Need help with latent heat involving ice and steam

AI Thread Summary
The discussion centers on a physics problem involving the thermal interaction between ice and steam in a well-insulated bucket. The initial equilibrium temperature after injecting steam into ice is confirmed to be 0°C. The user attempts to calculate the mass of ice remaining after the steam cools, using the specific heat of steam and the latent heat of fusion for ice. However, their calculations yield an incorrect mass of remaining ice, indicating a misunderstanding of the phase changes and energy transfers involved. The conversation emphasizes the need to account for the distinct energy changes during the steam's transition to water and the subsequent freezing of water into ice.
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Homework Statement



A well-insulated bucket of negligible heat capacity contains 177 g of ice at 0°C.

(a) If 20 g of steam at 100°C is injected into the bucket, what is the final equilibrium temperature of the system? I've already solved this part to be 0 degrees Celsius.

(b) What mass of ice remains?


Homework Equations



Q = mc(deltaT)

m = Q/Lf



The Attempt at a Solution



From the example in the textbook, it seems I only have to find the heat necessary to cool the steam from 100 degrees to 0 degrees, and then divide this number by the latent heat of ice (333.5 kJ/kg). 2.02 is the specific heat of steam. So, I did (.02)(2.02)(100). This gave me a heat of 4.04 kJ. I then divided this number by the latent heat of ice, 333.5, and came out with an answer of .01211 kg. I converted this to g (12.11 g), and subtract this from 177. My final answer was 164.886457 g, but this is incorrect. Help?
 
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Phase change for water is different going from steam to liquid and then to water:

Total energy change= that going from steam to water-that going to from 100 to zero degrees-and then that from going liquid to freezing.

There are three separate constants at work.
 

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