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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Adiabatic free expansion

Let us assume there is an ideal gas in a thermally insulated vessel and it is free to expand into vacuum through a small hole in the vessel.Would the mass flow rate be a constant? What would be the ...
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Entropy in isothermal expansion [closed]

A cylindrical container, which is immersed in a heating bath at constant temperature, is seperated into two chambers by a piston, which is at first held in position A. Both chambers are filled with an ...
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When the volume of a container of gases is decreased, does the Root mean square speed increase or decrease?

I'm a High School student learning the kinetic theory of gases, and this is something I'm a bit confused about. So say there's a container covered with a piston. When you lower the piston and ...
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Ideal Gas Equation Assumptions

The two assumptions are that the gases are points of mass that move, they have no volume and that there is no interaction between other molecules. But even the points of mass can collide with each ...
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Ideal gas temperature definition

I have been doing some statistical mechanics and at the beginning of the course, I had seen this statement: $$T^\circ (K) = 273.16\frac{\lim_{V\rightarrow \infty} (PV)_{\text{system}}}{\lim_{V\...
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How to calculate the velocity of a bb propeled out of a barrel by a syringe? [closed]

I'd like help breaking this scenario down into the different calculations I would need to perform. Suppose I have a syringe with the plunger pulled back, and the other end of the syringe is attached ...
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Can you use $W = pdV = nRdT$ for an ideal gas with non-constant pressure?

I am having trouble calculating the total work done on an ideal gas that is being adiabatically compressed. Using the ideal gas law I can derive -- assuming n is constant -- that. $$pV = nRT$$ $$V = \...
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Energy of Fermi Gas $T>0$

I'm trying to plot $ \frac{E(T)}{N\epsilon_F} $ vs $\frac{T}{T_F}$ I know that the total energy comes from $$ E(T) = \int_{0}^{\inf} \frac{3}{2}\frac{N}{\epsilon_F}(\frac{\epsilon}{\epsilon_F})^{1/2} ...
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Equation of state for ideal gas from Helmholtz free-energy

Starting from the definition of Helmholtz free energy: $$F:=U-TS$$ (where $U$ is the internal energy , $T$ temperature and $S$ entropy) we derive in few steps the following relation: $$F=-T\int \frac{...
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Sackur-Tetrode equation and Nernst's Theorem

Today, while doing some statistical mechanics, I came across a problem regarding the entropy of an ideal gas. The entropy of an ideal gas is determined by the Sackur-Tetrode equation $$\frac{S}{k_b N} ...
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Statistical distributions for non-ideal gases

Motivated by another question which implicitly suggests calculating the pressure of a gas on the walls of the container, while taking account for molecular scattering. We all know how this calculation ...
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Water pressure inside heated tank

Say I have a 1 liter sealed pressure tank, and I fill it with 500mL of water. Then, I slowly heat the tank up to 2000 degrees Celsius. Does the water inside vaporize and become steam? Does the steam ...
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Do too many molecules make a gas non-ideal?

Now, by this I don't mean the effect when pressure is too high such that the molecules are taking up a significant amount of space, however, I think it might be a different angle to approach the ...
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Why does the internal energy of an ideal gas depends only on its temperature?

In university physics textbook he says : The internal energy of an ideal gas depends only on its temperature, not on its pressure or volume. I know that the only contribution to the internal ...
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Equipartition theorem for the second moment of the energy

The equipartition theorem provides a convenient way to derive a relation between the hamiltonian of an ideal gas to the temperature of the system. For an extreme relativistic ideal gas, the kinetic ...
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Work done by an ideal gas in an adiabatic free expansion

A system consists of the volume ($V_1+V_2$) within a container with a partition separating it into two volumes $(𝑉_1, 𝑉_2)$. In $V_1$, $𝑛$ moles of an ideal gas are present, and the surrounding is ...
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Is a mixture of water vapor and air more 'elastic' than dry air?

