A Two Character Problem

A 15.0 g metal spoon at 15^oC is placed into 150.0 g of hot water at 96.5^oC. If the final temperature is 92.8^oC, what is the specific heat of the metal?

Let’s think about what is going on in this situation – a cold spoon is placed in hot water.

The two characters in this problem are the spoon and the water. Each has its own “story.” The spoon will take in heat and get warmer. The water will give away heat and get colder.

We know that the heat that the spoon is taking in is the same heat that the water is giving away so we have the formula:

Remember that the "-1" is because the spoon's "story" involves giving away heat (q has a negative sign), while the water's "story" involves taking in heat (q is positive. Since a positive can NEVER be equal to a negative, we need to change the sign. Note: it does NOT matter which side we change, just that we change one of them.

Since both spoon and water are undergoing temperature changes, this formula becomes

Now, pulling the information out of the problem above, here is what we know...

mass spoon	15.0 g
spec. heat of spoon	?
initial T of spoon	15oC
final T of spoon	92.8oC
mass of water	150.0 g
spec. heat of water	1 cal/g oC
initial T of water	96.5oC
final T of water	92.8oC

Notice that the final temperature of both the spoon and the water are the same. This makes sense if you remember that heat transfers from one thing to another until the temperatures are the same. So, the only way that temperature can be final is if it is the same.

We are now ready to do the calculations. They can be found here.