Ice cube placed in water - find final temperature

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SUMMARY

The discussion centers on calculating the final temperature of a system consisting of a 75-gram ice cube at 0 degrees Celsius and 825 grams of water at 25 degrees Celsius. The correct approach involves using the principle of conservation of energy, accounting for both the melting of the ice and the heat transfer between the water and the ice. The final temperature of the mixture is determined to be 16 degrees Celsius, after correcting for unit inconsistencies and including the latent heat of fusion for the ice.

PREREQUISITES
  • Understanding of heat transfer principles
  • Knowledge of specific heat capacities (2.108 kJ/kg·K for ice, 4.184 J/g·°C for water)
  • Familiarity with the concept of latent heat of fusion
  • Ability to manipulate equations involving energy conservation
NEXT STEPS
  • Review the concept of latent heat and its role in phase changes
  • Learn how to convert units consistently in thermodynamic equations
  • Study the conservation of energy in thermal systems
  • Practice similar problems involving heat transfer between different states of matter
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, physics educators, and anyone interested in understanding heat transfer and phase changes in thermal systems.

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Homework Statement


A 75 gram ice cube at 0 degrees celsius is placed in 825 grams of water at 25 degrees C. What is the final temperature of the mixture?


Homework Equations


What is the best formula to use in this question?


The Attempt at a Solution

I have attempted this problem multiple times. The last time I plugged in these variables:
(75g)(2.108kJ/kg-k)(T2-0)=(825g)(4.184J/g*degrees C)(T2-25 degrees C)
The answer is supposed to be 16 degrees C. I can't seem to figure this one out. Any help will be greatly appreciated. Am I missing variables?
 
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Well, I can think of two things you might check on the left side of your equation you seem to have mixed units you have 75g of ice but write J/kg.

Also, don't you have to melt the ice and wouldn't that involve latent heat?
 

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