Heat capacity is a measure of the amount of heat required to change the temperature of a given amount of a substance by some amount. A common unit for heat capacity is "calories / (gram)(°C)". For water, heat capacity is 1 calorie / (gram)(°C), so if I have 1 gram of water and I want to increase its temperature by 1°C, I have to add 1 calorie of energy to the water. What if I have more than 1 gram or I want to increase the temperature by more than 1°C? Multiply!

The reverse of this problem is really the same problem, it just requires some different math. What if I have 18.00mL of water that is initially at 12.6°C and I add 49calories of energy to that water? First part… the density of pure water is 1 g/mL so 18.00mL of water has a mass of 18.00g. Now, if the heat capacity of water is 1 calorie / (gram)(°C), and we have 18.00g of water, we can again multiply to get:

{1 calorie / (gram)(°C)} x 18.00g = 18.00 calories per °C

So for every 18.00 calories of energy we add to *this specific sample*, we will increase the temperature by 1°C. We are adding 49 calories to

*this specific sample*so:

49 calories / 18.00 calories per °C = 2.7°C

This is how much the temperature *changes*when we add this amount of energy. Since the sample was initially at 12.6°C and we

*added*energy, the new final temperature must be 2.7°C

*higher*than the initial temperature, 12.6°C + 2.7°C = 15.3°C.

There are some assumptions in this description (like the density of water) that simplify the problem… if you want to get the absolutely perfectly correct answer, you'd have to take some of those assumption into account, but this is close enough for our purposes.

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