# Question #961df

Feb 25, 2016

Boyle's law holds that for a given quantiy of gas, $P$ $\propto$ $\frac{1}{V}$, or $P \times V = k$; so if the pressure is doubled the the volume is halved, and vice versa.

#### Explanation:

Given that $P$ and $V$ are inversely proportional, if the pressure doubled, the volume should reasonably be HALVED; i.e. $P V = k$. Think of a piston (which could be as simple as a syringe). If we depress the piston (reducing the volume), the pressure increases proportionally.

So, for a given quantity of gas at constant temperature, ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$.

Feb 25, 2016

${P}_{2} = 2 \times {P}_{1} \implies {V}_{2} = \frac{{V}_{1}}{2}$

#### Explanation:

Boyle's law states: At constant temperature, and for the same gas in a container, $P V = k$.

Therefore, ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$.

Since the pressure is doubled, thus ${P}_{2} = 2 \times {P}_{1}$

$\implies {P}_{1} {V}_{1} = {P}_{2} {V}_{2} \implies \cancel{{P}_{1}} {V}_{1} = \left(2 \times \cancel{{P}_{1}}\right) {V}_{2}$.

$\implies {V}_{2} = \frac{{V}_{1}}{2}$

Therefore, according to Boyle's law, when the pressure is doubled, the volume is halved.