Equilibrium Question with water and ice

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Homework Help Overview

The problem involves a thermal equilibrium scenario where 5.0 kg of ice at 0°C is mixed with 3.0 kg of water at 20°C. The participants are exploring how much ice remains after the system reaches equilibrium, considering specific heat capacities and latent heat.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the energy balance equation involving the latent heat of ice and the specific heat of water. There are questions about whether all the ice melts and how to account for the mass of ice that may remain. Some participants suggest using (5 - mf) to represent the mass of ice that melts, raising concerns about having multiple unknowns in their equations.

Discussion Status

The discussion is ongoing, with participants questioning the assumptions about the melting of ice and the final temperature of the system. There is recognition that additional equations may be needed to resolve the unknowns, but no consensus has been reached on the final temperature or the amount of ice remaining.

Contextual Notes

Participants are working under the assumption that the system is isolated, and they are grappling with the implications of having two unknowns in their calculations. The problem constraints and the requirement for equilibrium are central to the discussion.

Lisa Marie
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Homework Statement


5.0 kg of ice at 0◦ is put into 3.0 kg of water at 20◦C. Assuming that they are isolated, that cH2O = 4186 J /kg K , and that L = 3.3 × 105 J/ kg how much ice is left when the system comes to equilibrium?

Homework Equations


Q= +/- mL
Q=mcΔT

The Attempt at a Solution


mLice+mcΔTwater=0
5(3.3×105)+3(T-293)(4186)=0
T=266.7K
This answer is clearly incorrect as it would give you a negative Celsius temperature. Also how would you find mass from this?

Any help would be much appreciated!
 
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If there is some ice left when the system comes to equilibrium, what is the final temperature of the system?

Lisa Marie said:

The Attempt at a Solution


mLice+mcΔTwater=0
5(3.3×105)+3(T-293)(4186)=0
Why do you use 5 here? Does all of the ice melt?
 
TSny said:
If there is some ice left when the system comes to equilibrium, what is the final temperature of the system?


Why do you use 5 here? Does all of the ice melt?
Ok I see so you have to use (5-mf) but then there are two unknowns...
 
Lisa Marie said:
Ok I see so you have to use (5-mf) but then there are two unknowns...
TSny asked two questions.

You answered regarding using (5 - mf) rather than using 5.

He also asked "If there is some ice left when the system comes to equilibrium, what is the final temperature of the system?"

So, what is the final temperature in that case?
 
SammyS said:
TSny asked two questions.

You answered regarding using (5 - mf) rather than using 5.

He also asked "If there is some ice left when the system comes to equilibrium, what is the final temperature of the system?"

So, what is the final temperature in that case?

Um I'm not really sure because there is two unknowns... so I guess I need another equation?
 
Lisa Marie said:
Um I'm not really sure because there is two unknowns... so I guess I need another equation?
If the system reaches equilibrium and some ice remains along with the (liquid) water, what is the temperature?
 
Lisa Marie said:
Ok I see so you have to use (5-mf) but then there are two unknowns...
There will be only a single unknown. If at equilibrium ice is present with water, then think about the temperature of the ice.
 
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