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The short answer is ideal gas behavior is NOT only valid for hydrogen. The statement you were given in school is wrong. If anything, helium acts more like an ideal gas than any other real gas. There are no truly ideal gases. Only those that sufficiently approach ideal gas behavior to enable the application of the ideal gas law. Generally, a gas behaves more ...


39

The school question is wrong. What were they thinking? (My guess is that it was a simple slip-up and they meant helium.) The ideal gas equation of state works for any gas in the limit of low density. In order to give a quantitative estimate of how well the equation models a gas, one can compare it with measurements or with other equations which do a somewhat ...


27

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 using that term for unbound atoms. If you have a container of He, there are no "molecules" in it. So when it says "molecules or atoms", it means "molecules or ...


25

One important answer is simply that experimentally ignoring the interaction with the walls is clearly a terrible approximation. If that were true any gas would instantly escape from any container we put it in. More theoretically, an idea gas does not assume there are no interactions between particles, it assumes that the interactions have 0 range (i.e. the ...


21

If gas A and gas B are of different density, then the situation sketched is not in equilibrium: the water level on the side of the light gas will be higher. There, the containers are moving down, and you have to push your containers through this net difference in level. You do need to put in energy here, which is probably the piece that you are trying to ...


20

When they say "assume interactions are negligible," they really mean "assume the only interaction is when they elastically bounce off each other". What this really means is you are ignoring any attractive or repulsive force between the molecules, but you are allowing them to bounce off each other like billiard balls. You make the same approximation for the ...


18

There's actually not one simple answer to your question, which is why you are a bit confused. To specify your problem fully, you must specify exactly how and whether the gas swaps heat with its surroundings and how or even whether it is compressed. You should always refer to the full gas law $P\,V=n\,R\,T$ when reasoning. Common situations that are ...


17

Ideal gas In thermodynamics, the fact that the energy of an ideal gas depends only on temperature is an experimental observation from the free expansion of a diluted gas (which is approximately ideal) 1. In statistical mechanics, it can be proven 2. Ultimately, the reason is that the atoms of an ideal gas are non-interacting point particles. They only ...


16

The internal energy of an ideal gas is independent of volume when considered as a function of volume and temperature. If we choose to consider internal energy as a function of volume and some other thermodynamic variable we will find that the dependence of the energy on volume will change because we are keeping a different variable constant as volume is ...


15

You have to realize first that Charles' law is the change in volume with respect to temperature for constant pressure while Boyle's law is the change in volume with respect to pressure for constant temperature. So when you combine them, you need to account for these If I take a gas of volume $V_1$, pressure $P_1$ and temperature $T_1$ and let it change have ...


15

When most gasses dissolve into a solution it's an exothermic process. The gas molecules give up energy to do so. An increase in temperature leads to an increase in kinetic energy. Higher kinetic energy causes the gas molecules to break their intermolecular bonds and escape from solution. Note I say solution and not water. It's not just water that has this ...


15

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 explicit parameters for both behaviors. Compare the equations of state for these two models \begin{align} Pv &= k_B T \tag{ideal gas} \\ \left(P + \frac{a}{v^2}\...


14

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 colliding particles the momentum remains the same. Each pairwise collision has a different center of mass. In the laboratory frame, which is the frame one is ...


13

The joule is the amount of energy needed to apply one newton of force for a distance of one meter: $$ \rm J=N\cdot m=\frac{kg\,m^2}{s^2}\tag{1} $$ Where the 2nd equality comes from the definition of the newton (mass times acceleration): $\rm N=kg\,m/s^2$. The pascal is defined as one newton of force applied to a one-square-meter area: $$ \rm Pa=\frac{N}{m^2}=...


13

This formulation of Boyle's law $$PV=\text{const}$$ is very misunderstandable. Actually the constant on the right side is only meant to be independent of $P$ and $V$. But it may still depend on other parameters, like $T$ (temperature) and $N$ (number of molecules). So a better way to write this law is $$PV=a(T,N) \tag{1}$$ where $a(T,N)$ is some unknown ...


13

The connection is simply this... Van der Waals postulated that there were attractive forces between gas molecules even when these weren't in contact. The $a/V^2$ term in his gas equation is a simple way to take account of such forces, without knowing how they vary with separation between molecules, beyond their being short-range. We now know that these ...


