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As the hot iron is placed into cool water, the temperature of the iron decreases as the temperature of the water increases. During this process, heat energy is transferred from the iron to the water.

Use the following equation to determine the amount of heat energy, which is transferred from the iron to the water.

∆Q = mass in Kg * Specific heat * decrease of temperature

In my physics book, the specific heat of iron is 450 J/(Kg*˚C)

Decrease of temperature = 90 – Tf

∆Q1 = 0.025 * 450 * (90 – Tf) = 1012.5 – 11.25 * TF

This is the amount of heat energy, which the iron released!

The second equation determines the effect that this heat energy has on the water.

For water, specific heat = 4180 J/(Kg*˚C)

For water, increase of temperature = Tf – 15

∆Q2 = 0.060 * 4180 * (Tf – 15) = 250.8 * Tf – 3762

This is the amount of heat energy, which the water absorbed!

These two amounts of energy are equal.

1012.5 – 11.25 * Tf = 250.8 * Tf – 3762

Add 11.25 * Tf to both sides

1012.5 = 262.05 * Tf – 3762

Add 3762 to both sides

4774.5 = 262.05 * Tf

Tf = 4774.5 ÷ 262.05

The final temperature is approximately 18.22˚C

I hope this helps understand how to solve this type of problem.

Check:

1012.5 – 11.25 * 18.22 = 807.525

250.8 * 18.22 – 3762 = 807.576

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You could do this type of experiment at home. Pour cool water into a Styrofoam cup. Place a piece of metal into boiling water. Measure the temperature of the cool water. Then use tongs or pliers to carefully move the metal from the boiling water to the cool water. Place the thermometer into Styrofoam cup and wait until the temperature of the water stops increasing. Read the final temperature of the water.

When you are home schooled, you may need to do some labs like this so you can see how the physics applies to the real world.