# Question #c3048

Mar 22, 2017

The volume will quadruple (i.e. become 4 times the original volume).

#### Explanation:

The combined gas law states that $\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$.

Let's say ${P}_{1} = P$, ${V}_{1} = V$, and ${T}_{1} = T$.

That means that ${P}_{2} = \frac{1}{2} P$, and ${T}_{2} = 2 T$.

Now, let's plug in all of these variables and solve for ${V}_{2}$.

$\frac{P V}{T} = \frac{\left(\frac{1}{2} P\right) {V}_{2}}{2 T}$

$\frac{P V}{T} = \frac{P {V}_{2}}{4 T}$

$\frac{\textcolor{red}{\cancel{P}} V}{\textcolor{b l u e}{\cancel{T}}} = \frac{\textcolor{red}{\cancel{P}} {V}_{2}}{4 \textcolor{b l u e}{\cancel{T}}}$

$V = {V}_{2} / 4$

$4 V = {V}_{2}$