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. J

    I Application of the ideal gas law

    Hi, I want to calculate the amount of liquid nitrogen (at boiling temp.) needed to build a pressure of 10.1 bar in a vessel of volume 66 m3. The liquid will be poured slowly into the vessel, boil off and fill the volume with gas at the specified pressure. I make the assumption that the process...
  2. H

    Find the change in the Kinetic energy of an Ideal Gas

    Homework Statement Let 3/2kT be the kinetic energy of ideal gas per molecules. T the absolute temperature and N the avogadro number. Answer the following questions : 1) when the volume doubled at constant temperature. How many times the kinetic energy per molecule become greater than before...
  3. mjda

    I How to describe the Sun's interior?

    My question to you is this... Can the interior of the Sun be described as an ideal gas? From my knowledge, to describe a body of gas as an ideal gas, the separation between the particles must be much greater than the size of the actual particles. How could one justify whether the Sun fits this?
  4. House

    Understanding the Molar Heat Capacity of an Ideal Gas

    We know that for an ideal gas the differential of the internal energy function is: dU = n Cv dT But is Cv the molar heat capacity or not?
  5. H

    Heat and work when temperature increases by 1 degree

    Homework Statement Kinetic energy per mol is 3/2KTHomework Equations Q = nC##\Delta##T U = Q + W W = -P##\Delta##V The Attempt at a Solution 1) internal energy = 3/2NKT 2) heat needed to increase temperature of 1 mol ideal gas by 1 degree at constant volume? Since constant volume, W = 0 Q =...
  6. NFuller

    Statistical Mechanics Part II: The Ideal Gas - Comments

    Greg Bernhardt submitted a new PF Insights post Statistical Mechanics Part II: The Ideal Gas Continue reading the Original PF Insights Post.
  7. G

    Specific heat for an ideal gas

    Homework Statement If Cp for an ideal gas is 35.4 J/mol⋅K, which of the following is Cv for this gas? a. 12.5 J/mol⋅K b. 20.8 J/mol⋅K c. 29.1 J/mol⋅K d. 27.1 J/mol⋅K e. 43.4 J/mol⋅K Homework Equations ΔH = ΔE + Δ(PV) = Q + W + Δ(PV), and for ideal gas, ΔH = nCvΔT + Δ(nRT) = nCvΔT + nRΔT =...
  8. G

    Why Might Statement (b) Be Incorrect in Ideal Gas Processes?

    Homework Statement Which of the following statement(s) is (are) correct when an ideal gas goes from an initial to a final state in a single process? a. No work is done on or by the gas when the volume remains constant. b. No energy is transferred into or out of the gas as heat transfer when the...
  9. J

    Ideal gas - percentage of fraction of molecules

    Homework Statement Homework EquationsThe Attempt at a Solution Honestly speaking , I have absolutely no idea about this problem .This doesn't happen often .In the KTG chapter , only definition and formula of Average , RMS and Most probable speeds is given . This question is for an...
  10. T

    B Adiabatic or Isobaric process?

    Consider the following problem: Gaseous helium (assumed ideal) filled in a horizontal cylindrical vessel is separated from its surroundings by a massless piston. Both piston and cylinder are thermally insulating. The ambient pressure is suddenly tripled without changing the ambient temperature...
  11. physea

    B Equations that describe ideal gas processes

    Hello! Is there a table to show the equations that describe ideal gas processes? For example, I know for isothermic, it's P1V1=P2V2, what about the others? Also, how are these derived? Is it from Q-W=dU? or PV=nRT? Any help? thanks!
  12. Spinnor

    I Calabi-Yau manifold + ideal gas + point disturbance?

    Because it is a closed space, can it make sense to fill a Calabi_Yau manifold with an ideal gas and consider waves from a point disturbance? Would the Ricci-flat condition of Calabi-Yau manifolds have anything to say about possible sound waves? Thanks!
  13. AbbeyC172

    Thermodynamics: Ideal Gas Law, find the temperature

    Homework Statement A 3-ft^3 container is filled with 2-lbm of oxygen at a pressure of 80 psia. What is the temperature of the oxygen?Homework Equations pV= nRT T= PV/nR R= 10.7316 psia x ft^3/ lbmol x R The Attempt at a Solution Hi everyone! So I understand how to use the Ideal Gas Law but my...
  14. H

