What is final temperature?

ymehuuh

1. The problem statement, all variables and given/known data
A 81-g ice cube at 0°C is placed in 878 g of water at 25°C. What is the final temperature of the mixture?


2. Relevant equations
No heat is loss therefore m*Cp*deltaT+m*Cp*deltaT=0
Cp ice=2.09
Cp water=4.19


3. The attempt at a solution
878*4.19*(Tf-25)+81*2.09*(Tf-0)=0
3678.82Tf+169.29Tf=91970.5
Tf=23.9C

The answer is wrong...don't know why...

LowlyPion

What about the latent heat of fusion for ice?

nasu

So you think you'll have ice at 23 degrees?
The ice will melt (at least partially). This will take energy (heat) from the water so teh final temperature will be lower.
You have to take into account the melting heat Q=m_ice*l_melting
where m_ice is the mass of ice that melts (may be equal to the initial mass) and l_melting is the latent heat (heat of fusion) for ice.

In order to see if the ice melts completely (or not) you can compare the heat necessary to melt all th e ice with the heat released by the water when it cools to zero degrees.

ymehuuh

Qmelt=81g*333j/g
=26973
So...
878*4.19*(Tf-25)+81*2.09*(Tf-0)+26973=0
3848.11Tf=64997.5
Tf=16.89

Which is still wrong...what am I doing wrong now?

nasu

You don't have ice heating up. It's already at 0 degrees. There is no term like 81*2.09*(Tf-25)
It's the water from melting that will heat up.

ymehuuh

So then it should be...

878*4.19*(Tf-25)+26973=0
Tf=17.668

That's not correct either...

rl.bhat

After melting completely, the ice water takes heat from water to reach the final temperature.

ymehuuh

Ok...if that is so...then...
81g*4.190j/kg*Tf + 878g*4.19j/kg*Tf -91970.5 + 81*333 = 0
so Tf = 16.1757

rl.bhat

Appears to be correct.