What is Ideal gas: Definition and 853 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.)

View More On Wikipedia.org
  1. G

    Determine all of the Physical Chemistry Variables of the System

    Homework Statement A weather balloon is filled with Helium gas and released from the ground. It goes up 18km and achieves a diameter of 15m. Determine if the following values are greater than zero, less than zero, or equal to zero: ΔV, ΔP, ΔT, ΔU, ΔH, Ssys, surr, Stot Homework Equations ΔU =...
  2. S

    Work done isothermal, adiabatic ideal gas

    Problem statement, work done, and relevant equations: One mole of ideal gas is initially at 1 atm and has a volume of 5L. a) Calculate the work done on the gas during an isothermal, reversible compression to a volume of 2L. ##W_isothermal = - \int_{v_i}^{v_f} p dv = - \int_{v_I}^{v_f}...
  3. predaylight

    De Broglie wavelength and ideal gas entropy derivation

    When the ideal gas entropy is derived, we consider N atoms in a box of volume=Lx*Ly*Lz. Then, we make the assumption that Lx,Ly,Lz >>de Broglie wavelength of atoms. I am not sure why we need to make this assumption? Thanks!
  4. MexChemE

    Psychrometry -- Ethanol in dry air

    Homework Statement Ethanol evaporates in a 10 x 20 x 50 ft3 room. Air is initially dry at a temperature of 30 °C and 765 mmHg of pressure. a) If the partial pressure of ethanol after vaporization is 40 mmHg, how many pounds of ethanol evaporated? b) The same air is compressed until it reaches a...
  5. P

    Isochoric Process with Unknown Ideal Gas

    I was assigned a problem in my Engineering Thermodynamics class as follows: Problem: An ideal gas in a rigid closed container undergoes isochoric heating from T1 = 27 C to T2 = 77 C. Initial gage pressure is 300 kPa, pressure of surroundings is 1 atm. Find the final gage pressure. The way to...
  6. T

    Relationship between pressure & chem potential in ideal gas

    Homework Statement (Excerpted from a longer, multipart problem but essentially) Show that for an ideal gas, $$ \frac{\partial p}{\partial T}\bigg)_\mu = \frac{S}{V}. $$ Homework Equations • The ideal gas law, of course $$ pV = Nk_{\rm B}T $$ • Pressure, temperature, and chemical potential...
  7. I

    Deriving equations for pressure & number density for centrif

    Homework Statement Consider particles in a gas centrifuge. This device is used to separate gases of different molar mass by rotating a cylinder at high rates. Derive two equations: one for the pressure (P) and one for the particle number density (nv) as functions of M, r, w and T, where r is...
  8. MexChemE

    Free energy in the free expansion of an ideal gas

    Hello PF! Consider the free expansion of an ideal gas. The process occurs at constant temperature, therefore, ΔU = 0, Q = 0, and W = 0. Suppose we are given the initial and final pressures of the gas, and we calculate ΔG = nRT ln(P2/P1). As P2 < P1, ΔG < 0. This is intuitive, as a free expansion...
  9. K

    Size of a cube for a molecule of ideal gas

    Homework Statement The temperature of an ideal gas is 00C and the pressure is 1[atm]. imagine every molecule is enclosed in a cube, what's it's side length? Homework Equations PV=nRT Avogadro's number: 6.023E23 The Attempt at a Solution I assume volume of i liter: $$1[atm]\cdot...
  10. T

    Ideal Gas Law Problem: Finding Pressure with Temperature Change and Fixed Mass

    does anyone know how to do this question. it feels like there's a part of the question missing as i don't know how to complete the equation The pressure of a fixed mass of gas in a sealed sphere is measured to be 1.02 x 10^5 Pa at a temperature of 253K. Assuming the volume of the sphere doesn't...
  11. L

    Thermodynamics: ideal gas chemical potential

    Can someone explain me why we could put pi, μi and μiο in this equation: and we get this: (this is The chemical potential of a component in a perfect mixture of ideal gases wher pi is partial pressure)
  12. Rugile

    Oxygen and mercury in a tube problem

    Homework Statement We have a tube with the top end open and the bottom end closed. There is some oxygen gas in the tube and on top of the oxygen there is 10 cm high column of mercury. The initial temperature is 20oC. Then the tube is flipped over and heated to 40oC. The column of mercury shifts...
  13. kelvin490

    Should diatomic gas be regarded as ideal gas?

