Hey. Heres the question i was given:(adsbygoogle = window.adsbygoogle || []).push({});

I am studying year 11 physics, and this is one of the harder questions ive had to face so far. Im going to explain my theory of whats happening as i go along. If Any of my theory is incorrect, PLEASE correct me on it. Im not only doing this to get the answer correct, but to further improve my understanding of heat. 0.22kg of ice at -16 degrees celcius was mixed with 4kg steam at 104 degrees celcius. What is the final temperature of the mixture?

____________________________________

I understand that the steam will condense, and the ice will melt, to produce a final mixture of liquid water. Before the ice and steam changes phase, they must reach 0 degrees and 100 degrees respectively.

I need to calculate the energy it takes for the ice to increase to 0 degrees, and the steam to decrease to 100 degrees, using the Q=mcT formula, and knowing that the specific heat capacity of ice is 2100, and steam is 2000.

[tex]Q_{Ice}=mc\Delta T[/tex]

[tex]=0.22\times 2100\times 16[/tex]

[tex]=7392J[/tex]

Therefore, 7392J of energy is required to increase the temperature of the ice to 0 degrees.

[tex]Q_{Steam}=mc\Delta T[/tex]

[tex]=4\times 2000\times 4[/tex]

[tex]=32000J[/tex]

Therefore, 32kJ of energy is required to cool the steam to 100 degrees.

From what i understand, a hotter substance transfers energy to a cooler substance, so in this case, the steam transfers to the ice. When the ice has recieved 7392J of energy, it is 0 degrees, but the steam isnt yet 100. It still needs to transfer 24608J of energy before it is 100. Since the ice is already at 0 degrees, the extra energy from the steam will begin to cause fusion/melting of the ice. If 24608J of energy is to be used in fusion of ice (latent heat=334000), the following will give how much of the ice melts:

[tex]Q=mL[/tex]

[tex]24608=334000m[/tex]

[tex]m=0.0727kg[/tex]

Therefore, when the steam becomes 100 degrees, 0.0737kg of ice will have melted.

So from what i understand, this is what we currently have:

4kg steam (100 degrees)

0.0737kg water (0 degrees)

0.1463kg ice (0 degrees)

For the final temperature to be calculated, all the substances must be in the same phase. So now i must calculate the energy levels for fusion and condensation to occur. (knowing that the latent heat for vaporization of water is 2250000).

[tex]Q_{Ice}=mL[/tex]

[tex]=0.1463\times 334000[/tex]

[tex]=48864.2J[/tex]

Therefore, 48864.2J of energy is required to completely melt the remaining ice.

[tex]Q_{Steam}=mL[/tex]

[tex]=4\times 2250000[/tex]

[tex]=9000000J[/tex]

Therefore, 9MJ of energy is required to completely condense the steam.

Again, the energy transfers from the steam to the ice. Once the ice recieves 48864.2J of energy, it will be water at 0 degrees celcius. But for the steam to completely condense, it must transfer 8951135.8J more. In doing this, the temperature of the water increases.

[tex]Q=mc\Delta T[/tex]

[tex]8951135.8=0.22\times 4200\times T[/tex]

[tex]T=9687.3764 degrees[/tex]

Therefore, once the steam has reached full condesation, the water will have become 9687.3764 degrees.

Now, from what i know, that is impossible, because water wont exceed 100 degrees without vaporizing. This is where i think ive gone wrong, and i dont know where to go from here.

From here id usually apply a formula to find the final temperature of the 0.22kg water mixed with the 4kg water, but since im pretty sure ive made a mistake, i wont bother going further.

Thank you to anyone who can put me on the right track for this question, or correct me on any of my understandings on what is happening.

Dan.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# What did i do wrong? Am i on the right track?

**Physics Forums | Science Articles, Homework Help, Discussion**