How to Calculate Mass of Aluminum Needed to Melt 20 g of Ice with Heat of Fusion

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SUMMARY

To calculate the mass of aluminum required to melt 20 grams of ice at 0°C, one must utilize the heat of fusion equation Q = mLf, where Q is the heat absorbed by the ice. The heat of fusion for ice is 79.7 cal/g, resulting in a total heat requirement of 1594 cal for 20 g of ice. The aluminum's heat transfer can be expressed using Q = mcΔT, where c(Al) = 0.215 cal/g°C. The final temperature of the aluminum must be determined to find its mass, as the system will reach thermal equilibrium.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically heat transfer.
  • Familiarity with the heat of fusion concept.
  • Knowledge of specific heat capacities, particularly for water and aluminum.
  • Ability to solve equations involving mass, specific heat, and temperature change.
NEXT STEPS
  • Learn about thermal equilibrium and its implications in heat transfer problems.
  • Study the concept of specific heat capacity in more detail, focusing on different materials.
  • Explore advanced thermodynamic equations and their applications in real-world scenarios.
  • Investigate the practical applications of heat of fusion in phase change materials.
USEFUL FOR

This discussion is beneficial for students in physics or chemistry, educators teaching thermodynamics, and anyone interested in understanding heat transfer in phase changes.

dmolson
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Homework Statement


How many grams of aluminum at 90 C would have to be dropped into a hole in a block of ice at 0 C to melt 20 g of ice.


Homework Equations


Q = mcdelta T and Q = mLf
c(H2O) = 1 cal/g.C
c(Al) = 0.215 cal/g.C

The Attempt at a Solution



I can find the heat of fusion Q = (20 g)(79.7 cal/g) = 1594 cal.
The next step I thought would be to set that equal to mcdeltaT of the aluminum, but there is no final temp for the aluminum. I don't know if I am supposed to find the final temp first or how I would do that to find the mass of the aluminum.
 
Last edited:
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dmolson said:
...but there is no final temp for the aluminum.
Only a small portion of the block of ice melts. So what must be the final temperature?
 
Do you know anything about equillibrium? It could be easily shown that this system would reach steady state right?
 

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