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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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Infinite entropy in ideal gas

Does it make sense that entropy goes to infinity as temperature goes to infinity? For an ideal monoatomic 1D gas I have an expression for entropy \begin{equation} S=Nk_{B}Ln(\frac{Ve^{\frac{5}{2}}\...
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Would setting the ideal gas constant to $1$ yield an attractive natural temperature scale? [on hold]

In this recent question, there was a comment 'The "zero point" of Kelvin is natural, but the scale is not'. This led me to wonder whether setting $R = 1$ in the ideal gas law would be an attractive ...
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Conversion of $R = 8317\ \mathrm{\frac{J}{kg\cdot mol\cdot K}} $ to $ 8317\ \mathrm{\frac{J}{kg\cdot mol\cdot {^\circ C}}}$

I'm trying to understand the unit conversions when one unit is obtained by shifting the value of another one by some constant. In particular, the unit conversions from Kelvin to Celsius scale: $$T(\...
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Why doesn't the equipartition theorem force the rotational energy of a monoatomic molecule to be significant?

I'm reviewing the Feynman Lectures and in them he states that the rotational kinetic energy of a monoatomic molecule in a gas is insignificant due to a small moment of inertia. But wouldn't the ...
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Transfer of gas particles during pressure change

There is a room with a known volume. The temperature and pressure are known too (STP). It is given that the window is open and there will be a pressure drop outside due to wind. I need to find the ...
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Collision frequency of ideal gas and velocities of molecule

Is collision frequency of gas molecule $ = \frac{V_{RMS}}{\lambda}$ where $\lambda$ is mean free path. Shouldn't it be $\frac{V_{average}}{\lambda}$? (I often see that in theories books suggest that ...
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Thermodynamics problems with a cycle (insufficient data?)

I am having some troubles in solving the following problem a professor gave us, and in my opinion I think that either there are insufficient data or the solutions are infinite. We have a perfect gas,...
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Question about a hand-waving estimation done by Landau

I was reading the book written by Landau on statistical mechanics (Statistical Physics I 3rd Ed). In §1 there is a footnote that Landau wants to illustrate how accurate a statistical average can be ...
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Does the ideal gas law apply to a moving vehicle?

If for example you have a car travelling along a road. There is obviously a high pressure region in front of the car, where the air is forced around the vehicle. Likewise, I understand that cars will ...
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How to calculate the actual pressure in chamber with reduced pressure but at increased temperature?

I would like to find out the actual pressure in a chamber (constant volume) where the pressure within is reduced to 1.5 kPa but with increased temperature to 65˚C. How to calculate this? Assuming 0....
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Kinetic Molecular theory ideal gases, deriving the equation $PV = \frac{1}{3}mN C^2$

The problem I have with this proof is how to acquire the fraction $\frac{1}{3}$. In theory we were taught by taking into consideration a rectangular vessel which obviously has three paths which a ...
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Momentum average on phase space for free particle

I'm studying from Greiner statistical mechanics, and he uses an approximation which I don't really understand. On averaging over many phase-space points we have $$\langle\vec{p}^2\rangle=3\langle ...
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Entropy density (entropy per particle)

How I can get this definition for an ideal gas: $s=C v \ln (Pρ^{−\gamma})+ \text{constant} $ ? In this answer it is mentioned that there is a connection with the Sackur-Tetrode relation of the ...
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Ideal gas equation vs Kinetic theory equation

From the ideal gas equation: $PV = NkT$, since Pressure times Volume = Energy, my understanding is that the total (internal) energy of $N$ molecules of a gas $= NkT$. However from the kinetic theory ...
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What is the PDF of relative collision speeds in an ideal gas?

In the Kinetic theory of gases, the speeds of particles follow a Maxwell-Boltzmann distribution. However, what if one is interested in the distribution of relative collision speeds, aggregated over ...
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Do atoms in an ideal gas ever collide?

