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Questions tagged [ideal-gas]

A gas that behaves as randomly moving, non-interacting molecules. This allows a simplified equation of state.

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8answers
1k views

Visualising gas temperature and gas pressure

Gas pressure is created when gas molecules collide with the wall of the container creating a force. Gas temperature is a measure of how fast the molecules are moving / vibrating. However, they both ...
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Euler Equations, Sod shock tube & conservation

Conservation of momentum? I am considering the Euler equations in conservative form and solving the Sod shock tube problem I have written a Godunov finite volume type solver. It solves for density ρ, ...
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Simple explanation of relation between speed of sound and r.m.s. speed?

In an ideal gas, the speed of sound $v_s$ is related to the r.m.s. molecular speed $v_m$ by $$\frac{v_s}{v_m}=\sqrt{\frac{\gamma}{3}} \qquad ,$$ where $\gamma=C_p/C_v=7/5$ for a diatomic gas. I ...
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Can the Sun's core be treated as an ideal gas?

I know that a gas behaves more like an ideal gas at higher temperature, and that is very well achieved in the Sun's core. But also low pressure is needed for a gas to behave like an ideal gas, and the ...
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2answers
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Internal energy of an ideal gas?

From my past studies I have had the presumption that for an ideal gas the equation: $du=c_v dT$ ( where $du$ is the density of internal energy, $c_v$ is the specific heat capacity at constant ...
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How does a gas of particles with uniform speed reach the Maxwell-Boltzmann distribution?

Take an empty container and fill it with $N$ gas particles (ideally a monoatomic gas), each having the same kinetic energy $E$, then isolate the container. Since initially the speeds don't follow the ...
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5answers
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What happens to the temperature when an ideal gas is compressed?

I am rather confused about this. I know from Charles' law that under constant pressure, the volume of a gas is directly proportional to its absolute temperature i.e. $$\frac{V_1}{T_1} = \frac{V_2}{...
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1answer
611 views

7/2 versus 9/2 for diatomic heat capacity

Question I calculated the classical heat capacity of a diatomic gas as $C_V = (9/2)Nk_B$, however the accepted value is $C_V = (7/2)Nk_B$. I assumed the classical Hamiltonian of two identical atoms ...
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$E=kT$ or $\frac32kT$?

Basically, which is the correct formula for thermal energy, and is this the same as kinetic energy? My notes are pretty conflicting on this topic, and I'm getting pretty confused.
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2answers
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Would the temperature of a gas change when accelerated in a train?

I was thinking about a situation where some gas is enclosed inside a container and kept in a train at rest. The train accelerates, gains a maximum speed and then suddenly stops. Would the temperature ...
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4answers
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How long does it take to equalize pressure of two gas containers?

I'm looking for an equation that will tell me how long it takes for two gases at two different pressures to equalize their pressures. As a more concrete question, Container 1 has gas at pressure P1. ...
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1answer
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How do you explain the fact that when air expands freely into an evacuated chamber from a constant pressure atmosphere, its temperature increases?

I came across this paper: Baker, B. (1999). An easy to perform but often counterintuitive demonstration of gas expansion. American Journal of Physics, 67(8), 712-713. http://scitation.aip.org/...
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1answer
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Simpler derivation of Sackur-Tetrode equation

Is there a reason the following derivation for the Sackur-Tetrode equation is not common? I am teaching a lower undergraduate level class and would like to derive it with simpler terms of only using ...
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1answer
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Derivation of the virial expansion

It is easy to derive the ideal gas law form the kinetic theory of gases, but how do you derive the other coefficients of the virial expansion? Is it even possible to get a closed-form formula for the ...
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1answer
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Calculating the entropy of a monatomic ideal gas

I am looking at the start of the consider how to calculate the entropy of a monatomic ideal gas. We need to determine the number of microstates in $E \leq \mathcal{H}(\Gamma) \leq E+\Delta$. The ...
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1answer
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Is there an Ideal Liquid Law? Or Solid Law?

