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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Derivation of pressure in the kinetic theory of gases
According to Wikipedia,
The pressure exerted by the collisions of the N gas particles with the surface can then be found by adding the force contribution of every particle and dividing by the ...
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Discrepancy in the Derivation of Maxwell-Boltzmann Distribution
I am reading Maxwell-Boltzmann distribution for describing the velocities of ideal gas molecules. I went through the PSE question Derivation of the Maxwell-Boltzmann speed distribution and the ...
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The mean kinetic energy of a gas particle
I'm in undergraduate stat mech/thermo. In the context of the Maxwell-Boltzmann distribution, the mean kinetic energy of a gas particle is $\langle KE \rangle = \frac{1}{2}m \langle v^2 \rangle$.
I do ...
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Counting Microstates to get the Entropy Generation in Free Expansion of an Ideal Gas
In Elliot and Lira's Introductory Chemical Engineering Thermodynamics on p.134,
the authors derive the entropy generated from an ideal gas expanding from a volume V to 2V, by the removal of a ...
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Does the density form of Ideal gas law hold under condition of changing mass?
I'm trying to get a deeper understanding of this particular form of the ideal gas law I have seen. That form is $P=\rho R T$. I believe this form is not valid when mass or volume is changing. Am I ...
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Could compression make gas colder not hotter?
In classical thermodynamics compression always makes gas hotter because of the mechanical work it inputs. However, if the particle density is too high, particles will become degenerate and obey the ...
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Trouble understanding why ideal gas law explains that can of compressed air gets cold when you spray it [duplicate]
I was told that a canister of compressed air gets cold because of the ideal gas law, you are lowering the pressure and since the density of air is the same, the temperature of the can gets cold. I was ...
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Determine the entropy of an ideal bosonic gas
I am struggling with this problem.
So we're told that any macroscopic state of a gas can be characterized by microscopic stated of a single particle. We divide the microscopic states into groups. So $...
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Validity of $C_p-C_v = R$
This might be a very novice question but i got confused over derivation of $C_p-C_v = R$ which is derived using $dQ= n C_p dT,$ which is valid only for isobaric process. Thus $C_p-C_v = R$ must also ...
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Why does the temperature of an ideal gas decrease when expanded? [duplicate]
I understand that when an ideal gas is compressed using a piston, the piston does work on the gas and increases the gas's kinetic energy (so temperature). However, I do not understand why a gas is ...
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When to use multivariable chain rule in thermodynamics?
If I take $U(P,V)$, I can do:
$$ \frac{dU}{dT} = \frac{\partial U }{\partial P } \frac{dP}{dT}+\frac{\partial U }{\partial V} \frac{dV}{dT} \tag1$$
But, I see the following used in books,
$ dU = ...
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What would be the pressure, temperature and density gradients with altitude of atmosphere with ideal gas?
What would be the pressure, temperature and density gradients with altitude of atmosphere with ideal gas considerations? That is no convection or radiation.
Most of the answers I have seen are ...
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Entropy change due to surroundings?
What is the entropy generated by opening up a vacuum chamber of volume $V$ to the atmosphere? (let's say with some constant ambient pressure $P_{atm}$)
I was reading about Joule expansion, but it ...
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Mass balance for gas in a fixed volume
I am trying to generate an equation that describes the mass balance of a gas in a fixed volume. The application is simulating the sweep out time of the cell in a laser-based instrument which measures ...
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Temperature increase in fixed volume due to gas injection
I have a vessel of fixed volume with adiabatic boundary which is initially filled with air at pressure of 1 atm and temperature of 300 K. Now, I inject air from an external source at a fixed flow rate ...
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Modeling of an ideal gas from a Classical Mechanics perspective
Say we have a box with a (large enough) side $L$ in which there is are $N$ indistinguishable particles, each having a speed $\vec{v}_i$. Let us also say these particles don't interact with eachother ...
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Virial Theorem for Gas Particles
My statistical mechanics professor stated the Virial Theorem as
\begin{equation}
\langle K \rangle = -\frac12 \sum_{i=1}^N \langle \mathbf{F}_i\cdot \mathbf{r}_i\rangle
\end{equation}
For an ideal gas ...
