# If the pressure on a gas sample is tripled and absolute temperature is quadrupled, by what factor will the volume of the sample change?

${V}_{2} = \frac{4}{3}$

#### Explanation:

The relationship between pressure, volume, and temperature can be expressed as:

$\frac{P V}{T}$

and we can compare one state to another by this expression:

$\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$

In this case, we can say that ${P}_{1} , {V}_{1} , {T}_{1}$ are all equal to 1 and have the pressure triple so that ${P}_{2} = 3$ and the temperature quadruple so that ${T}_{2} = 4$ and see what it is that ${V}_{2}$ will equal:

$\frac{\left(1\right) \left(1\right)}{1} = \frac{\left(3\right) {V}_{2}}{4}$

$1 = \frac{3}{4} {V}_{2}$

$\left(1\right) \textcolor{red}{\frac{4}{3}} = \left(\frac{3}{4}\right) \left({V}_{2}\right) \textcolor{red}{\frac{4}{3}}$

${V}_{2} = \frac{4}{3}$