    We know that one model for ideal gas is monoatomic gas with no attractive force between atoms, elastic collision and some other assumptions. I would like to ask if there exist a gas behave exactly the same but the only difference is it's a diatomic gas (or more complicated structure), should it...
  14. gracy

    Understanding Velocity Vector Components in a Gas Molecule Bouncing Back?

    can someone help me .In this video from 2.00 to 3.00 how the velocity vector drawn with red color can be broken into x-y-z components and why after bouncing back only x component of velocity changed and y ,z components remained same?
  15. M

    Spherical bubble rises to surface, Ideal Gas, Thermal Energy

    Homework Statement A spherical air bubble in a lake expands as it rises slowly to the surface. At the point it starts to rise, the pressure is 2.00 atm, the temperature of the water is 10.0 ∘C, and the radius of the bubble is 5.00 × 10^−3 m. At the surface, the pressure is 1.00 atm and the...
  16. Soumalya

    Hydrostatic pressure distribution for an ideal gas

    Considering a unit mass of an ideal gas in a cylindrical container of volume 'V' at temperature 'T' the pressure exerted by the gas at the walls of the container is given by the ideal gas equation as, pV=RT where 'R' is the characteristic gas constant for the particular gas. Under equilibrium...
  17. ChristineMarie

    Calculating entropy for expansion

    How do you calculate the entropy of an ideal gas with n = 1, Cv,m = 1.5R, Ti = 300K, P=3bar and expands against Pext = 1bar until final volume is twice initial volume at Tf = 200K?
  18. SalfordPhysics

    Derive Entropy Change for Ideal Monatomic Gas

    A Monatomic gas passes from state 1 (pressure p1, volume V1) to state 2 (p2, V2). Derive an expression for the change in entropy of a monatomic ideal gas. The required final equation is: ΔS = Cv ln(T2/T1) + nRln(V2/V1) In my attempt, I am retrieving ΔS = Cv ln(T2/T1) + Rln(V2/V1) i.e.; the...
  19. K

    How Much Magnesium is Needed for 40 mL of Hydrogen Gas Production?

    Homework Statement Determine how many grams of Mg must react with HCl in order to produce 40 mL of hydrogen gas at 22 degrees Celsius and 1.02 bar. Also, If the Mg ribbon weighs 0.836 mg/mm, how many mm of the ribbon will you require? Homework Equations PV=nRT Mg(s) + 2HCl(aq) -->...
  20. F

    Ideal Gas Expansion - Finding final pressure and work done by gas

    Homework Statement a ideal monoatomic gas initally has a temperature of 315K and a pressure of 6.87atm . It then expands from a volume of 440cm^3 to volume 1550cm^3 . If the expansion is isothermal, what is (A) the final pressure (in atm's) and (B) the work done by he gas. Homework Equations...
  21. C

    How Much Hydrogen Is Needed for a Balloon to Float at 10km Altitude?

    Homework Statement At an altitude of about 10 km, the temperature of the Earth’s atmosphere is roughly -50°C and the air pressure is around 16 kPa. (Assume ideal gas) How many kilograms of hydrogen gas (H2, molecular mass 2g/mol) should be put in a balloon to fill it to 2000 m3?What is the...
  22. C

    Calculating the change in entropy of an ideal gas under compression

    Homework Statement Initial pressure: 140kPa Temperature: 25C or 298K Volume: 0.14m^3 Final Pressure:1.4MPa or 1400kPa It uses index compression, n=1.25. So PV^1.25 = constant. c_p = 1.041kJ/kg.K and c_v = 0.743 kJ/kg.K Homework Equations ¥ = c_p/c_v ΔS=c_v*ln(Tf/Ti) + R*ln(Vf/Vi) [i...
  23. MexChemE

    Isobaric/isochoric (?) heating of an ideal gas

    Homework Statement Consider an ideal gas with C_V=6.76 \frac{cal}{mol \cdot K}. Calculate \Delta H and \Delta U when ten moles of this gas are heated from 273.15 K to 373.15 K. Homework Equations \Delta H = \Delta U + P\Delta V Q=n C_V \Delta T The Attempt at a Solution As I'm given the heat...
  24. mef51

    [Thermodynamics] Heat Capacity for Polytropic Process

    Consider an ideal gas. For a polytropic process we have ##PV^n = const##. Different values of ##n## will represent different processes; for example isobaric (##n=0##), isothermal (##n=1##), and isochoric (##n=\infty##). The Wikipedia article on polytropic processes states that the specific heat...
  25. D

    Ideal gas configurational entropy -Swendsen 4.6?