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What is the internal pressure of a tethered hot air balloon?
This question is for the review portion of a thermodynamics class:
A small hot-air balloon has a volume of $15.0 m^3$ and is open at the
bottom. The air inside the balloon is at an average ...
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Leaking gas tank
Say we have a rigid tank of nitrogen gas ($N_0$ molecules) at temperature $T$. The tank is in vacuum. If we now punch a small hole on the tank, the gas will leak. Assume the hole is small enough so ...
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Principal of maximum Entropy (Two ideal gases in mechanical contact) [duplicate]
Consider a container with Volume V. The container is seperated by a non-movable, impearable wall, which allows heat flow. Both subvolumes are filled with an ideal gas. We can obtain informations about ...
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What is the most general and accurate real gas equation?
I've been presented in my thermodynamics course with both the ideal gas and Van der Waals state equations for the study of gases, being the latter more accurate in measurement than the first one.
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Why can we not describe matter as an ideal gas when the gas is degenerate
When a low mass stars core mostly consists of helium (after years and years of fusion reactions) its thermal pressure decreases and so the core gets denser due to gravitational pressure.
Why is it ...
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Justify uniform density of ideal gas at thermal equilbrium
I'm trying to convince myself that an ideal gas in an arbitrarily-shaped, zero-gravity, closed container has uniform density in space at thermal equilibrium, where I define an ideal gas to consist of ...
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Doubt regarding kinetic theory of gases
My school teacher had told me that one of the assumptions of Kinetic Theory of Gases was that the molecules of a given gas were all identical and to be considered as very small elastic spheres. ...
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Validity of the equation $dQ=CdT$ in different cases
I know this question may be too simple so I apologise for that but nonetheless very necessary. In my class we have defined the heat as $$\delta Q=CdT$$ with $C$ the heat capacity, but I'm unsure if it ...
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Would removing all nitrogen from the air cause altitude sickness effects?
The total pressure in the lungs is close to the external pressure of 101kPa, i.e. breathing requires little delta-P.
The removal of all nitrogen in the air would not change the 20kPa partial pressure ...
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Why expansion of real gases lead to cooling?
Paul Hewitt writes in his book
Expansion of real gases lead to cooling as average translational kinetic energy per molecule decreases.
The reason given is:
During Expansion molecules collide with ...
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Collision frequency of a 3D object in a container
Might be a silly questions but I had a thought while learning about the collision frequency of gas molecules on a single surface of a container using kinetic theory. For a 3D object in the container, ...
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Find the ideal gas law from the internal energy [closed]
I'm looking for a way on how to obtain the ideal gas law $PV=nRT$ by being given the internal energy $$U=U(S,V)=\alpha N k_b \left(\frac NV\right)^{2/3} e^{2S/(3Nk_b)}$$ I can find the pressure and ...
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What's happening in this approximation for the equation of state of an ideal gas of bosons
The way we arrived at the equation of state for an ideal fermion gas was to approximate the right handside of $$\beta PV=\sum_{\vec{p}}\log{(1+fe^{-\beta\frac{p^2}{2m}})}$$
as $$\frac{V}{h^3}\int \log{...
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Sackur-Tetrode eqation becomes negative
The Sackur-Tetrode equation, tells us the entropy of of an ideal microcanonical gas.
It looks like this:
$S(E,V,N) = kN\text{ln}(\frac{V}{N}(\frac{E}{N})^{3/2})+ kN\cdot c(m)$
Now let's fix the mean ...
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Mixing entropy for ideal gases is decreasing
Consider two ideal (microcanonical) gases with particle number $N_{1/2}$, energy $E_{1/2}$ in a box with volume $V$. Also let's assume $\frac{E_1}{N_1} = \frac{E_2}{N_2}$.
Let's call the corresponding ...
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Why is $\delta U$ not zero in $\delta H = \delta U + \delta(PV)$ while defining at a constant temperature for an ideal gas?
I was studying thermodynamics and came across the relation between change in internal energy and the change in enthalpy for an IDEAL gas, meaning $U=f(T)$ and not $f(T,V)$.
Then, while defining it for ...