According to Wikipedia: An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interactions are perfectly elastic collisions. The ideal gas concept is useful ...
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Derive the kinetic gas equation [closed]

I need a proof of high school level I have confusion in taking probabilities in all directions not yet concluded this, and I need a proof using momentum i.e I need a high school level proof
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Why is $dE = C_V dT$ for an ideal gas, even when the process is not constant volume? [duplicate]

I have come across the following derivation for the "equation of an adiabat for an ideal gas" in many textbooks. The following steps are referenced from a separate question: dE=dQ+dW dW=−pdV dQ=0 ...
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Thermodynamics : Pressure of a gas

While reading The kinetic Theory of gases in Feynman Lectures , i was hoping for an explanation concerning the factor (2) that shows that only half of the atoms are headed towards a piston, while the ...
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How to contain air ions inside a chamber without loosing their charge?

I would like to create an experiment where I would hold ionized air molecules. Most likely negative O2-1 ions. I am looking for the most appropriate enclosure so that the ions do lose as little of ...
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How to calculate energy stored in a hydraulic hybrid system?

My understanding is that hydraulic hybrid systems have two reservoirs - one at high pressure and one at low pressure. I also understand that the working fluid can then be pumped between these two ...
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Expansion of an ideal gas at constant pressure

I approach these expansion problems like so: The gas and the surroundings(piston+outside) are at the same pressure at first. We heat the gas. The pressure rises inside the syringe a bit. The gas ...
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Is it possible to calculate the mass of gas remaining in a cylinder simply by measuring temperature and pressure?

Given $pV=nRT$, where; $p$ = Pressure, $V$ = Volume, $n$ = Number of moles of gas, $R$ = Gas constant and $T$ = Temperature in Kelvin. Also, the mass can be calculated by; $m = nM \rightarrow n = \...
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Derivation of the wind load formula

I am trying to derive the wind load formula: $F_d = \frac{1}{2} \rho v^2 A C_d$ in which I assume the drag coefficient to be equal to 1. My starting point is that the momentum of a rectangular wall ...
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Partial derivative of $PV=nRT$ with respect to $T$

We all know for an ideal gas $PV=nRT$ then, if we differentiate it partially w.r.t $T$ shouldn't we get $$\frac{\partial}{\partial T}(PV)=P\left(\frac{\partial V}{\partial T}\right)_P+V\left(\frac{\...
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How can I calculate the speed at which a gas flows from one volume to another?

Suppose that there are two rigid Volumes A and B. Each of these contains a gas with know properties (pressure, temperature, number of moles, volume, composition). Suppose also that there is a pipe ...
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Why bulk modulus of air is initial pressure?

So in the definition of bulk modulus the strain part is defined as (∆v/v) where ∆v is change in volume and v is the initial volume and while driving it for air we use the ideal gas law PV= constant ...
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Heat transfer of a monatomic ideal gas at room temperature

I have done parts a) and b) but have been stuck on c) for hours I have tried to come up with a formula but can’t come up with a reasonable one - I can’t even see how it is possible. Any help would be ...
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How was $C_p-C_v=\left(\frac{\partial P}{\partial T}\right)_{Vn}\left(\frac{\partial \:V}{\partial \:T}\right)_{Pn}$ dervied

I found the following relationship whilest on wiki reading up about heat capacity and cannot figure where the relationship has come from. Would it be possible for someone to maybe outline where it has ...
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Thermodynamics - please check my proof that $\partial C_p/\partial p$ = 0 for an ideal gas

Prove $$\left(\frac{\partial C_p}{\partial p}\right)_T = 0$$ for an ideal gas. All the $\partial$s are partial derivatives Please check to see if this makes sense. We know that $$C_p = \left(\...
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Why does entropy of an ideal gas break the third law of thermodynamics? [duplicate]

I was recently looking at the entropy equation for an ideal gas, show below $$S=NR\left\{\frac{5}{2}+\ln\left[\frac{V}{N}\left(\frac{2\pi mRT}{h^2}\right)^{3/2}\right]\right\}$$ And what troubles me ...
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Does thermal equilibration affect compression work for an ideal gas?

