# Why is pressure considered as an intensive property in the study of thermodynamics?

Shouldn't pressure decrease when no of moles of the substance is reduced from the system ? Since, the no of molecules hitting the surface of the system is now less ?

Yes, if only the amount of substance is reduced, pressure will decrease. But that is not exactly what intensive and extensive mean. They refer to the behavior of a quantity under a change of system size which includes volume too.

If not only the number of particles but also the system's volume is scaled by the same factor, i.e. density is kept constant, pressure will indeed remain unchanged, while internal energy for example will decrease by that factor.

• So that means for pressure to be an intensive property, the no of particles and volume should always be scaled by same factors ? – user298796 May 9 at 8:09
• Yes. Look at the ideal gas law for instance. Only under the same rescaling of N and V does pressure remain constant. – Nephente May 9 at 8:10

An intensive property is one that is independent of mass. Pressure and temperature are both inherently intensive properties.

Suppose you are in a room at 1 atm pressure and 20 $$^0$$C. You cut the room in half by installing a barrier. Each half of the room has half the mass of the whole room, but the temperature and pressure is still the same.

At the molecular level, pressure is proportional to the number of collisions per unit time between the molecules and the walls of the room. While half the room has half the molecules, the mean time between collisions is also halved due to halving the volume.

Temperature is a measure of the average translational kinetic energy of the molecules in the room. Although the total kinetic energy in half the room is less than the whole room due to half the molecules, the average kinetic energy per molecules is the same in half the room as the whole room.

Extensive properties depend on the mass. An example is internal energy, $$U$$. In the above example each half of the room has half the internal energy of the whole room.

An extensive property can be made intensive by diving the property by the mass. If you divide the internal energy by the mass of the entire room, you have the internal energy per unit mass, which is called the specific internal energy. We usually designate this by a lower case letter, i.e., $$u=U/m$$. Now if you divide the room in half the specific internal energy $$u$$ of each half is the same as the specific internal energy $$u$$ of the whole room.

Hope this helps.

Intensive quantities are independent of the material body's atoms $$N$$. And, in thermodynamic limit we have $$N/V=fixed$$, in which the system is translationally invariant.

Under equilibrium conditions, the pressure must be uniform throughout the whole parts of the body. By definition, it is the force per unit (imaginary) area that the body exerrs on a wall. We conclude that it's not important at all how much is the system big or small which proves pressure is an intensive quantity.

I learned this from Huang. Hope this helps.