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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The ideal gas equation is $pV=nRT$. Prove that $p=\frac{\rho RT}{M}$

The ideal gas equation is $$pV=nRT$$ Show that the pressure exerted by a fixed mass of gas is given by the equation $$p=\frac{\rho RT}{M}$$ Where $\rho$ is the density of the gas and $M$ is the mass ...
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How do I determine the relationship between initial and final volume in this case?

Some total volume contains two compartments separated by a wall that allows for mechanical and thermal interaction, each compartment having a different amount of an ideal gas. For the initial ...
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How to predict deviation from ideal gas behaviour?

Molar masses of H2, N2, CO2, and NH3 are 2g, 28g, 44g, and 17g and respectively. The gases deviate from ideal behavior in the following order: $$\require{mhchem} \ce{H2<N2<CO2<NH3}$$ ...
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An ideal gas expands into vacuum in an insulated rigid vessel. Which of the followings happens? [closed]

This question came in the Dhaka university admission exam 2018-19. An ideal gas expands into vacuum in an insulated rigid vessel. Which of the following happens? A. no change of internal energy B. a ...
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Mean energy of ideal gas using MonteCarlo methods (from Mark Newmann - Computational Physics )

while trying to replicate Mark Newman's book problems I found this problem about the Monte Carlo simulation of an ideal gas (example 10.3) where the goal is to calculate the internal energy of the gas....
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Why is there no temperature difference in the Joule expansion experiment?

The whole system is adiabatic, and no heat exchange can take place. If the volume of the gas now doubles, it should actually cool down. That's why I don't understand $dT=0$
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Does Gas constant depend on molecular weight?

I came across the following question recently Calculate the difference between two specific heat of 1 g of helium gas at NTP. Molecular weight of helium = 4 and J = $4.186×10^7$ erg $cal^{-1}$ The ...
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What causes the volume of an ideal gas in a container that changes volume (like a balloon)?

As we don't consider molecular volume or any interaction between molecules in an ideal gas, what causes its volume? What is the volume given by PV=nRT? If we take a balloon as an example, what ...
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Can we have constant volume, and pressure in a system?

I was given a system where heat was added to a mass of Nitrogen gas in a canister at constant pressure? And given the volume of the canister as 1L, I assumed that the gas would expand to fill the ...
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How small is $dt$ in this derivation of the kinetic energy of ideal gasses?

I was reading the derivation of the average translational kinetic energy of an ideal gas in Sears and Zemansky's University Physics. This derivation uses a cylinder with height $|v_{x}|dt$ and base ...
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Isochoric gas process taking heat from surrounding environment

this is a $pV$-diagram of Stirling cooler: A => B and C => D processes are isothermal, co temperature in D is same as temperature after cooling on high temperature side. Although, temperature ...
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Mixing identical gases in different states (Gibbs paradox)

Background It is well known that if we take a container separated into two volumes $V_1$ and $V_2$ by an insulating membrane and containing some moles $n_1$ and $n_2$ of the same gas at the same ...
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Heating and cooling a gas [closed]

I'm sure this will be easy for many of you but I'm Googled out. I'm working on a game with hot air balloons/airships. I have a 'burner' with a yet undetermined ability to heat a gas (BTU, Joules, etc....
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Is thermal vibration a property of a particle moving back and forth by itself, or of a system of particles colliding?

When we say gas has a given temperature, it means the particles vibrate, or move back and forth, in the aggregate. Is this movement back and forth only due to each particle moving linearly and then ...
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How do the macroscopic observables $T$, $ρ$, and $P$ change in an ideal gas after flowing through a turbine?

I’m trying to better understand how turbines effect the flow of gas and gain or expend energy in the process. It’s easy to understand with incompressible fluids as all you need to know is the pressure ...
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Does the air pressure inside a box remain the same after it is sealed?

Let's assume that the pressure is 1 atm outside the sealed box. I think that the pressure inside the box will be the same at 1 atm. But why? Isn't the giant column of air above causing pressure ...
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How is a Carnot engine in quasi-equilibrium?