    I am teaching myself Stat Mech / thermo from Swendsen's "An Introduction to statistical mechanics and thermodynamics". To this point I find the book interesting and clear to follow. But in section 4.6, Probability and Entropy, he confuses me by concluding that the entropy that he defines there...
  26. C

    Ideal gas temperature/pressure/volume problem

    Homework Statement A mass of gas at an initial pressure of 38 bar, and with an internal energy of 1400kJ, is contained in a perfecty insulaed cylinder of volume 0.06 meters cubed. the gas is allowed to expand behind a piston until its internal energy is 1300kJ. the law of expansions is...
  27. fluidistic

    Statistical mechanics, ideal gas, Helmholtz FE and chem. pot.

    Homework Statement I am trying to solve a problem but I am confused on what's going on with an approximation. I have to find the pressure in function of V, T and N of an ideal gas using the partition function, then obtain the chemical potential in function of T, p and N and I must graph it in...
  28. alpha358

    Thermodynamics: ideal gas chemical potential pressure dependence

    I don‘t understand one step in derivation of ideal gas chemical potential. Generally Gibbs free energy is: (1) (2) We observe that: (3) From equation (3) we make differential equation and integrate it: (4) (5) We get Gibbs free energy dependence on pressure...
  29. I

    Experiment on piston cylinder, issues with Ideal gas law

    Hello everyone, I have an rather large piston-cylinder containing gas that is compressed when the piston extends. Using three sensors I am measuring the pressure, temperature and volume of the gas while I force the piston out using a winch. The system is closed and no gas is released or added...
  30. T

    Adding heat to a Non Ideal Gas problem

    Homework Statement When 120J of heat are added to this gas, the temperature of the gas changes. Find the change in temperature if the heat is added at (a) constant volume. (b) constant pressure. Homework Equations The equation of state of at the gas is (p + 50)V = 10T The...
  31. A

    Density and r.m.s of an ideal gas

    Homework Statement A can which is sealed of a volume 0.035m3 contains an ideal gas with a pressure of 150kPa, at a temperature of 350K. Calculate the gas density and the root mean squared speed of the gas molecules (P.S. the molecular mass is stated as 28) Homework Equations...
  32. M

    Thermodynamic equilibrium of ideal gas and mechanical system

    Homework Statement Hi I am new to Physics Forums and desperately need some help! This is my first class back since undergrad and my math skills have gotten a little rusty. I think that's where I am failing. Okay here goes: http://tinypic.com/r/2zqf04k/8 There is a 4 subsystem...
  33. T

    Ideal gas expansion between two tanks (Thermodynamics)

    Homework Statement Two interconnected tanks are of equal volume. One is filled with methane at 500bar and 293K, the other is initially evacuated. A valve connecting the two tanks is opened only long enough to allow the pressures to equilibrate. If there is no heat transfer between the gas and...
  34. D

    How to Calculate Temperature Change in Ideal Gas Law Problem for One Mole?

    Homework Statement for one mole of an ideal gas this relation holds good P= P0 /{1+(V0/V)^2}, where P0and V0 are constants, what will be its change in temperature in terms of P0,V0 and R, if volume is doubled? Homework Equations for one mole of ideal gas we know PV=RT Then...
  35. S

    PV diagrams for ideal gas: Finding Work Done

    Homework Statement Imagine a graph of pressure in kPa (y-axis) against volume in L (x-axis). There is a straight line moving from point A at 300kPa, 0.5L to point B at 500kPa, 1L. The false origin on this graph is 200kPa, 0L. What is the work done by the gas? Homework Equations W=pV...
  36. jerry0696

    How work is done on an ideal gas?