There is an Ideal Gas Law, but why isn't there one for liquids or solids? Is it because they are much too hard to predict or that solids and liquids vary drastically in their reaction to temperature ...
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1answer
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Why do we ignore rotational energy in monatomic gases? [duplicate]

I understand that the average energy of each degree of freedom in a thermodynamic system is $\frac12kT$. And so, for an ideal monatomic gas, there are three degrees of freedom associated with the ...
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2answers
555 views

Is mean kinetic energy related to temperature of a system of interacting classical particles?

I'm trying to intuitively understand what temperature is for a system of classical particles. The usual definitions via Gibbs measure or entropy appear very unintuitive me. But, as for ideal gas ...
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2answers
557 views

Entropy of an ideal gas in $T\to 0$ limit

After deriving the entropy of an ideal gas we get to : $$S = Nk \left[\ln(V) + \frac{3}{2}\ln(T) + \frac{3}{2}\ln\left(\frac{2\pi mk}{h^2}\right) - \ln(N) + \frac{5}{2} \right]$$ In the zero ...
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Limitations of the ideal gas law: When does it fail?

Motivation I ask this question precisely because I am looking for a fundamental, quantitative explanation of the limitations of the ideal gas law and when it should not be used. Note, I have found ...
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2answers
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Derivation of ideal gas law

I looked up on the ideal gas law which our high school textbook derives with the empirical Combined Gas Law. However, the textbook did give a good explanation for this equation $$pV = \frac{N}{3}m\bar{...
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Work done by isothermal expansion from two different viewpoints

Consider an adiabatic system as follows. It consists of a gas in a container and a piston. Initially, the system is at equilibrium and the gas inside it occupies a volume $V_i$ at a pressure $p_i$ ...
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1answer
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How to calculate the buoyant force on a balloon at different altitudes [duplicate]

For a project into balloon simulation I'd like to know how the force on a balloon changes with altitude: I know that the Buoyant force on a balloon is: $F = (\rho_{air} - \rho_{helium})gV$ Using ...
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Do ideal gases at zero Kelvin have potential energy?

Do ideal gases at zero Kelvin have potential energy?
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How to deduce $E=(3/2)kT$?

It says in my course notes for undergraduate environmental physics that a particle has so-called "kinetic energy" $$E=\frac{3}{2}kT=\frac{1}{2}mv^{2}$$ Where does this formula come from? What is $k$?...
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What does it take to derive the ideal gas law in themodynamics?

How can the ideal gas law be derived from the following assumptions/observations/postulates, and these only ? I'm able to measure pressure $P$ and volume $V$ for gases. I notices that if two ...
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3answers
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Differentiating the ideal gas law

In reading Fermi's Thermodynamics, to show that $C_p = C_v + R$, the author differentiates the ideal gas law for a mole of gas ($PV = RT$) to obtain: $PdV + VdP = RdT$. Now, the only way I am able to ...
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4answers
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Why does a gas get hot when suddenly compressed? What is happening at the molecular level?

My guess is that the molecules of gas all have the same speed as before, but now there are much more collisions per unit area onto the thermometer, thus making the thermometer read a higher ...
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Gay-Lussac's Law & the Patriots

This may be a question better suited for xkcd what if? section...but here goes: with all the hoopla around the patriots / colts game and allegations of cheating by deflating footballs, I've read/heard ...
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3answers
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What type of substances allows the use of the Ideal Gas Law?

I know that I can use the ideal gas law with pure gases or pure liquids. But can I also use the ideal gas law at saturated gases and saturated liquids as long as they aren't two phase substances?
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How slow is a reversible adiabatic expansion of an ideal gas?

A truly reversible thermodynamic process needs to be infinitesimally displaced from equilibrium at all times and therefore takes infinite time to complete. However, if I execute the process slowly, I ...
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2answers
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Internal energy of an ideal gas as a function of volume

Okay so I've been reading a bit on Thermodynamics and I found something that I couldn't wrap around my head. For an ideal gas, the change in internal energy is equal to $$\Delta U = Q + W$$ And also,...
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3answers
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Why is it difficult to mix helium and nitrogen gases?

I recently learned an interesting fact: That it's difficult to mix helium and nitrogen gases in a compressed gas cylinder. Gas suppliers that need to mix the two gases have to rotate the cylinders for ...
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2answers
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How is the degenerate electron gas state “degenerate”?