If the reversible isothermal expansion and adiabatic expansion both yield positive work (as the pv diagram indicates), it means that the gas inside the cylinder was compressed before those stages ...
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Barometric equation with different species [duplicate]

The barometric equation gives the pressure dependence of a perfect gas in a gravitational potential. In particular $$ P(h) = P_0e^{-\frac{mgh}{k_BT}} $$ where $m$ is the mass of molecules and $T$ the ...
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Why is the pressure inside the bottle lower than atm pressure?

When a balloon is placed inside a bottle (covering the entranace), it will not inflate, since the bottle is already filled with air particles with no escape route. When you punch a hole in a bottle, ...
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Dynamics of ideal gas during free expansion

I would like to compute (even numerically) the time evolution of the density profile of an ideal gas which undergoes free expansion. For concreteness, let's imagine an infinite cylinder with the axis ...
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Pressure becomes zero for ideal gas?

During a reversible process: $$du=dq-dw=c_vdT-Pdv=\left(\frac{\partial u}{\partial T}\right)_vdT+\left(\frac{\partial u}{\partial v}\right)_Tdv$$ From the above, I get $\left(\frac{\partial u}{\...
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Invariant Concentration of Ideal Gas Mixture with Altitude

Consider the following scenario, We have two gasses, $A$ and $B$, both approximately ideal mixed together in a gravitational field of constant magnitude $g$. Let them have masses per particle of $m_a$ ...
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Pressure variation within tank with hole exposed to a known outside pressure variation

I think this is best explained via a diagram, see below. Initial Conditions: Initially, everything is at standard atmospheric temperature, pressure, density etc. Boundary Conditions: Then, a known ...
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Question about derivation of multiplicity of ideal gas

I am looking at the derivation of multiplicity of an ideal gas as done in Schroeder's Thermal Physics (see the picture below). Could somebody clarify if my logic is correct? At this particular step ...
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What is the distribution on the speed of particles in a liquid? (analogous to the Maxwell-Boltzmann distribution)

I know, for gases, the distribution on the speed of particles is the Maxwell-Boltzmann distribution. What is the corresponding distribution for liquids (e.g. water)? You can assume that the liquid is ...
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Work in isobaric processes

while researching, I found a lot of conflicting information about this topic. Let me explain my thought process so far and talk about an example I came up with. An isobaric process is defined as one ...
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Free expansion of ideal gas dilemma

I have a question about free expansion of ideal gas. Firstly, we will take the entire (isolated) container to be our thermodynamic system. We know that the gas in the left-part of the container has a ...
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Henry's Law and Bunsen's solubility coefficient

Let's say I have a known Partial Pressure P of oxygen in mmHg or kPa in blood. Knowing the temperature, I also know the Bunsen solubility coefficient or Henry’s law constant (α) from given table: The ...
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Free Energy per Particle of an Ideal Gas in the Thermodynamical limit diverges to infinity

I know that the Partition function of an ideal Gas is: $$ Z_k = \frac{1}{N!} \left( \frac{V}{\lambda_T^3} \right) ^N $$ where $\lambda_T = \frac{h}{\sqrt{2 \pi m k_B T}} $. Now I want to calculate ...
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I can not understand following: "$P = \rho_m RT$", is the document of Wikipedia wrong? [closed]

Wikipedia says that, $P=\rho_m RT$ P is pressure, $\rho_m$ is mass density, R is gas constant, T is temperature. but I think it's wrong because of below equation. $PV = nRT \\ \leftrightarrow PV = \...
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Heat, work, energy and ideal gas law [closed]

I have encountered a textbook problem which I believe I have solved correctly, but my text book gives a slightly different answer. Any input will be greatly appreciated! PROBLEM: A container has a ...
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Kinetic energy of ideal gas particle and its electrons

Would the kinetic energy of electron be same as that of the individual ideal gas particle (in which it exists) at a non zero temperature?
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Kardar: The derivation of the Maxwell Boltzmann distribution function

In Mehran Kardar's volume 1: Statistical Physics of Particles, he introduces the Maxwell Boltzmann distribution function just after the discussion on the microcanonical ensemble as follows: The joint ...
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Why is time of contact not taken in finding rate of change of momentum in derivation of kinetic gas equation?