    Consider a system of volume V and pressure P ,if i add molecules of gases in the system while keeping its volume constant and not providing any energy nor absorbing energy from the system ,its pressure will increase and so does its temperature Why does the temperature increase? More molecules...
  37. J

    Ideal Gas Law solve for partial pressure

    1. Gaseous compound Q contains only xenon and oxygen. When 0.100 g of Q is placed in a 50.0 mL steel vessel at 0 °C, the pressure is 0.229 atm. When the vessel and its contents are warmed to 100 °C, Q decomposes into its constituent elements. What is the total pressure, and what are the partial...
  38. WannabeNewton

    Sphere immersed in classical ideal gas

    Homework Statement A small sphere, with initial temperature ##T##, is immersed in an ideal Boltzmannian gas at temperature ##T_0##. Assuming that the molecules incident on the sphere are first absorbed and then re-emitted with the temperature of the sphere, determine the variation of the...
  39. M

    How Much Heat is Needed to Raise a Piston in a Heated Ideal Gas Cylinder?

    An ideal gas is placed in a tall cylindrical jar of crosssectional area 0.080m^2. A frictionless 0.10kg movable piston weight is supported by the gas pressure in the jar. When the gas is heated (at constant pressure) from 25C to 55C , the piston rises 1.0cm. How much heat was required for this...
  40. A

    Change in internal energy of an ideal gas

    Given that U = (3/2)PV does this mean that ΔU = Δ(3/2)PV for an ideal gas? Hence when finding the change in internal energy using a P-V diagram, can we simply apply this equation instead of using ΔU = Q+W?
  41. P

    Pressure vessel ideal gas calculation

    Hello all, As part of a research project, I am trying to calculate the amount of water/dry ice I would need to put in a cylindrical pressure vessel to obtain an internal pressure of ~100 psi at 200C (from room temperature, ~23C). I haven't had to do a calculation like this in awhile, but...
  42. PsychonautQQ

    Thermal: Entropy of Ideal Gas (Sackur-Tetrode equation)

    okay so I suck at La-Tex so I'm not going to put the actual equation, but it's not important for my question. In the equation the entropy is dependent on the natural log with mass in the numerator of the argument. Why is mass involved when talking about entropy at all? I mean I think of...
  43. C

    Semi-Classical/Classical derivation of ideal gas partition function

    In the semi-classical treatment of the ideal gas, we write the partition function for the system as $$Z = \frac{Z(1)^N}{N!}$$ where ##Z(1)## is the single particle partition function and ##N## is the number of particles. It is semi-classical in the sense that we consider the...
  44. N

    Adding energy to an ideal gas without changing internal energy

    Hi everyone. I thought of a question which has been bothering me. It is: Is there a case where energy is added to an ideal gas of constant amount where the energy added will equal the work done by the gas. My thoughts: The energy of an ideal gas is proportional to the temperature. If the...
  45. Soumalya

    Derivation of ideal gas equation

    Is the following approach used for the derivation of the ideal gas equation correct? Here's the link: http://www.mikeblaber.org/oldwine/chm1045/notes/Gases/IdealGas/Gases04.htm
  46. gfd43tg

    Ideal gas and Ideal Gas solution

    Hello, I am wondering, if you have an ideal gas mixture, does that automatically mean that the solution is an ideal solution? Or is it possible to have an ideal gas mixture that is not an ideal solution. Thanks
  47. A

    Understanding Enthalpy of an Ideal Gas: Effects of Temperature and Pressure

    I have read that enthalpy of an ideal gas is a function of temperature only, I am having a little trouble getting it. Consider a cylinder filled with an ideal gas so if we increase the pressure by pushing the piston down on it , a/c to ideal gas equation the temperature also rises, which in...
  48. D

    Entropy of a Fermi dirac ideal gas

    Hello Homework Statement From the expression of the partition function of a fermi dirac ideal gas ln(Z)=αN + ∑ ln(1+exp(-α-βEr)) show that S= k ∑ [ <nr>ln(<nr>)+(1-<nr>)ln(1-<nr>) Homework Equations S=k( lnZ+β<E>) <nr>=-1/β ∂ln(Z)/∂Er <E>=-∂ln(Z)/∂β The Attempt at a Solution I...
Back
Top