What is "degenerate" in the degenerate electron gas state? Why is it called degenerate?
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2answers
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Canonical partition of a boson gas

I have a 1D gas made of $N$ particles placed in a harmonic potential well, so the Hamiltonian is: $$ \mathcal H = \sum_{j=1}^N \left ( \frac{p_j^2}{2m} + \frac{1}{2}m\omega^2 x_j^2 \right )$$ The ...
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3answers
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Atmospheric pressure, density and temperature variation with altitude

I'm trying to understand how one can calculate pressure, density and temperature of the atmosphere as a function of altitude. My assumptions are mostly sourced from https://en.wikipedia.org/wiki/...
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1answer
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Ideal gas temperature and pressure gradients?

Consider an ideal gas in a $d\times d\times L$ box with the $L$ dimension in the $x$-direction. Suppose that the opposite $d\times d$ sides of the box are held at temperatures $T_1$ and $T_2$ with $...
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1answer
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How fast will sublimed dry ice mix with air?

I saw this photo and wondered: Will the CO2 stay mostly in a layer on the floor with the rest of the atmosphere resting on top, or will it quickly diffuse throughout the room? This lab is probably ...
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How do gas molecules constantly bounce without losing energy?

From a related question (How does pressurized gas constantly push?), i asked myself this: How do gas molecules constantly bounce off each other without losing energy? If you drop a ball, it bounces a ...
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Is gravity Maxwell's demon in disguise?

Maxwell's demon is a thought experiment in which physicist James Clerk Maxwell suggested how the Second Law of Thermodynamics might hypothetically be violated. Basically, a demon controls a small door ...
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4answers
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Does a reversible heat engine exchanging heat with an ideal gas that does a transformation imply that transformation is reversible?

Consider a reversible heat engine working between two sources. Suppose that one of the sources is a thermostat, while the other is an ideal gas which follows a transformation and exchanges some heat ...
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1answer
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Do temperature and kinetic energy depend on overall motion? [duplicate]

Suppose I place a cylinder filled with ideal gas is placed on a train, which starts moving. Does the kinetic energy of the gas molecules increase? Will the temperature of the gas rise as a consequence?...
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2answers
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How does the bulk modulus of air change with rising pressure?

I can't seem to find the answer to what should be a trivial question: I have a rigid air-tight container of fixed volume and I am pumping air inside. The pressure is increasing (very slowly) from ~...
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1answer
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Why is molar specific heat at constant volume of a monatomic ideal gas a constant?

I thought specific heat varies depending on the substance. Why is it always $(3/2) R$?
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2answers
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Internal energy of an ideal gas independent of any thermodynamic variable at constant temperature

https://physics.stackexchange.com/a/199976/170242 In this answer (in the link), it is mentioned that "the internal energy of an ideal gas is independent of volume when considered as a function of ...
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1answer
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What does a sample of the Sun look like? Does it look like fire or gas?

Suppose that in the future a highly resistant spacecraft went to the Sun and collected three samples of the Sun: one from its surface, one from its core, and one midway. The three samples were put ...
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2answers
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Calculating air density lapse with altitude (specifically, pressures)

This might be a bit more of an engineering question, but I'm calculating air density drop-off with altitude, and I'm having some problems calculating the pressure (I'll run through my method). This ...
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1answer
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When to use ideal gas law in fluid mechanics?

The ideal gas law (aka the equation of state) is given by $$ p/\rho_N = k_BT, $$ where $\rho_N$ is number density. When am I allowed to use this to describe a fluid?
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Why Does A Ramjet Produce Net Forward Thrust

So every (non-technical) explanation of ramjets I've seen talks about how the intake slows and pressurizes the incoming air before combustion but then takes for granted the fact that burning fuel ...
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2answers
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RMS Speed of Gas Molecule for Polyatomic Molecules

Halliday in his book and also many people say that RMS speed, $v_{rms}$ is $\sqrt{\frac{3RT}{M}}$. However, he used this formula in showing that kinetic energy, $K$, is $\frac32kT$. but how about ...