# A calorimeter contains 15 grams of water. The water's temperature increases by 10 C°. How much heat energy was added to the water? (Hint: water's specific heat is 1 cal/g°C)?

Mar 3, 2017

$\text{150 cal}$

#### Explanation:

Unsurprisingly, the key to this problem is the hint.

The thing to remember about a substance's specific heat is that it tells you the amount of energy needed in order increase the temperature of $\text{1 g}$ of said substance by ${1}^{\circ} \text{C}$.

Now, water is said to have a specific heat of ${\text{1 cal g"^(-1)""^@"C}}^{- 1}$. This tells you that in order to increase the temperature of $\text{1 g}$ of water by ${1}^{\circ} \text{C}$, you must provide it with $\text{1 cal}$ of heat.

The thing to remember here is that you need $\text{1 cal}$ of heat for every $\text{1 g}$ of water and for every ${1}^{\circ} \text{C}$ in temperature.

So, you have $\text{15 g}$ of water to work with. You can use the specific heat of water to figure out how much heat is needed to increase the temperature of this sample by ${1}^{\circ} \text{C}$.

15 color(red)(cancel(color(black)("g"))) * "1 cal"/(1color(red)(cancel(color(black)("g"))) * 1^@"C") = "15 cal" ""^@"C"^(-1)

This tells you that for every ${1}^{\circ} \text{C}$ increase in the temperature of the sample, $\text{15 cal}$ of heat are needed. Since you want the temperature to increase by ${10}^{\circ} \text{C}$, you will need

$10 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{^@"C"))) * overbrace("15 cal"/(1color(red)(cancel(color(black)(""^@"C")))))^(color(blue)("for 15 g of water")) = color(darkgreen)(ul(color(black)("150 cal}}}}$

I'll leave the answer rounded to two sig ifgs, but keep in mind that you only have one significant figure for the increase in temperature.