# Tag Info

### If temperature is amount of kinetic energy of particles, then how can there be a cold breeze?

The average speed of an air molecule can be approximated by the following equation, which is exact only in the case of an ideal gas: $$\langle v \rangle = \sqrt{\frac{2RT}{M}}$$ This means at $25$°C ...
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### If liquid and gas are both chaotic states of matter, what's the difference between them on the molecular level?

Everything you've said is correct, which is why the conclusion is: there is no fundamental difference! Under the modern classification, they're just the same fluid phase of matter. For example, ...
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### If liquid and gas are both chaotic states of matter, what's the difference between them on the molecular level?

The described measurement would allow you to construct the Radial Distribution Function, the probability of finding another particle a distance r from a reference particle usually given as g(r), which ...
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### Why does the ideal gas law exactly match the van't Hoff law for osmotic pressure?

The law $PV = n RT$ gives the pressure $P$ of $n$ moles of ideal gas in volume $V$. Meanwhile, the law $\Pi V = n R T$ describes the osmotic pressure $\Pi$ due to $n$ moles of solute in volume $V$. ...
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### Why does it take so long for a gas to reach a thermal equilibrium?

The mean-free path of a nitrogen molecule in air at STP is about 60 nm, so the molecules may travel quite quickly, but they do not go very far before the run into another molecule and get stopped.
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### Is Avogadro's law applicable for atoms or just for molecules?

I notice that online definitions of this experimental law always say, molecules or atoms. The problem with just calling them all "molecules" and being done with it is some are uncomfortable with ...
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### Why does pressure increase with water depth?

The problem is that you're modeling the liquid like an ideal gas, whose molecules independently bounce off the ball, but liquids are characterized by strong interactions at short distances. A better (...
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### If liquid and gas are both chaotic states of matter, what's the difference between them on the molecular level?

In a gas the molecules move separately. In a liquid they cling together due to van der Waals forces which are strong enough that the vibrating molecules do not completely separate.
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### How many types of specific heat can a gas have?

The question may be aiming to expand one's scope beyond what's considered in introductory textbooks. This is the essence of scientific research. The heat capacity $C_X$ at a condition of constant $X$ ...
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### Does the term "diatomic ideal gas" make any sense?

Of course it does. It helps a little bit to compare the ideal gas to a model that does take note of the size of the molecules and the forces the exert on one another. The van der Waals gas has ...
Accepted

### Why can't the molecules of an ideal gas have the same speed?

No you cannot. we can show that (via conservation of kinetic energy and momentum) the speed of the particle before and after collision is the same. Only in the center of mass of two elastically ...
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### Is the Navier-Stokes equation valid in $d=2$ spatial dimensions?

There has actually been a fair amount of activity in this area recently, see, for example, this set of lecture notes. I would argue that the answer to your question is, "yes", if properly ...
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### Relaxation of the Boltzmann transport equation

If uniform distribution is promised as equilibrium, it means the zero external force $\mathbf{F}$, which means that the $\nabla_\mathbf{p}f$ can have any value. without violating the equation. As an ...
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