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So i have just started with Classical Thermodynamics..and i am reading Thermodynamics by Bruno LinderSo I could not understand what he means in this portion-

If intensive properties are uniform throughout the system or they are continuous (as air in a gravitational field) then it is called a homogenous system..

So i dont understand when he says continuous.

What does it mean for an intensive variable to be continuous?

If it means that it is a continuous function of something..in that case what is that something ?

Any sort of help will be great Thanks in advance

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    $\begingroup$ A continuous function of position within the system... $\endgroup$
    – lemon
    Mar 27, 2016 at 15:12
  • $\begingroup$ @lemon can you tell how can we define an intensive prop. Say pressure at a point (or a position) ...within the system $\endgroup$ Mar 27, 2016 at 15:15

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Imagine dividing your system into a grid of cells, each with a volume $\delta V$, and pick a single cell centred on $x$. Now multiply that cell an infinite number of times in all directions, like so:

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The standard thermodynamic definition of whatever intensive variable you're interested in (e.g. pressure, temperature, density, concentration, etc) can be applied approximately to the cell centred on $x$ within the context of this infinite ensemble.

If the property varies smoothly (continuously) over space, then you can take the limit $\delta V\to 0$ and get a well-defined scalar field. Note that a continuous property is locally uniform and may therefore be treated as homogeneous.

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  • $\begingroup$ So we do not need the concept of defining that variable at a particular point $\endgroup$ Mar 27, 2016 at 18:08
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    $\begingroup$ @HiteshPathak Sort of. We do assign a variable to each individual point, but it's interpreted to mean its value within an infinitesimal volume $dV$ centred on that point. A bit like the wave function in quantum mechanics, say. $\endgroup$
    – lemon
    Mar 29, 2016 at 7:34

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