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Calorimetrey Problem -- Final Temperature of water
In an insulated container, 0.50kg of water at 80C is mixed with 0.050kg of ice at -5.0C. After a while, all the ice melts, leaving only the water. Find the final temperature T_f of the water. The freezing point of water is 0 C.
Q=mcΔT
Q=mL (heat transfer in a phase change)
specific heat of water c = 4186 J/kgK
specific heat of ice c = 2100 J/kgK
latent heat of fusion for water = 3.34 x 10^5 J/kg
Here's my attempt at a solution which came to 68 degrees C (the correct answer is 65C). I've checked my math, so I don't think it was a simple computational error. I think I'm making a mistake in terms of my signs perhaps when it comes to heat entering and exiting.
Anyway, here's what I did.
Q(water) + Q(ice) + m(ice)L = 0
(.5)(4186)(T-80) + (.05)(2100)(T+5) + (.05)(3.34x10^5)=0
I understand that in the case of Q(water), heat is exiting, and in the case of Q(ice) heat is entering. And since the ice melts, in the case of mL, heat is also entering. I guess I'm just not getting something crucial, here.
Any help would be greatly appreciated! Thank you.
Homework Statement
In an insulated container, 0.50kg of water at 80C is mixed with 0.050kg of ice at -5.0C. After a while, all the ice melts, leaving only the water. Find the final temperature T_f of the water. The freezing point of water is 0 C.
Homework Equations
Q=mcΔT
Q=mL (heat transfer in a phase change)
specific heat of water c = 4186 J/kgK
specific heat of ice c = 2100 J/kgK
latent heat of fusion for water = 3.34 x 10^5 J/kg
The Attempt at a Solution
Here's my attempt at a solution which came to 68 degrees C (the correct answer is 65C). I've checked my math, so I don't think it was a simple computational error. I think I'm making a mistake in terms of my signs perhaps when it comes to heat entering and exiting.
Anyway, here's what I did.
Q(water) + Q(ice) + m(ice)L = 0
(.5)(4186)(T-80) + (.05)(2100)(T+5) + (.05)(3.34x10^5)=0
I understand that in the case of Q(water), heat is exiting, and in the case of Q(ice) heat is entering. And since the ice melts, in the case of mL, heat is also entering. I guess I'm just not getting something crucial, here.
Any help would be greatly appreciated! Thank you.