Equilibrium Question with water and ice

[Lisa Marie]

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 c_H2O = 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

mL_ice+mcΔ_Twater=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!

 

[TSny]

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

The Attempt at a Solution

mL_ice+mcΔ_Twater=0
5(3.3×10⁵)+3(T-293)(4186)=0

Why do you use 5 here? Does all of the ice melt?

 

[Lisa Marie]

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-m_f) but then there are two unknowns...

 

[SammyS]

Ok I see so you have to use (5-m_f) but then there are two unknowns...

TSny asked two questions.

You answered regarding using (5 - m_f) 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?

 

[Lisa Marie]

TSny asked two questions.

You answered regarding using (5 - m_f) 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?

 

[SammyS]

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?

 

[Halo CX]

Ok I see so you have to use (5-m_f) 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.