In derivation of kinetic gas equation, the time taken for rate of change of momentum is taken as 2l/u but the force is change of momentum divided by time of contact so why are we taking time for gas ...
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Can there be thermal equilibrium of a gas at non-uniform distribution of its particles?

Sometimes thermal equilibrium of a thermodynamic system is defined as a state when the system’s temperature is uniform and constant at a given moment of time. Now, look at the picture below and ...
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Why temperature increases with increase in volume?

If We heat an ideal gas, its temperature rises and it's molecule becomes energetic hence they move more and more away from equilibrium position. But when we increse the volume of gas , why does its ...
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Thermodynamics and dalton's partial pressure law

By kinetic equation of ideal gas, $$PV=\frac{1}{3}mNu_{rms}^{2}$$ Where, $P$ is pressure $m$ is mass of molecule $N$ is number of moles considered and $u_{rms}$ is root mean speed. In my book to prove ...
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Derivation of astrophysical entropy

The definition of entropy in astrophysics is often actually just the adiabatic constant $K$ relating $P=K\rho^\gamma$ where $\gamma$ is the usual adiabatic index, $P$ is the pressure and $\rho$ is the ...
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Can we derive Boyle's law out of nothing?

My textbook states Boyle's law without a proof. I saw Feynman's proof of it but found it to be too handwavy and at the same time it uses Boltzmann's equipartition theorem from statistical mechanics ...
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Pressure being equal in a vessel

An open vessel at $27^{\circ} C$ is heated until $\frac{3}{5}$ of the air in it has been expelled. Assuming that the volume of the vessel remains constant, find the temperature to which the vessel has ...
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Dependancy of molar mass

$\require{mhchem}$ Graham's law states that rate of effusion of a gas is inversely proportional to its molar mass which is mathematically written as $\frac{R_A}{R_B}=\sqrt{\frac{M_B}{M_A}}$. Here we ...
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What am I doing wrong in this estimation of the mass of the atmosphere?

I'm trying to approximate the mass of the atmosphere. I'm treating it as an ideal gas and therefore its density follows: $$\rho(z) = \rho(0)e^{(\frac{-mgz}{k_BT})}$$ Where I'm using $m=4.2122\cdot10^{-...
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Would an isobaric expansion of an ideal gas go, if the gas is pushed by a second piston instead of getting heat?

There is such thing as isobaric expansion or compression of a gas when it takes or gives away heat, respectively. Isobaric expansion of a gas can be illustrated as follows: Here is some load with ...
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What would the pressure inside a leaking container be?

I had a question posed to us in Physics Class about determining the pressure inside a container when a volume of gas is expelled out of it at a contant rate, the question was as follows: A Vessel of ...
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Why average energy of gas particles in equilibrium is $\bar{\epsilon}=E / N$

Reif, statistical physics (By random the author means "A situation, which can be obtained in many different ways". The most random situation therefore means the situation that can be ...
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Calculation of dry air density without relative humidity

I would like to estimate the density of dry air at different temperatures and constant pressure (1 bar) just using the densities of nitrogen (79%) and oxygen (21%). I consider the number of other ...
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How to simulate gas diffusion from a mixed gas composition to room air?

I am trying to program a pretty simplistic gas model, so you can assume the most ideal situation. I have a gas circuit that can be disconnected and leak all of its containing gases into a room. The ...
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Conservation of momentum of ideal gas in pipe

I was reading this question Pressure drop in a pipe due to cooling and have a follow up question. Please note that the question is about an ideal frictionless pipe. In the question, it is stated $$ \...
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Ratio of mean free paths between two equal volumes at different temperature, separated by a partition with pinhole

Question: A container is divided into two equal parts I and II by a partition with a small hole of diameter $d$. The two partitions are filled with same ideal gas, but held at temperatures $T_I$​= ...
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High school thermodynamics question

Here's the question: Two identical balloons are blown to the same size, one at sea-level and the other is at the top of a mountain. Both balloons are at the same temperature. Which one of the ...
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