# Pressure in Ideal Gas Law

In Boyle's law ($p$ inversely proportional to $V$ for constant $n$ and $T$), $p$ refers to the applied (external) pressure on the gas.

However, in the ideal gas law, my textbook says that $p$ refers to the pressure of the gas, which I think refers to the pressure applied by the gas. How is this possible, since the ideal gas law is derived from Boyle's law (and Charles' and Avogadro's laws)?

Shouldn't the $p$ in the ideal gas law then refer to the applied (external) pressure like in Boyle's law, not the pressure of (i.e. applied by) the gas?

• Everything should refer to the pressure exerted by the gas. The line on Boyle's law that you read was probably written with the assumption in mind that the internal and external pressures are equal. – orthocresol Oct 12 '15 at 12:24
• But doesn't Boyle's law make more sense when P is the applied pressure? I thought the P in the ideal gas law needed to be changed, not the one in Boyle's law. – Leponzo Oct 12 '15 at 12:39
• "Make more sense" is very vague... It makes more sense from an experimental point of view because the only way you can vary the volume is by varying the external pressure. However in that case the internal pressure will increase to match the external pressure, and Boyle's law will hold equally well regardless of which pressure you use. Which is why I said, it was probably written with the implicit assumption that the internal and external pressures were equal. – orthocresol Oct 12 '15 at 13:02
• That is in the case of a container with movable walls, which will allow for equilibration of the internal and external pressure. In the case of fixed walls, you cannot experimentally verify Boyle's law anymore; however, the ideal gas law still holds true as long as you use the internal pressure. The ideal gas law relates properties of a system to each other, and in this case where the system cannot "see" anything outside since the walls are fixed, the external pressure cannot have any influence on the volume or temperature of the gas inside. – orthocresol Oct 12 '15 at 13:09