12

The fog you are seeing is condensation of atmospheric water, not sublimed $CO_2$. The water fog is made very near the boiling surface, and then sinks slowly, exactly as it does in rainclouds. Therefore, just because you can see fog gathering on the floor does not mean that the $CO_2$ is confined there. The $CO_2$ molecules have a speed, in random directions,...


12

The equation $$PV^{γ}=Constant$$ Or $$P_{1}V_{1}^{γ}=P_{2}V_{2}^{γ}$$ Is for a reversible adiabatic process. The free expansion is an irreversible process. $$P_{1}V_{1}=P_{2}V_{2}$$ Only defines the end points at equilibrium for an ideal gas. It is not the same as $$PV=constant$$ which describes an isothermal process, the path between the end points....


11

If your an engineer and your looking for a material to spin your turbine, your goal should be to maximize pressure and minimize temperature. Well no. Temperature is generally a constraint of your heat source, and your goal is to maximize profit. That goal does, however, map to physical properties in logical ways, but it's much more complicated that what ...


11

Constants in physics are not just unit matching things. They are actually very fundamental. Yes, it is an heuristic and easy way to explain constants as unit keepers and I have nothing against that; but constants represent a sort of privileged group in nature. They are like symmetry points were everything moving around most do so in a way to keep their ...


11

The ideal gas law is routinely used in engineering for calculations regarding air, natural gas, water or other vapor, ICE exhaust gases and almost everything that is sufficiently away from condensing pressure/temperature and some other conditions like the molar volume not being too low. It works. The condition "sufficiently away from condensing pressure/...


11

If you write $pv = RT$ then $v$ is the molar volume i.e. the volume occupied by one mole of the gas. We often do this because we don't know or aren't interested in exactly how much gas is present. For example if you were calculating the properties of air you don't need to know the total amount of air in the whole atmosphere. If you write $pV = nRT$ then $V$ ...


10

According to a NASA page, the density in the middle of the Sun is about 150 g/cm3. That's about 9 × 1025 protons in a 1cm3 box, or 450 million to a side, and using that spacing for a voltage calculation reveals a typical interaction energy of 65 eV or so. (If you've never seen this unit before, that is the energy used by a 1V battery to move an electron's ...


10

The potential energy for a diatomic molecule is not $$ U(\vec{q}_1, \vec{q}_2) = \frac{\alpha}{2} |\vec{q}_1 - \vec{q}_2|^2 $$ but is instead $$ U(\vec{q}_1, \vec{q}_2) = \frac{\alpha}{2} (|\vec{q}_1 - \vec{q}_2| - r_0)^2, $$ where $r_0$ is the equilibrium bond distance. The important difference here is that in your version, any displacement of the vector $\...


10

Even if initial speed of all the particles was same, the molecular collisions will disrupt this uniformity. I want to show this happens based on a diagram (on the left) from one of Maxwell's papers. The centre and right diagrams are for two particles with the same mass travelling at the same speed $u_1 = u_2$ and for ease of presentation it is ...


9

There are two main groups of processes leading to atmospheric escape: thermal and non-thermal processes. The first group includes Jeans escape, where particles with high thermal energies (and thus high kinetic energies) manage to reach speeds in the upper atmosphere greater than escape velocity. The equation for the Jeans flux for particles of mass $m$ is $$\...


9

Experimentally it has been found that dissolution of a gas in a liquid is an exothermic process. Gas + Liquid -> Gas/Liquid + heat (∆H = -ve) ....(i) So according to Le Chatelier's principle, if I decrease the temperature, the reaction will move in that direction which doesn't let this change (decrement in this case) take place. For that to happen the ...


9

Ideal gas law works best for monatomic gasses at low pressures and high temperatures. It doesn't take into account molecular size and intermolucular interactions, so when the effects of those are significant, then the equation will be less accurate. It generally works well for gasses like air in the temperatures and pressures we are used to (air has a ...


9

The speed of sound is defined as $c^2 = \frac{\partial p}{\partial \rho}$, which for an ideal gas becomes $c^2 = \gamma \frac{p}{\rho}$. For a real gas, the relationship to an ideal gas can be found through the compressibility factor $z$. This is a measure of how much a real gas deviates from an ideal gas. It shows up in the equations as: $$ P = z \rho R ...


8

Chemical factors The more "localized" the electrons are the higher frequencies they naturally vibrate at (like a shorter guitar string playing a higher note). Gases must be simple, small molecules otherwise they would condense. Small molecules can't have electrons that are delocalized over many atoms. All substances have tightly localized electrons that let ...


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