# Question 2208d

Dec 1, 2017

$q = 6276 \text{ J}$

#### Explanation:

The formula you use is:

$q = m c \Delta T$

where
- $q$ is the amount of energy needed ($J$)
- $m$ is the mass ($g$)
- $c$ is the heat capacity (J/(g * °C)
- $\Delta T$ is a change in temperature (°C).

For water, the heat capacity is 4.184 J/(g * °C.

We just plug in everything:

$q = 100 \left(4.184\right) \left(30 - 15\right)$
$\implies q = 6276 \text{ J}$

You may have seen problems where you have this same equation with different units. For example, you may have moles instead of mass, you may have °F instead of °C, and so on and so forth.

How do you work these out? Well, it all lies in the units of the heat capacity. For example, if you were working with moles and °F, what would be the units of heat capacity?

Well, you'd eventually get J/(mol * °F)#.

So if you get different units, it isn't the end of the world; just find a heat capacity that has matching units.

Hope that helps :)