# Ideal gas Definition and 106 Discussions

An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions.
Under various conditions of temperature and pressure, many real gases behave qualitatively like an ideal gas where the gas molecules (or atoms for monatomic gas) play the role of the ideal particles. Many gases such as nitrogen, oxygen, hydrogen, noble gases, some heavier gases like carbon dioxide and mixtures such as air, can be treated as ideal gases within reasonable tolerances over a considerable parameter range around standard temperature and pressure. Generally, a gas behaves more like an ideal gas at higher temperature and lower pressure, as the potential energy due to intermolecular forces becomes less significant compared with the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them. One mole of an ideal gas has a volume of 22.710947(13) litres at standard temperature and pressure (a temperature of 273.15 K and an absolute pressure of exactly 105 Pa) as defined by IUPAC since 1982.The ideal gas model tends to fail at lower temperatures or higher pressures, when intermolecular forces and molecular size becomes important. It also fails for most heavy gases, such as many refrigerants, and for gases with strong intermolecular forces, notably water vapor. At high pressures, the volume of a real gas is often considerably larger than that of an ideal gas. At low temperatures, the pressure of a real gas is often considerably less than that of an ideal gas. At some point of low temperature and high pressure, real gases undergo a phase transition, such as to a liquid or a solid. The model of an ideal gas, however, does not describe or allow phase transitions. These must be modeled by more complex equations of state. The deviation from the ideal gas behavior can be described by a dimensionless quantity, the compressibility factor, Z.
The ideal gas model has been explored in both the Newtonian dynamics (as in "kinetic theory") and in quantum mechanics (as a "gas in a box"). The ideal gas model has also been used to model the behavior of electrons in a metal (in the Drude model and the free electron model), and it is one of the most important models in statistical mechanics.
If the pressure of an ideal gas is reduced in a throttling process the temperature of the gas does not change. (If the pressure of a real gas is reduced in a throttling process, its temperature either falls or rises, depending on whether its Joule–Thomson coefficient is positive or negative.)

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1. ### Trouble solving for end state of two control volumes in a rigid tank

TL;DR Summary: Struggling to structure the problem and derive an analytical solution for gas expanding into other gas in a rigid tank. Preferred formulation is fixed control volumes. This is not a homework problem. The problem: Two control volumes (A and B) are in a rigid tank filled with air...
2. ### Why is temperature constant after gas has expanded?

The answer given for part (c) in the back is that temperature doesn't change as the gas in cylinder A expands to fill cylinder B. The thermodynamic system here is composed of the two cylinders A and B joined by some pipe. But, I cannot find a satisfactory explanation for temperature...
3. ### I Cannot understand formula for molar heat capacities of an ideal gas

Homework Statement:: I am trying to understand a formula given in our book for determining molar heat capacity of an ideal gas under different thermodynamic processes using a single formula, but it is confusing. The exact formula for different processes is in the screenshots below. Can someone...
4. ### B Does the Maxwell Boltzmann distribution change depending on the shape of the container?

1.Does the Maxwell Boltzmann distribution change depending on the shape of the container? Pressure and the volume is constant. How is the Distribution affected whether the gas is in: a,sphere b,cube c,cuboid? Why does/doesn’t the distribution change depending on the shape of the container...
5. ### A Free expansion of an ideal gas and changes in entropy

For a freely expanding ideal gas(irreversible transformation), the change in entropy is the same as in a reversible transformation with the same initial and final states. I don't quite understand why this is true, since Clausius' theorm only has this corrolary when the two transformations are...
6. ### Question about the collisions of the molecules in an ideal gas

(The equation of ideal gas is PV=NRT.if P=1atm,N=1mole,T=0°K,R=gas constant then volume = zero. Hence, the volume of an individual molecule of ideal gas is zero) An individual molecule of ideal gas is assumed to have zero volume. The molecules of ideal gas are assumed to be dimensionless points...
7. ### Calculate the depth to which a balloon full of Kr must be pushed underwater to make it sink to the bottom of the sea

Hello. Firstly, I've calculated the density of Kr ( = 3.74 g/dm3), and I know that the p (fluid) = ρ * h * g. And then I've used the following equation: p1*V1 = p2*V2, and therefore: p1*V1 = ρ * h * g * (m/ρ) => p1*V1 = h * g * m. (h = 3.0153 m) Is that correct? Please, how could I calculate...

11. ### Thermodynamics: Ideal gas model

Do particles have air in between them in the ideal gas model? I think the answer is 'no, but I am not quite sure about the explanation. Is it because in an ideal gas model, the volume of the particles is negligible? Thank you.
12. ### Non-interacting gas in homogeneous gravitational field

It even gives a hint, it says "consider two horizontal surfaces z1 and z2 and think about what thermodynamic equilibrium means for particles traveling from one surface to the other". This really trips me up because I am not sure what to do with this. Obviously in equilibrium the number of...
13. ### Problem related to the Ideal Gas equation -- Nitrogen under pressure

Solution from the textbook: My work: I constantly get 1.55kg. I also tried dividing the first and the second equation (pxV=m/M x R x T with different values). How did they come up with the equation in the solution? Also, I am sorry if I posted it in the wrong place and didn't follow the...
14. ### What will be the number of collision per second in a unit area?

By using PV=nRT formula, I have found the volume of the vessel. As far as I have learned to calculate the number of collision in a unit volume. So, it is being difficult for me to find the right way to solve. I searched on the internet and have got this...
15. ### Chemistry Question on partial pressures

I've first calculated the partial pressures of each gas: ##N_2: 0.4\times 7.4\times 10^4=3.0\times 10^4 Nm^{-2}\\## ##O_2: 0.35\times 7.4\times 10^4=2.6\times 10^4 Nm^{-2}\\## ##CO_2: 0.25\times 7.4\times 10^4=1.9\times 10^4 Nm^{-2}\\## From here, I do not know how to continue. Could someone...
16. ### Question about calculating the minimum temperature in hot air balloons

First, I tried using the Archimedes principle and calculated the weight of the surrounding air displaced when taking off. ##W = 2500\times 1.29\times 9.81 = 31637.25 N## But then, I got stuck and do not know how to proceed from here on. I don't want the full solution yet but can I get some...
17. ### Entropy and the Helmholtz Free Energy of a Mass-Piston System

Attempt at a Solution: Heat Absorbed By The System By the first law of thermodynamics, dU = dQ + dW The system is of fixed volume and therefore mechanically isolated. dW = 0 Therefore dQ = dU The change of energy of the system equals the change of energy of the gas plus the change of energy...

50. ### Ideal gas pressure from Maxwell-Boltzmann distribution

Hi everyone I'm having trouble with solving an exercise in statistical physics. I need to argue why the average number of particles with a velocity between ##v## and ##v+dv## that hit a surface area ##A## on the container wall in a time interval ##\Delta t## is N_{collision}=v_{x}A\Delta t...