You are asked to mix equal masses of of ice and steam at 0.00°C and 100.00°C respectively, What will the final temperature of the mixture be? The mixture is in a perfect insulator.
ms=mass of steam
mi=mass of ice
LHV,s=Heat of vaporization of steam=2257J/g
LHF,i=Heat of fusion of ice=334J/g
2. Relevant equations
3. The attempt at a solution
I am fairly confident that my thought process is correct. I just keep making algebra mistakes(I assume) but I can’t find what my error is. Please let me know where my process breaks down please.
I did this in 3 parts
So first I consider the situation.
Since the mixture is in a perfect insulator, that means no heat is lost to the surroundings.
That means that the heat lost by the steam is gained by the ice. Q for the steam will be negative since it is losing heat.
From here, the Qlost is given by the sum of energy used to turn steam into water, then to bring the steam-turned-water to thermal equilibrium
and Qgained is given by the sum of energy used to melt the ice, then to bring the ice-turned-water to thermal equilibrium.
Again, since there is no heat lost to the surroundings, and the mixture is allowed to reach thermal equilibrium then…
Now we plug in to be able to solve for Teq
Moving all terms containing Teq to one side
Factor out Teq
and finally solving for Teq results in
We can do one more thing, since the masses are equal, we can factor out the mass.
Plug in known values
Teq=552K Obviously incorrect
Please let me know where I am making my mistake. I seperated my work into 3 parts to make it easier to point out where i made an error. Thank you I have a test on Friday I NEEEEEED to understand how to do this properly. Thank you