My teacher explained to me that we volume is an extensive property because it is additive in nature. But he also told us that pressure is an intensive property. Now according to the gas law equation $PV=nRT$, pressure is dependent on volume. Increasing pressure should increase volume. So shouldn't pressure be extensive as well.
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asked Nov 15, 2015 at 12:28
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4$\begingroup$ Possible duplicate of How is pressure an intensive coordinate? $\endgroup$– user36790Nov 15, 2015 at 12:40
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$\begingroup$ Increasing P will decrease, not increase, V for constant T and n. $\endgroup$– RolNov 15, 2015 at 12:58
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$\begingroup$ Look at the right hand side, $nRT$. It involves a physical constant ($R$), an extensive variable ($n$), and intensive variable ($T$). The left hand side, $PV$ must similarly involve the product of an extensive variable and an intensive variable. The extensive variable is $V$. $P$ must be (and is) an extensive variable. The ideal gas law is a linearized idealization. You'll rarely see the product of two extensive variables in thermodynamics because the result would inherently be non-linear. $\endgroup$– David HammenNov 15, 2015 at 13:01
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$\begingroup$ The mistake is that you are expecting $p$ to change when $V$ changes and at the same time assuming that the rest of the parameters ($n$ and $T$) are constant. But why not the other parameters? What if it is $n$ that changes with changing $V$ while the rest ($p$ and $T$) are constant? The point is that this argument doesn't hold. Extensive and intensive properties are not defined by the ideal has equation. $\endgroup$– SteevenNov 15, 2015 at 13:32
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2 Answers
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From the ideal gas equation,
$$P=\frac{nRT}{V}$$
Now assuming the gas is uniformly distributed over space (has constant density for a given temperature), halving the number of moles will divide the volume by the same amount. Essentially, if we divide the number of moles by any number, we will end up dividing the volume by the same number to maintain constant temperature. So it doesn't matter how many moles of gas you take at a given temperature, you will always end up with the same pressure. You could also look at it as ratio of two extensive quantities will always give an intensive quantity.
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$\begingroup$ What if the density varies? Then both pressure and density would be extensive properties? $\endgroup$ Feb 7, 2020 at 19:48
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$\begingroup$ If gas is in a box , volume is fixed , and if we decrease moles , pressure decreases. Doesn't that make it extensive? $\endgroup$ Jan 15, 2021 at 18:24
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1$\begingroup$ The definition of extensive/intensive property of a system is that the property changes/doesn't change if we take part of it from the whole for a given system. If you vary the density, or the number of moles inside whole system then it is no longer the same system. Here, the volume of the whole system is the same throughout our analysis. We're looking at parts of the volume as some fraction, say V/2, and trying to find out what's the pressure in that volume considering it's still the same system. We're not changing the volume, number of moles or the density. $\endgroup$– SkawangJan 16, 2021 at 18:58
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Its because if we divide the container in two halves then the volume of the gas will also get half. But the pressure applied on the walls of both the containers will be same.
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$\begingroup$ But, if volume gets halved, pressure should theoretically and practically decrease. $\endgroup$ Oct 12, 2016 at 6:33
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