If pressure is intensive, why does Dalton’s low decomposes pressure into sum of partial pressures?


According to what I know, intensive physical properties are those that are not equal to sum of partial quantities, and extensive properties are the opposite, i.e number of moles is extensive, but temperature is intensive (we can’t say that mixing a 30C body with a 40C body would make temperature of the mix 70C obviously).

Accordingly, why do we say that total pressure is the sum of partial pressures (Dalton’s law of pressure) since pressure is intensive, just like temperature? Is it the fact that pressure=force/area, and by keeping the same area and applying different forces having the same directions, the forces sum up which makes pressures sum up? But if this was correct, why do we consider pressure intensive from the beginning?

I’m lost here.

In: 1

Intensive just means that it does not depend on the amount you measure, like you can measure the same pressure if you divide the container in two unequally sized parts and measure the same pressure, which is pretty easy to see

you can add more gas and the pressure will increase, but no matter how much of the volume i measure the pressure of, it’s still the same

if instead i were to measure the weight, then a smaller volume will necessarily weigh less

First, “extensive” vs “intensive” properties isn’t a terribly important concept in the first place, as they’re seldom strictly true anyway. But the definition is whether or not the property depends on the amount of substance, “intensive” properties are ones that don’t.

Pressure can be extensive. e.g. the ideal gas law pV = nRT; double the amount of gas in a box and you double the pressure. In that case, pressure is extensive but volume is intensive, the box stays the same size. But if I have a rubber balloon in a room, the gas inside it is at atmospheric pressure regardless of how much gas is in it, but the balloon’s volume is an extensive property. In other words, it’s context dependent. (hence not a terribly useful or important distinction IMO) Temperature isn’t ‘intensive’ at the extreme either, since a single particle does not have temperature, it’s a statistical property and the fewer energy states you have, the less meaningful the term is.

Anyway, Dalton’s law follows directly from ideal gas law and the underlying physical model, which is a gas of particles that do not interact with each other but only the sides of the container they’re in. So adding molecules of a second ideal gas to a container does nothing to the first gas, and does not change the pressure the first gas exerts on the container, but you add additional pressure from additional collisions coming from the added second gas molecules. I.e. Total pressure is a linear sum of partial pressures, insofar the ideal gas law is a valid approximation. (Dalton’s law is not exact) In this system, pressure is _not_ intensive.

However, that does not mean Dalton’s law’s validity is dependent on whether pressure is intensive in your system. If you have a 50-50 gas mixture in a balloon it’s the volume that’s changing when you add or remove gas, but the total and partial pressures remain constant.