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# Chilling water problem

How much ice at -10 degrees C is necessary to get 500 g of water down to 0 degrees C? Created by Sal Khan.

## Want to join the conversation?

• if the Heat out of the system is 125,340 would that be negative because it is leaving the system and not being put in? •   Yes, this was confusing to me in the beginning too, but after some work on heat engines, I got it. Here's how I think about it.

You could have four posibilities:

1) Heat INTO the system = + (Positive)
2) Heat INTO the system = - (Negative)
3) Heat OUT of the system = + (Positive)
4) Heat OUT of the system = - (Negative)

Case one: You have positive heat going into the system, increasing the total energy in the system.
Case two: A double negative. You have negative heat going into a system, which is equivalent to heat going out of a system, dceasing the amount of energy in the system.
Case three: Similar to case two, but not as confusing. You have heat going out of the system, decreating the energy of the system.
Case four: Another double negative. Negative heat out of the system is heat into the system, like case one, increasing the total energy in the system.

125,340 J out of the system is the same as -125,340 into the system. The into and out of are very important in distinguishing what is happening to the system.
• Why didn't you convert it into Kelvin before multiplying? The 4.18 that you gave us is Joules over Grams multiplied by Kelvin but you ended up multiplying it by Celsius and still this was able to cancel out. I thought that you have to add 273 to it to change it to Kelvin. •  Because it's a change in temperature, there's no need to convert it. A one degree change is equivalent in both scales: 0°C = 273.15K, 1°C = 274.15K, and so on, so the difference between the temperatures will be the same in C or in K.
• Is there a scientific explanation of why ice usually cracks when put into a cup of water? • when water turns to ice it expands(volume increases) and when ice turns to water it again contracts(volume decreases)
when you put ice in a cup of water the temperature suddenly decreases which due to which volume must also decrease, but there is a large temperature difference so the molecules of ice which are strongly bonded do not separate easily but the ice tries to shrink which gives rise to cracks!
• I was marginally confused by this video because you included the energy of the phase change capacity of the ice when the question was posed to suggest you intended to have 500g of chilled water at the end of the experiment. In your calculations, because you included the potential of the phase change you actually ended with 854. whatever grams of chilled water and no ice, not an answer to the question as it was posed. You would need a larger block of ice to move that 500g of water -10C so that the amount of water would not be amended by a phase change. • Your argument is a question of semantics. I believe what was implied, was figuring out the quantity of ice required to lower the temperature of the water by 60 degrees, not making any attempt to maintain a certain final quantity of water. A larger quantity of ice would not have made any difference in maintaining the original quantity because the same amount of ice (354.02 grams) would have melted into the water regardless. The total quantity of liquid water would still be 854 grams, but with a large ice cube still remaining in it.
• Hey Sal, I was wondering why you need to include the Latent Heat of Fusion in this equation. I know that when two object come into thermal contact they will transfer heat in a way that their temperature becomes the same. Since heat gained is equal to heat lost, cant you say that the amount of energy that's needed to be extracted to bring water from 60 to 0 C is equal to the amount of heat needed to bring Ice from -10 to 0 C? • At Sal said that the temperature difference is 60 degrees. Why is it positive 60? Wouldn't it be -60? Since , Change of temp = Final Temp - Initial Temp. So, F (0) - I (60) = -60 ? Please Explain , Thank you • I had the same question at first. But this actually is still correct because this is when he is calculating heat out. So it would make sense that technically it would be negative in regards to the system.. I think why the negative doesn't matter as much here is because he already refers to it as heat "out" not just heat transferred where a negative sign would indicate that this is heat leaving the system not being added to it. So if you were doing this in a technical way and were to calculate just the heat transfer in general terms the negative would be necessary for indicating the direction of the change. But in the case of the video this direction is indicated by calling it heat out and a negative sign would just be redundant.
• I don't understand that 'HEAT OUT = HEAT ABS'? I understood up to the point where he got '20.5xJ and 333.55xJ'. But why did he set up the equation like '20.5xJ + 333.55xJ = 125340J'?
How could they be equal to?
Is 0 water -> 60 water = -10 ice -> 0 water? • Sal set up the equation 20.5(X)j + 333.55(X)j =125340j for the following reasons; 20.5(X) joules is the amount of heat the solid ice can absorb, the 333.55(X) joules is the amount of heat the "melted" ice can absorb (this is the flat spot on the phase diagram), and the 125340 joules is the amount of energy the existing water has to lose. The X was a variable for the grams of ice required. By adding the 20.5(X) and the 333.55(X) together that gives the total amount of absorption of the ice in both the solid phase and the liquid phase. By setting the other side of the equation to 125340 he was able to apply the ices' absorption capacity to that of the water. Finally by solving for X he was able to find the quantity of ice required to chill the water.   