From the state equation for an ideal gas $$PV_o=mRT$$ and $$dm= \rho dV$$ you can derive an expression relating change in volume wrt change in pressure; defined as compliance (C) of the fixed volume $...
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How is $\mathrm dU=C_V\,\mathrm dT$ always true? [duplicate]

For ideal gases, in case of an isochoric process it is pretty straight forward: $\mathrm dU=Q+W$ $\Rightarrow\mathrm dU=C_V\,\mathrm dT+p\,\mathrm dV$ $\Rightarrow\mathrm dU=C_V\,\mathrm dT$ But ...
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Is heat $\delta Q$ an exact differential for an isochoric process (ideal gases)?

Generally speaking, heat and work are path-dependent, thus $\delta Q$ and $\delta W$ are not exact differentials. By first law of thermodynamics, we know that $dU=\delta Q - \delta W$ but $\delta W=0$...
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Deriving $pV=RT$ from Joule expansion [closed]

$\newcommand{\pdifft}[3]{\left(\frac{\partial#1}{\partial#2}\right)_{#3}}$ I'm going over some past exam papers. One question reads Boyle observed that the pressure of an ideal gas varies ...
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Speed of sound in ideal gases

The equation of state for an ideal gas is given by: $$p = \rho r T \tag{1}$$ In the other hand, the speed of sound is calculated by: $$c = \sqrt{{\partial p\over \partial \rho}}\tag{2}$$ Using (1) ...
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Do gases become more opaque as they are cooled or compressed?

So recently I was thinking gases (at least colourless ones) are more transparent in their gaseous state than liquid state. And as we talk of continuity in liquid and gaseous state (fluids) is it ...
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How does the Joule-Kelvin effect apply to the liquefaction process of Hydrogen? Why do we need to cool Hydrogen before taking advantages of this?

I am currently writing a report around Hydrogen at a first year university level. On the below section i discuss the liquefaction process of Hydrogen and how the Joule-Kelvin effect is used in the ...
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How to calculate the Avogadro constant from the Loschmidt constant and ideal gas law?

Josef Loschmidt use Kinetic Molecular Theory and calculate number density, now I want to use number density in law gas to calculate Avogadro constant: $PV = nRT$ number density $= n/V$ $V = n/$...
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How can a system of 2 gases be in thermical equilibirum but not in mechanical or chemical equilibrium?

This question is asked on my Thermodynamics course, and I don't know the answer, at least to the 1st part. Regarding the 2nd part: I do believe that some chemical reactions may occur when 2 reactants ...
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Partition function of an ideal gas (taking gravity into account)

I am trying to solve the following problem from an old qualifying exam: "Ideal gas in gravitational potential" Consider an ideal gas of N indistinguishable molecules of mass m in a cylindrical ...
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Two versions of Diffusion coefficient

I found two versions of the Diffusion coefficient, first: $$D=\frac{\pi \lambda }{8}\overline{c}$$ Where $ \overline{c}$ ist the particles mean thermal velocity and $\lambda$ the particles mean free ...
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Is it possible to deduce the second law of thermodynamics from the first?

Considering the First law of thermodynamics as an axiom dU=dQ-pdV for any infinitesimal process, we should be able to prove that for any reversible(quasistatic) and cyclic transformation, there is at ...
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Can a gas molecule theoretically have zero velocity?

According to Maxwell's speed distribution law gas molecule can have speed which lies between zero to infinity. But in the graph of the distribution curve it seems to touch zero velocity. So can a gas ...
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Relation between volume of a room and temperature inside

I don't know whether it is based on some people's assumptions or it is a fact that the smaller the room, the hotter it is (say, during summer), considering the heat is only supplied from outside the ...
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A Maxwell-Boltzmann distribution, written as a Gamma distribution [closed]

Introduction I have read that a Maxwell-Boltzmann distribution can be written equivalently as a Gamma distribution, however I have not managed to find or derive the parameters used to do so. The ...
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Question about model proposed by Boltzmann for the ideal gas

The following text is from the book Introdução à Física Estatística (Introduction to Statistical Physics), Silvio Salinas. There's something in it that i didn't understand. In order to highlight ...
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${\rm CO}_2$ Pressure Vs Temperature in Supercritical Phase

