# If the pressure exerted on a confined gas is doubled, what happens to the volume of the gas?

Oct 27, 2016

$\text{Boyle's Law}$ holds that at constant,,,,,,,,,,,,

#### Explanation:

$\text{Boyle's Law}$ holds that at constant temperature, and constant amount of gas, pressure is inversely proportional to volume:

$P \propto \frac{1}{V}$, or ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$.

And thus ${V}_{2}$ $=$ $\frac{{P}_{1} {V}_{1}}{P} _ 2$

But the boundary conditions of the problem state that ${P}_{2} = 2 {P}_{1}$:

Thus ${V}_{2}$ $=$ $\frac{\cancel{{P}_{1}} {V}_{1}}{2 \cancel{{P}_{1}}}$

So ${V}_{2} = {V}_{1} / 2$

So the volume is HALVED.