# Why does pressure seem to be an extensive variable considering Dalton's law?

I learned that in thermodynamics, pressure is regarded as an intensive variable, while properties that you can add up such as mass or volume, are considered extensive.

However, to me, Dalton's law seems to contradict this idea. Dalton's law states that the total pressure of a mixture of gases is the sum of the partial pressures of each gas.

Given this, my question is: if the pressure can be added up, why is pressure intensive? What am I understanding wrong? Why is Dalton's law not a valid argument for pressure being an extensive property?

To give a simple example, let's say that I have a "mixture" of two same gases (i.e. oxygen gas), at a total pressure of 1 bar. Now, if I "divide" the gas into two mole fractions and determine their partial pressures, the sum of those partial pressures would also be 1 bar. So clearly, in this example, I'm adding the two pressures to get a larger, total pressure. So, to me, this makes it appear that pressure can be an extensive property, since it can be added up. However, I know that I'm wrong somewhere but don't know where, so can someone explain why my example would not prove that pressure is extensive?

• If you double the total volume and double the mass of each gas, its partial pressure will not change – Chet Miller Sep 5 at 0:44
• @ChetMiller Thanks for the reply; that makes sense. However, I'm curious as to why my reasoning using Dalton's law is invalid. I know pressure is intensive, but I'm having a hard time understanding why Dalton's law makes it appear to be extensive. – F16Falcon Sep 5 at 0:57
• The way I see it is that the definition implicitly assumes that when you add the systems you put them next to each other and in contact, but you do not mix them. – Wolphram jonny Sep 5 at 1:08
• @Wolphramjonny That's a great way to think about "addition" in extensive systems; your comment helped, thanks! – F16Falcon Sep 5 at 2:24