Patrick Reany
11 March 2024
I find the treatment of the presentation of the extensive-intensive dichotomy in thermodynamics a bit glib
for my tastes. Certain subtleties get ignored. I discussed my concerns with ChatGPT 3.5
Patrick:
I'd like your comments on an issue I have with the extensive-intensive dichotomy in thermodynamics.
ChatGPT:
The extensive-intensive dichotomy in thermodynamics is a fundamental concept that helps to
distinguish between properties of a system based on their behavior under certain transformations or operations.
Extensive properties are those that scale with the size or amount of the system, such as mass, volume, energy,
and entropy. In contrast, intensive properties are independent of the size of the system and are more related
to its state, such as temperature, pressure, and density.
The distinction between extensive and intensive properties becomes particularly relevant when considering
thermodynamic processes and interactions between systems. Extensive properties generally add up when systems
are combined, while intensive properties remain unchanged. This distinction allows for the formulation of various
thermodynamic laws and principles, such as the conservation of energy and the definition of temperature and pressure.
However, some issues and nuances can arise with the extensive-intensive dichotomy, particularly in complex
systems or non-equilibrium situations. For example, certain properties may exhibit behaviors that blur the
distinction between extensive and intensive, such as surface tension in fluids or certain thermodynamic potentials
in statistical mechanics.
Additionally, there can be debates or differing interpretations regarding the categorization of specific
properties as extensive or intensive, especially when dealing with systems at small scales or in non-standard
conditions. In some cases, properties that are traditionally considered intensive may exhibit dependence on
system size or other factors under certain conditions.
Overall, while the extensive-intensive dichotomy provides a useful framework for understanding thermodynamic
systems and their properties, it is important to recognize its limitations and be aware of the complexities that may
arise in certain contexts. Understanding these nuances can lead to a more comprehensive understanding of
thermodynamics and its applications.
Patrick:
Extensive properties are those that scale with the amount of mass or moles of a substance. This notion
applied to volume makes a lot of sense for fluids and solids, but the trouble comes with gases. I can double
the amount of a gas (say by moles) in a cylinder but keep the volume fixed. I can do this by letting temperature
and pressure vary. This is an issue that doesn't come up with solids and liquids under normal conditions. If we
treat the gas as ideal, then we have the relation PV = nRT. Or we can write P/RT = n/V. Therefore, in this case,
if we want volume to scale with moles, we need to keep the ratio of P to T constant. Comments?
ChatGPT:
Your observation about the treatment of gases in the context of the extensive properties is astute and
highlights an important consideration in thermodynamics, particularly when dealing with ideal gases.
In the case of ideal gases, the relationship PV = nRT (where P is pressure, V is volume, n is the number of
moles, R is the gas constant, and T is temperature) governs their behavior. From this equation, we can derive
the expression P/RT = n/V, which indicates that the pressure times the volume divided by the product of the
gas constant and the temperature equals the number of moles divided by the volume.
As you rightly pointed out, if we want the volume to scale with the number of moles in the context of ideal
gases, we need to maintain the ratio of pressure to temperature constant. This means that if we double the number
of moles of an ideal gas while keeping the volume constant, the pressure and temperature must adjust in such a
way that their ratio remains constant.
This scenario indeed poses a challenge to the traditional understanding of extensive properties, especially
when considering gases. While the extensive property concept generally holds true for solids and liquids under
normal conditions, gases, particularly ideal gases, exhibit behaviors that can complicate this notion, as seen
in your example.
In summary, your observation underscores the need for a nuanced understanding of thermodynamic principles,
especially when dealing with ideal gases and their behavior under various conditions. The extensive-intensive
dichotomy remains a useful framework in thermodynamics, but it requires careful consideration and adaptation
when applied to gases, particularly ideal gases, where properties such as volume may not behave as expected
under certain conditions.
My Comments:
ChatGPT did mostly all right, but it seemed to forget the purpose of holding P/T constant, which is to keep V
scaling with n. Therefore, it is wrong to say that 'while keeping the volume constant'. Instead, it should have
said 'while keeping the volume scaling with n' or 'while doubling the volume'.