Question

water has 5 times the heat capacity as soil. If i add the same amount of water and soil, i find the temperature of the soil increases to 50 degrees Celsius. what is the temperature of the water?

Answer 1

I'm guessing that you're adding the same amount of energy to water and soil separately. Otherwise we'll have heat transfer messing things up!

Well, heat capacity is heat (not work) energy transferred per temperature raise. So it tells you the heat energy needed to raise the temperature to some amount.
\(\dfrac Q{\Delta T}=C\)
So, it's useful when finding the temperature change given heat energy because, with algebra,
\(\Delta T=\dfrac QC\)

Now, what we know is the the \(Q\) (heat energy) is the same for both, and the heat capacity of water is \(5\) times that of soil.
So
\(\color{blue}{\large C_\text{water}=5C_\text{soil}}\)
Now we'll substitute in for that. Usually it's a good idea to look at what's given and see if those relationships can be helpful. Since they tell you how the heat capacities compare and you know the heat energy is the same, we can probably work something out with the relative temperature changes.

So, first,
\(Q_\text{water}=Q_\text{soil}=Q\)
because we are given that the same energy is added. This will simplify things.

So,
\(C_\text{water}=\dfrac{Q_\text{water}}{\Delta T_\text{water}}=\dfrac{Q}{\Delta T_\text{water}}\)

Now, you can finish up! What is \(C_\text{soil}\)? Next, use the relation between the heat capacities that I wrote in blue. Then see what happens! You can solve for \(\Delta T_\text{water}\).

Take care!