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-1

The gas gets hotter because the energy has no where to go and it must convert into heat. The molecules bounce back and forth with one another creating more and more energy and less space, so the molecules began to compress through the helical rotors.


1

Air pressure exists because if we place something in a gas, then the molecules/atoms flying around will keep banging into it, and in this way produce a net constant force per unit area. As explained by @Chris2807 in the neat formula $P=n k_{B} T$, this is proportional to how many particles there are (since this is proportional to the amount of "banging" in ...


3

In some sense yes. Let me explain a little. If we were to take a sealed container of gas and put it into free space far away from other bodies so that the gravitational force on the box is negligible would you agree that there would still be some pressure in the container? If we assume we have an ideal gas then the pressure is simply given by $$P=nk_{B}T$$ ...


3

In general, air pressure in the Earth's atmosphere is hydrostatic pressure, caused by the Earth's gravitational field. If there was no gravity then there wouldn't be any centripetal force and all the air molecules would just float away into space. This is why there is no atmosphere on the moon - because it doesn't have enough gravity to sustain one.


0

I think the $\Omega_N$ in your question is the number of states inside an energy sphere $E$; Now we need to consider micro-canonical ensemble, which means we need to get the number of states in an energy shell between $E$ and $E+\Delta$: $\Omega'=\frac{1}{N!h^{3N}} V^N \frac{\pi^{3N/2}}{(3N/2)!}\{[2m(E+\Delta)]^{3N/2}-(2mE)^{3N/2}\}$ Which is equal to: ...


3

The thermal energy $k_{B} T$ is really referring to the probability of finding a system in a state of energy $E$, given that it is in a surrounding enviroment at temperature $T$. This probability is proportional to $e^{-E/(k_{B} T)}$. Using this you can derive a great many things, including the Boltzmann/Fermi distributions. The proportionality constant is ...


5

Giving the value simply of $k_B T$ is generally more useful, because I can plug that into anything. Sure, I might need to know the ideal gas energy, and multiply by $3/2$. But maybe I need to put it into a partition function, and I just need $k_B T$. Maybe I'm worried about a harmonic oscillator and I just have the two degrees of freedom. The 3/2 is ...


3

In gases, under normal conditions, the average distance between molecules is large compared to size of the molecules so the molecules spend most of their time far apart. Interactions between molecules, or at least strong interactions between molecules, tend to be short range. This means that interactions between molecules don't have much effect on the ...


0

The reason why a gas heats up when it is compressed into a smaller space, is because the ambient heat that the gas possessed in its original volume, has now been confined to a smaller volume—same amount of heat but now more concentrated—the temperature goes up. When the vessel storing the newly compressed gas cools off to the ambient temperature of its ...


1

Sounds like constant amount of substance (as in the dimension or physical quantity, "mol" being it's unit). Could also mean mass, but mass is often not strictly constant. If you add energy (e.g. heat), the mass of the gas increases slightly via E=m*c2. Could you provide more context?


0

In thermodynamics physicists and engineers use the concept of 'control volume' that specifies a bounded region of space in which thermodynamic properties of a gas are analyzed. The boundary of the control volume can be used to either isolate or otherwise define a specific flux of energy and/or matter to/from the control volume. I believe the "fixed ...


0

I had thought that if you placed two electrons in a vacuum that they would accelerate away from each other without limit. However after speaking to shminux I realised that although they accelerate forever they reach a limiting velocity which depends on their potential energy. So the particles in my sim will reach a limited v. Problem was v was too large ...


0

First law of thermodynamics is the extension of Law of Conservation of Energy for non-isolated system. There are two forms of first law of thermodynamics(both are actually same): Followed by physicists best suited for dealing with heat-engines: $$\partial E = \partial q - \partial w$$. Here $\partial w$ is the work done by the system. Followed by chemists ...


2

Consider a container containing n moles of an ideal gas. The gas exerts a pressure P on the container and the piston. If P equals the atmospheric pressure, then the piston does not move, as it experiences equal forces from in and out of the container. When you increase the external pressure, the gas in the container is compressed. If the compression of the ...


3

At constant pressure the volume of an ideal gas is given by Charles' law: $$ V \propto T $$ and this law tells us that when the temperature $T$ falls to zero the volume $V$ also becomes zero. But no gas is ideal and real gases show all sorts of non-ideal behaviour. For example real gases liquify then solidify as the temperatue falls. Real gases deviate ...


2

The distribution of speeds in an ideal gas is given by the Maxwell-Boltzmann distribution. There are a variety of average speeds e.g. the most probable speed, the mean speed and the root mean square speed. Which one you use will depend on the application. The two equations you give are for the RMS speed: $$ \sqrt{\langle v^2 \rangle} = \sqrt{\frac{3kT}{m}} ...


1

The equations above thus represent conservation of mass, momentum, and energy. Mass density, Flow velocity and pressure are the so-called physical variables, while mass density, momentum density and total energy density are the so-called conserved variables. So three unknowns, right? Actually, there are four variables: density, velocity, pressure ...


0

Charle's Law: $\frac{V}{T}=k$ The idea is that, given an ideal gas, as the temperature rises the system instantly responds by balancing the potential increase in pressure with an actual increase in volume. In the case of the piston, you can easily measure the work done by measuring how much the piston moved. But in a general case: $dW = Fdx$ $Fdx$ or ...


0

Steam is just gaseous H2O. Here is a Chemkin format curvefit: H2O V1C1 Curve-fit from ChemKin V-0.1450E-04 0.3855E-06 0.6725E-11-0.2230E-13 0.6445E-17-0.8578E-21 0.4490E-25 C 0.1921E+03 0.5710E+01 0.8708E-02-0.3621E-05 0.7376E-09-0.8109E-13 0.3761E-17 and a NASA curvefit: H2O ...


4

To a reasonable approximation steam at 100°C can be treated as an ideal gas. The molar volume of an ideal gas is 22.4 litres, so at 0°C (273K) and one atmosphere 18g of steam occupy 22.4 litres or in more useful units 0.018kg occupy 0.0224 cubic metres. You can work out the volume at 100°C (373K) using Charles' Law, and then calculate the density of steam at ...



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