Physics question

[rozmaaate]

here's the question I am stuck on

0.50 kg of ice at 0°C is mixed with 0.10 kg of steam at 100°C. What will be the final temperature? (5 marks)


thanks in advance:))))

[Erutepa]

here's the question I am stuck on

0.50 kg of ice at 0°C is mixed with 0.10 kg of steam at 100°C. What will be the final temperature? (5 marks)


thanks in advance:))))

Hi rozmaaate!

Upon this ice and steam mixing, the system will move towards, and reach a state of equilibrium where the energy gained by the ice is going to be equal to the energy lost by the steam.
Its important to realise that becuase there is ice and steam involved, there the latent heat of fustion/vapourisation will be involved in calculations - you can't just consider the specific heat capacity of water. The steam will lose energy as it transforms into liquid water, and then will lose energy as it reaches an equilibrium point, while the ice will gain energy as it transforms into liquid water and will continue to gain energy as it reaches this equilibrium point. As such, our equations will be combining the calculation for the energy needed to change states and the energy needed to change temperature.

So now lets set up seperate equations to show the change in energy for the steam and the ice
Equation 1) As the steam transforms into water and reaches a point of equilibrium:

notice the negative in the above equation - this is becuase water is loosing energy so we want our change in energy to be a negative.

Equation 2) As the ice transforms into water and reaches a point of equilibrium:


Now we can combine them to calculate the final temperature.
One way to think about this is that the total energy of the system doesnt change, so the sum of the energy lost by the steam and the energy gained by the ice will be zero:




Another way to think about this is that the energy lost by the steam is equal to the energy gained by the ice. For this we equate the magnitude of the two changes in energy:

(Notice the negative applied to the LHS  - this is to make the LHS a positve value as what we are actually doing is equating the magnitude of energy lost to the magnitude of energy gained).
You will notice that both of these above combined equations are actually the same, but in slightly differnet forms.
From here you will substitute the values for m, c, and L. What will be left is an equation with the two unknowns:
We can re-write this as: where we know the initial temperature (which we can substitute in) after doing this, you will be left with an equation with only one unknown (Tf) which you can now solve for to obtain the final temp.

Hopefully this helps you get the answer, but if I haven’t explained something very well or if there’s something here that you still don’t understand, feel free to bring it  up and I (or someone else) can have another go at clarifying it .
As a little side note, you have posted a couple questions by creating new topics in the VCE physics board, but you might want to post future question in the dedicated VCE physics thread here. This might help with people seeing your questions and will help with keeping all the physics questions in one place .