Consider compression of an ideal gas that is uniform in pressure but nonuniform in temperature, from volume $V_1$ to $V_2$. For simplicity of the problem let's say the gas is divided into 2 regions $A$...
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Partition Function of an Ideal Gas

Which is the correct partition function for an ideal (bosonic) gas at high $T$: 1) Sum over the number of particles in each momentum state: $$ z_{\vec{p}} = 1 + e^{- \varepsilon_{\vec{p}}/T} + ... = ...
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What happens to pressure when a liquid turns into a gas in a confined chamber?

I'm doing an experiment requiring immense pressures. Since I do not have access to a pump that can create these pressures I settled on something different... Instead of using a pump I want to utilize ...
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How long does it take a gas to equilibrate with a container's temperature?

Initial Conditions in a vessel: P~my unknown, but ~100torr, V=5000cc, T=35C, gas is 50/50 N2/He Laser drill a hole in the initial volume of diameter=10mils through a chamber wall thickness of 0.75mm. ...
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What happens when a photon hits a particle (radiative heat transfer, photoelectric effect)?

By relating temperature to particle motion, the kinetic theory of gases gives an intuitive explanation of conductive heat transfer; faster particles collide with slower ones to transfer kinetic energy....
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Assumptions and limitations for ideal gas

Assumption: In the assumption for ideal gas law, it is stated:"The time it takes to collide is negligible compared with the time between collisions." For, this assumption, can i just say there is only ...
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Determining Gas Constant $R$ from Boyles Law?

I have done an experiment (Boyles Law experiment using Boyles Law Apparatus) in order to determine the value of the gas constant $R$. I have also taken into account the dead space volume in my ...
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Insert sensors in an aerostat with helium?

Hy is possible for you insert sensors (to calculate pressure and temperature) inside an aerostat with helium ? I ask this because... I have an helium balloon anchored to the ground by a rope with a ...
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Is the Ideal gas approximation still valid if I have sizeable dynamic pressure

Say, if I have a hose blowing or sucking air into/outo a bigger compartment, can I still regard the static preassure as obeying ideal gas law?
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How to calculate the specific weight of air?

First of all sorry for my bad English ... I have to calculate the specific weight of air knowing that in the air there is actually a small percentage of water vapor. Therefore the specific weight of ...
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Modell for the buoyancy of a hot air balloon

I was just working on a problem concerning a ballon for my introdouction to thermodynamics class. The helium ballon is emerged in air and surrounded by earths gravitational field, which shall be ...
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Why use a cube as a reference volume in the kinetic theory of gases?

In basic kinetic theory we often use cubes. For example, the derivation of the ideal gas law is done with a cubical volume. Is a cube necessary for it to work? If not, wouldn't a sphere be more ...
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Work done on a gas enclosed in a container

According to everywhere work done on system of a gas is equal to $p\,\mathrm dV$ but here $p$ is just the external pressure. Shouldn't internal forces be considered while calculating work done thus ...
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Derivation of density of states for a gas with $N$ states

I am trying to find any information on the derivation of the density of states for a system with periodic boundary conditions in 3D. I know how it works with 1 particle since I have seen the ...
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Does $PV\propto T$ apply to a photon gas?

For an ultrarelativistic ideal gas, I know that $p=\frac{u}3$; $TV^3 =$ constant; $pV\propto T$. For a photon gas, I know that the first two results apply as well. However, I am unsure if the third ...
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Bouyancy of ozone gas

If ozone is $O_3$ why is it an outer layer of the atmosphere? It seems $O_3$ would sink in a solution of $O_2$, rather than float on it.
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Ideal gas as balls in boxes in different ensembles

I have some questions about the ideal gas in different ensembles. Often boxes with moving balls are used to explain an ensemble. Now I am confused what the difference would be in the corresponding ...
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Applying ideal gas law to every day problems

Three classical examples of seeing the ideal gas law in action: crumpled water bottle in cold car crumpled water bottle after your flight lands fridge door harder to open a second time after first. ...
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Boltzmann transport equation for granular gases

I am researching about granular gases and their collisions, and have come across this Boltzmann transport equation: $$\frac { \partial f ( v ) } { \partial t } = \iint d u _ { 1 } d u _ { 2 } f \left( ...