# Question #8ae7b

Apr 5, 2017

You say that this is predicted by Boyle's Law.

#### Explanation:

Boyle's Law states that the volume $V$ of a gas is inversely proportional to its pressure $p$ if all other factors are kept constant.

In symbols,

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} p = \frac{k}{V} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

where $k$ is a proportionality constant.

We can rearrange this formula to give

$p V = k$

In words, the product of $p$ and $V$ is a constant, no matter what the value of $p$ is.

We see this in the plot of $p V$ vs. $p$ above.

The plot is a horizontal straight line.

Apr 6, 2017

The product of the Pressure and Volume of a gas at constant temperature will always be the same.

#### Explanation:

That is, if the pressure is increased, the volume must have decreased, or it the volume is increased, the pressure must decrease. ${\left(P V\right)}_{1} = {\left(P V\right)}_{2}$.

Why? Temperature is really just a measure of thermal energy. Pressure is a measure of average kinetic energy in gases. Volume is the “system”.

Within that volume, energy cannot be created or destroyed, only changed in form. Because we cannot change the net energy in this system (we have a pre-existing Pressure (kinetic) and fixed temperature (thermal) energies), any change to the pressure must change the volume in order to maintain the constant thermal energy.
The average kinetic energy (pressure) is less if the molecules are traveling farther (more volume) and greater when they have less distance (smaller volume) to travel before impacting the surface (pressure).

The “combined” or Ideal Gas Laws include the temperature factor as a variable. ${\left(\frac{P V}{T}\right)}_{1} = {\left(\frac{P V}{T}\right)}_{2}$
Boyle’s Law is one part of that, looking at only the change of pressure and volume.