the math fun. m

_{ice}= m

_{steam}= m

Heat absorbed by the ice melting is:

Q

_{melt}= mL

_{f}=3.34*10^5 J

Heat released by vapor condensing:

Q

_{cond}= mL

_{v}= 2.256*10^6 J

If the steam melts all of the ice, the excess energy would be the difference between the two:

2.256*10^6 - 3.34*10^5 = 1.931*10^6 J

And the heat required to get all of the 0°C water up to 100°C is:

Q

_{heat up}= mCΔT = 4186 * 100 = 4.186*10^5 J

which is less than the excess steam heat, so the steam should in fact melt all of the ice and turn it to 100°C

Now to find the remaining energy in the steam:

1.931*10^6 - 4.186*10^5 = 1.5124*10^6 JOh wow, while typing this i thought of what to do lol. I will continue in hopes that my line-by-line explanations will help others. Edit: But I do have one question at the end!And the heat required to transform the 100°C hot water to steam would be:

Q=mL

_{v}= 2.256*10^6

And since the remaining energy in the steam is not sufficient enough to transform all the 100°C hot water to steam, we will have the original steam, hot water, and some newly created steam.

So my guess is that the ratio of remaining energy to the energy needed to complete a full phase change will be equal to the ratio of the masses that have changed.

So for this example, the percentage of hot water that turns into steam is

1.5124 / 2.256 = 67%

So we started with:

1) 50% ice... 50% steam

2) 50% water... 50% steam

3) 16.5% water... 83.5% steam

This would be mass percentage, right?

Thank you in advance :)