Say we have a compressed gas cylinder half full of liquid CO2 under its own vapor pressure. Below 31C the pressure and temperature in the cylinder follows the saturation line. If you know the ...
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Time between collisions and collision time

I’m having a hard time really getting how the relationship between pressure and square mean velocity of a gas is derived for one single reason...seems like I don’t really know what impulse is. From ...
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Air pressure dependence on temperature

I have around 200 barometers (altitude up to 200 m above sea-level) of which some in direct sunlight that can become relatively hot. I am investigating whether there is any relation between measured ...
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Does pressure of a closed box with air in it change as a function of the gravitational acceleration?

If I took a hypothetical box of fixed volume and filled it with 1 mol of N2 at home, measured the pressure, then teleported this box to increasingly distant points from the Earth, would I see the ...
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Problem from the Open Latvian Physics Olympiad 2019: “Reactive Reaction”

A rockets engine is supplied with a mass $m$ of hydrogen every second and just enough oxygen to burn all of the hydrogen. Determine the thrust force of the engine given that the exhaust openings cross-...
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Work done by a piston after energy has been added

The question: Enclosed beneath the movable piston in the drawing is 4.8 moles of a mono-atomic ideal gas. The gas performs work on the piston as 2300 J of heat are added from the surroundings. ...
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Confusion in first law of thermodynamics

Our teacher while explaining first law of thermodynamics showed us an example of a piston inside a chamber. He said when heat is applied the particles move, i.e the kinetic energy increases. Due to ...
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Pressure on wall by gas molecules

Pressure by gas molecules of an ideal gas on the walls is P = nRT/V But by derivations P=1/3 nmv², where v is velocity. Are they equal, if yes, then it means that we can deduce volume of free path ...
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Boyle's Law and hot air balloon

A bit dumb question because it is really difficult to imagine it. :- Pressure is force per area. Talking about gases, the pressure is said to be the force molecules exert on walls of let's say a ...
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Temperature and kinetic energy of a particle

We know that heating an object makes the atoms in it vibrate. But in case of ideal gases we say that heating them increases their kinetic energy. But how does kinetic energy increase and not ...
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Entropy change of the Universe for an ideal gas under free expansion

The entropy change of the Universe for the free expansion of an ideal gas is calculated by replacing the irreversible path between the initial and final equilibrium states with a reversible, ...
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What is a “perfect fluid”, really?

In Statistical Mechanics, unless I'm making a confusion mistake, a perfect fluid is defined as a large collection of particles without any "internal" interactions (except maybe from point collisions). ...
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What pressure should be used when calculating Work in gas expansion?

The formula for the work done by a gas is $W = \int_i^f P dV$. What pressure should be used here? I'm asking because I thought you use the gas pressure at every instant of an expansion. For an ideal ...
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Definition of an ideal gas

Zemansky and Dittman's Heat and Thermodynamics (6th ed, p. 108) defines an ideal gas as one that satisfies the equations: $PV=nRT$ and $(\partial{U}/\partial{P})_T=0$. However, Rossini and Frandsen's ...
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Irreversible, Compression and expansion work for a piston with ideal gas

How can we calculate the work done by the piston or on the piston by including the internal pressure of the piston and not the external one. Because if the external pressure is doing work, the ...
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Operation Of A Constant Volume Gas Thermometer

Concerning the mechanism of a constant volume gas thermometer, I was wondering how the adjustment of the second tube upon the open side increases the pressure. I know how the gas placed in the ...
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Weight exerted on scale by balloon filled with ideal gas

I want to compute the weight of a spherical balloon (with radius $r$) in vacuum filled with ideal gas. The balloon is laying on a scale. Using the barometric formula $$ P(h)=P(h_0) e^{-\alpha(h-h_0)},$...
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Perfect gas relationship between pressure and density

I've been given the following equation for a perfect gas: \begin{equation} p = k \rho^\gamma \end{equation} Where $k$ and $\gamma$ are constants. I'm trying to find out where this comes from or a ...

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