# Pressure: extensive or intensive property?

I know that there are already some relevant questions.

I am a physics professor and I do know that pressure is considered as an intensive property and the justification for this.

Nevertheless, I am puzzled about something I read from a book (Engineering Thermodynamics Michael Horsley, Chapman and Hall 1993).

The author has a progress type question: "If I have some gas in a rigid container (...), is its pressure an intensive or extensive property?"

My quick answer was intensive based to the common "half the container" argument. The author's answer is (to my surprise): extensive.

Below is (in his own words) the justification: "If (...) I let half the gas out of the cylinder, then the pressure inside the cylinder will certainly fall and the pressure of the released gas will also be quite different from its initial value. Thus the pressure is an extensive property."

What am I missing here?

• I think you've mixed up "intensive" and "extensive?" Volume is extensive and temperature is intensive, for instance, which seems to be the opposite of your usage. – Chris Jan 18 '18 at 11:18
• Writing down the question I did mixed up intensive/extensive. I made the proper edit. I hope everything is ok. Thanks for pointing me out. Pressure is widely considered an intensive property. Nevertheless, I was puzzled to read that the author regard it as an extensive property and see also the accompanied justification. – Dimitris Jan 18 '18 at 11:30

Intensive properties are the properties which remain constant despite varying the number of molecules $N$ and varying the amount of volume $V$ in the thermodynamic limit, i.e. where $N$ and $V$ both are large and are varied in a way that their ratio remains constant. In the example of the book you mention, $N$ is varied but $V$ is kept constant (the volume of the container) and thus, under such a scenario, an intensive property is not obliged to remain constant.

• Thanks for the answer. So the author's answer is incorrect, I guess. – Dimitris Jan 18 '18 at 11:35
• @dimitris My pleasure. And yes, I think so. – Dvij Mankad Jan 18 '18 at 11:36
• Should I accept one of the replies or should I wait for another possible one? – Dimitris Jan 18 '18 at 12:18
• +1, short and good answer. – santimirandarp May 2 '18 at 7:51

Pressure is intensive. I think the way you understand extensive and intensive is a bit wrong.

An intensive property is a property which is same for any part of a system regardless of the size and shape of the part you are considering.

An extensive property is different for different parts of the system if the size is different.

In the example that the author gave, the pressure does change but still the the pressure of any part of the system you take will be same as the rest of the system regardless of the size. The pressure inside whole system has changed since it has gone through a process. After undergoing a process the intensive properties also change but the intensive property of any part of the system will be same as rest of the system at a particular time( not the same as intial value though).

EDIT ( question edited) : So I think the author's answer is wrong here.

• I made the correction. I mixed up intensive/extensive in the typing of the question. – Dimitris Jan 18 '18 at 11:33
• I don't know what the author is trying to say then. Pressure does change but it doesn't make it extensive according to me. Pressure is still intensive. – SR810 Jan 18 '18 at 11:35
• Thanks for the replies. I also consider it an intensive property. Considering that I really enjoy the book (I use it to my courses) I was really puzzled about the author's reply. That's why I put the question into the forum despite having been already answered. I really apologize for the inconvenience I certainly caused with the initial mixing up of the terms. – Dimitris Jan 18 '18 at 11:41
• @dimitris no problem. such mistakes do happen. But nice that you corrected it. – SR810 Jan 18 '18 at 11:43

Take two systems, $S_1$ and $S_2$. Let $S_{12}$ be a system obtained by putting these two together.

A property $P$ is said to be extensive if

$$P(S_{12})=P(S_1)+P(S_2)$$

Examples: mass, volume, number of particles...

It is said to be intensive if

$$P(S_{12})\neq P(S_1)+P(S_2)$$

Examples: temperature, density, pressure...

• Thanks for the answer. I wish I could pick up all of the replies:-)! – Dimitris Jan 18 '18 at 13:00