# What will happen to the volume of a fixed mass of gas when its pressure and temperature (in Kelvin) are both doubled?

## A. It will not change B. It will increase C. It will decrease D. The change cannot be predicted

Jun 8, 2018

No change in volume.

#### Explanation:

We can use the Ideal Gas Equation to solve this question:

$P V = n R T$

• $P$ is pressure in $\text{Pa}$
• $V$ is volume in ${\text{m}}^{3}$
• $n$ is number of moles of gas
• $R$ is the universal gas constant, $\text{8.31 J/K mol}$
• $T$ is temperature in Kelvin

In your scenario, when mass is fixed, the number of moles will be fixed, too. So we can combine both constant terms $n$ and $R$ to give us:

$P V = k T$

where $k$ is a constant.

Now, since we want to work out how volume changes, let's put $V$ on the left-hand side and move $P$ to the right-hand side:

$V = \frac{k T}{P}$

So from the equation, we can deduce that when temperature and pressure are both doubled, the Volume $V$ will remain unchanged as the numerator term $T$ and the denominator term $P$ are both affected by a multiple of $2$, hence can be cancelled away:

$V = \frac{k T \left(\times 2\right)}{P \left(\times 2\right)} = \frac{k T}{P}$

Hope this helps!