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

• dmolson
In summary, the question asks how many grams of aluminum at 90 C would be needed to melt 20 g of ice at 0 C. The equations used are Q = mcdelta T and Q = mLf, with specific heat values of c(H2O) = 1 cal/g.C and c(Al) = 0.215 cal/g.C. The heat of fusion for the ice is calculated to be 1594 cal. However, there is no final temperature given for the aluminum, so the next step is unclear. Additional information is needed to determine the final temperature and therefore the mass of aluminum needed.
dmolson

## 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:
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?

## What is the heat of fusion?

The heat of fusion is the amount of energy required to change a substance from a solid to a liquid state at its melting point.

## What is the melting point of ice?

The melting point of ice is 0°C or 32°F at standard atmospheric pressure.

## How does the heat of fusion affect the melting of ice?

The heat of fusion plays a crucial role in the melting of ice. As heat is added to ice, the molecules gain energy and vibrate faster, eventually breaking the bonds holding them in a solid state. This process requires a specific amount of energy, known as the heat of fusion, to overcome the forces holding the molecules together and allow the ice to melt.

## Why does ice melt at 0°C?

Ice melts at 0°C because at this temperature, the heat energy added to the ice is equal to the heat of fusion required for the molecules to break their bonds and transition from a solid to a liquid state.

## Does the heat of fusion vary for different substances?

Yes, the heat of fusion is different for different substances and can vary depending on factors such as pressure and purity of the substance. For example, the heat of fusion for water is 334 J/g, while the heat of fusion for iron is 272 kJ/kg.

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