Math Snap
PROBLEM
The data represents a sample of gas that has a constant volume and number of particles. Use the data to answer these two questions.
When the Kelvin temperature of the gas quadruples (increases by a factor of four), the volume of
\begin{tabular}{|c|c|c|}
\hline Trial & \begin{tabular}{c}
Temperature \\
\end{tabular} & \begin{tabular}{c}
Volume \\
(mL)
\end{tabular} \\
\hline 1 & 200 & 400 \\
\hline 2 & 300 & 600 \\
\hline 3 & 400 & 800 \\
\hline 4 & 600 & 1200 \\
\hline 5 & 800 & 1600 \\
\hline
\end{tabular}
the gas becomes -
STEP 1
What is this asking?
If we multiply the temperature of some gas by 4, what happens to its volume?
Watch out!
The table gives a lot of data, but we only need two rows to figure out the relationship between temperature and volume.
Don't get distracted!
STEP 2
1. Find the relationship
2. Calculate the new volume
STEP 3
Let's look at the table and see what's up.
When the temperature is K, the volume is mL.
When the temperature is K, the volume is mL.
Hmm, interesting!
STEP 4
It looks like when the temperature doubles from K to K, the volume doubles from mL to mL.
This suggests a direct relationship between temperature and volume!
In other words, if we multiply the temperature by some number, the volume gets multiplied by that same number!
STEP 5
The problem says the temperature quadruples, which means it gets multiplied by 4.
Since temperature and volume have a direct relationship, the volume will also get multiplied by 4!
STEP 6
Let's pick a starting temperature and volume from the table.
Let's use trial 1: K and mL.
If we multiply the temperature by , we get K.
STEP 7
Now, let's multiply the volume by : mL.
So, when the temperature quadruples to K, the volume quadruples to mL.
Awesome!
SOLUTION
When the Kelvin temperature quadruples, the volume of the gas also quadruples.
