What Determines the Final Temperature of Ice and Water Mix?

In summary, the final temperature of the mixture of an 81-g ice cube at 0°C and 878 g of water at 25°C is approximately 16.1757°C. This takes into account the melting heat of the ice and the heat exchange between the ice and water during the melting process.
  • #1
ymehuuh
19
0

Homework Statement


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?


Homework Equations


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


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...
 
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  • #2
What about the latent heat of fusion for ice?
 
  • #3
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.
 
  • #4
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?
 
  • #5
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.
 
  • #6
So then it should be...

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

That's not correct either...
 
  • #7
After melting completely, the ice water takes heat from water to reach the final temperature.
 
  • #8
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
 
  • #9
Appears to be correct.
 

1. What is final temperature?

The final temperature is the temperature at which a system or substance reaches equilibrium after undergoing a change in temperature or thermal energy.

2. How is final temperature calculated?

Final temperature can be calculated using the equation Q = mcΔT, where Q represents the heat energy transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

3. What factors affect the final temperature of a substance?

The final temperature of a substance can be affected by factors such as the initial temperature, the amount of heat energy transferred, the specific heat capacity of the substance, and the type of substance.

4. Can the final temperature be lower than the initial temperature?

Yes, the final temperature can be lower than the initial temperature if the substance undergoes a decrease in thermal energy or if heat is transferred to another substance.

5. Why is final temperature important in scientific experiments?

Final temperature is important in scientific experiments as it helps to determine the amount of heat energy transferred and can provide insight into the behavior and properties of different substances.

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