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Can a fixed amount of ideal gas undergo a reversible process when 2 of either pressure, volume, or temperature are held constant?
I've seen some problems where this was the case: a fixed amount of ideal gas underwent a reversible process where temperature varied while pressure and volume were both held constant. How could that ...
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How would I calculate the heat change of compressed air?
My friend is working on a snow gun, which involves using compressed air to blow apart water coming out of a pressure washer. I read that you can cool air by compressing it, which makes it hot, then ...
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$U = (3/2)nRT$ proof on Khan Academy [duplicate]
I’m in the middle of the thermodynamics unit with my AP Physics 2 students and I’m attempting to understand how the expression for total internal energy of an ideal gas is derived.
I’ve taught for 15 ...
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Pressure in a container with constant outflow
Given is a container with a volume of 100 cubic meters. The content (CO2) is under a relative pressure of 100 mbar and has a constant temperature of 35 °C.
A constant flow of 60 cubic meters per hour (...
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What is the average distance $\langle r \rangle$ of a particle in an ideal gas in a potential from the origin?
I have an ideal gas in three dimensions of N identical particles with mass $m$ in a potential $u(\textbf{q})= \alpha ||\textbf{q}||,$ where $\alpha>0.$ The Hamiltonian is
$$
H(q^N, p^N) = \sum_{i=1}...
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Partial pressure and Le Chatelier Principle when external pressure is increased
Suppose I have a container of ideal gases $A,B$ and $C$ with a chemical reaction taking place, say the following,
$$
A+B \rightleftharpoons C
$$
Now Le Chateliers principle states if the overall ...
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Does internal energy depend only on temperature?
In isothermal expansion of an ideal gas, $ \Delta U=0$ because there is no change in temperature.
But at 290K, if we compare the internal energies of Nitrogen, Neon and Ozone, Ozone has maximum ...
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Extension of classical first law of thermodynamics
The first law of thermodynamics is typically stated as conserving total energy in the context of a heat engine running on an ideal gas (or other gas whose equation of state is known). However, I read ...
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Does collisions of ideal gas molecules effect its equation of state?
I have been reading Statistical Mechanics by R. K. Pathria & Paul D. Beale , 4th edition . In this book they used a quantity called Virial , which is defined as $\mathcal{V} = \langle\Sigma q_iF_i\...
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Pseudopotential model to reproduce quantum statistics from ideal gas
A pseudo-potential $V_{12}$ between every pair of particles in an ideal gas is to be constructed which will reproduce the effects of quantum statistics if the gas particles are bosonic in nature. A ...
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When does steam or any gas be deemed ideal gas?
I am studying a chapter on pure substances in thermodynamics book by Yunus Cengel, where the author explains that a gas or vapour can be treated as ideal gas, when the temperature is sufficiently ...
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Can the pressure distribution seen in a Venturi tunnel be explained on a molecular level?
If we consider the flow of an ideal gas through a Venturi tunnel and we assume it to be incompressible we can show through mass conservation that the velocity must increase as area decreases and vice ...
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What does reduced saturation pressure mean in acentric factor?
I'm currently learning about acentric factor and I don't understand what P_r^sat means... Is there a saturation pressure at critical point? Moreover, is the reason for setting reduced temperature as 0....
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Can we apply thermodynamics processes for real gas too? And how
Like in adiabatic process there is closed system but in reality we know there is no such thing as closed system there will be still exchange of heat so it will not work adiabatically means it is only ...
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Statistical mechanics of a gas in a rotating cylinder
The theoretical premises that allow us to study the statistical mechanics of a substance in a rotating equilibrium are not completely clear to me. For example, consider a gas ($N$ non-interacting ...
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Work done by adiabatic expansion derivation
I know that $W=-C_v(T_2-T_1)$ for an adiabatic expansion, and I know how to derive it. However, in this video (https://youtu.be/gaZmZjBtgAM?si=Px3v2qDG3CIdupgi&t=358) it mentions the formula $W=-\...
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How does refractive index of an ideal gas depend on temperature, pressure, and density? [duplicate]
Is there a reasonably simple (pen and paper) yet good approximation for the refractive index of an ideal gas as a function of temperature, pressure, and density. How would one derive this?
Thanks for ...