# If the pressure on a gas increases, does the volume of the gas also increase?

If the pressure on the gas increases, the volume of the gas does not increase. Instead, the volume decreases.

#### Explanation:

According to the general equation of the ideal gases, we have:
PV = nRT ............................................. (1)
Therefore, for a given quantity of the gas (n = constant), and at a given temperature (T = constant), equation (1) will be reduced to:
PV = constant ............................ (2)
In other words, the volume "V" is inversely proportional to the pressure "P". Thus, if the pressure "P" increases, the volume "V" will decrease.

With kind regards
Dr. Mamdouh Younes

Jan 30, 2017

Maybe, maybe not.

As $P V = n R T$ for ideal gases, if $P$ increases, then $V$ must decrease, if nothing is held constant. Otherwise one side of the equality increases while the other does not, which disobeys mathematics.

If the gas is in a closed rigid container, and it already spreaded out to fill the entire container, then if pressure increases (for instance, by adding more of the same gas), its temperature can increase.

This would be then, an example of constant-volume (isovolumetric/isochoric) compression. From the ideal gas law:

$V \Delta P = R \Delta \left(n T\right)$

or ${P}_{1} V = {P}_{2} V = {n}_{1} R {T}_{1} = {n}_{2} R {T}_{2}$

or $\frac{{P}_{1}}{{n}_{1} {T}_{1}} = \frac{{P}_{2}}{{n}_{2} {T}_{2}}$

If pressure increases, $\Delta P > 0$. Since volume and mols are always positive, $\Delta T > 0$ as well, meaning that the container gets hotter.

Again, this would occur when the volume is held constant, which is quite feasible. In this case, the volume of the gas, again, would not change.