    Find the work done on a monoatomic gas in this P-V diagram

    Homework Statement Homework Equations internal change = $$\frac{3}{2}n.R.(T2 - T1)$$ Work = P.ΔV The Attempt at a Solution 1) T2 = $$\frac {P2. V2 . T1 }{P1 . V1} = 1.2 * 10^3$$ 2) Q = Internal change = $$\frac{3}{2}n.R.(T2 - T1) $$ $$ = \frac{3}{2} * 1 *8.3*10^{-3}*(12*10^2 - 3*10^2) $$...
  15. Pushoam

    Free energy per unit volume of an ideal gas

    Homework Statement Homework EquationsThe Attempt at a Solution [/B] I am taking the free energy as the internal energy of the ideal gas. Then the average internal energy per unit volume is ## \frac { 3 nk_B T } {2 } ##. So, the correct option is (c). Is this correct?
  16. VSayantan

    Energy of a Gas in equilibrium with BB-radiation

    Homework Statement A closed, thermally-insulated box contains one mole of an ideal monatomic gas G in thermodynamic equilibrium with blackbody radiation B. The total internal energy of the system is ##U=U_{G}+U_{B}##, where ##U_{G}## and ##U_{B} (\propto T^4)## are the energies of the ideal gas...
  17. M

    Ideal Gas Law Homework: Calculating Number Density and Spacing Between Molecules

    Homework Statement Consider an ideal gas at 25.0 degrees Celsius and with a pressure of 1.00 atm. a) What is the "number density" of the molecules, expressed as molecules per unit volume? (Cubic meter, cubic centimeter or liter) b) What is the typical spacing between molecules in the gas? Of...
  18. J

    What is the Ideal Gas Law for a Two-Bulb System with Varying Temperatures?

    1. Two equal glass bulbs are connected by a narrow tube and the whole is initially filled with a gas at a temperature of T0 and pressure of P0. Then, one of the bulbs is immersed in a bath at a temperature, T1 and the other in a bath at a different temperature, T2. Show that in this problem, the...
  19. H

    Ideal Gas Equation and Temperature change?

    During a thermodynamic process, the state variables of an ideal gas, measured in kPa, m3, and oC, varied in the following way: P2 = 2P1 V2 = 3V1 T2 = 8T1 What is the temperature increase of the gas, T2 −T1 ? I've been given an answer of 4780 and I'm not sure how to get there?
  20. J

    Internal energy of an ideal gas as a function of pressure?

    Assuming all gases in the combustion reaction of benzoic acid (C6H5COOH) behave ideally, what is the "exact" change in internal energy? The context in which this question is being asked is after a calorimetry experiment. For all the intents and purposes of calorimetry, the change in internal...
  21. H

    How to Calculate Ideal Gas State Properties Using Molecular Dynamics?

    Dear all, I want to calculate thermodynamical properties of my molecule which I am calculating its thermodynamical properties of non-ideal part using Molecular dynamics. I need ideal gas state total energy, Cp, and Cv in several different temperatures. I am using opt+freq at B3lyp/6-311++G(d,p)...
  22. Pushoam

    I Internal energy of any ideal gas

    The internal energy of monoatomic ideal gas is due to the kinetic energy of the molecules. Using Boltzmann Maxwell distribution, it is calculated that the kinetic energy due to translational motion of gas molecules of an ideal gas depends only on the temperature. In case of monoatomic gas, since...
  23. F

    Energy of an ideal gas given its multiplicity

    Question: The multiplicity of an ideal gas is given by g(U) = A.U3N/2, where U is the energy of the gas, A is a constant and N is the number of particles in the gas. Prove that the energy of the gas given a temperature T is U = (3/2).N.kb.T Attempts: My first thought was to...
  24. F

    Work done pumping air into a bottle

    Hi there, i am struggling with the following problem. Air is pumping into a bottle with volume V and pressure Pi until it reaches a final pressure Pf. The temperature remains the same during the process and the gas is an ideal one. We have to calculate the work that is done. I am not quite...
  25. runningman19

    Adiabatic Compressor: Ideal Gas Temperature Change

    Homework Statement A mixture of hydrogen, carbon monoxide and carbon dioxide is being fed to a compressor at 2.0 bar and 25 C. The overall flow rate is 17.47 SCMS and its composition is 73.5 mol% H2, 13.7 mol% CO and the balance CO2 The compressor operates adiabatically and reversibly with a...
  26. E

    Internal energy of an ideal gas as a function of temperature

    Homework Statement Two containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas but container B has twice the volume of container A. The internal energy of the gas in container B is (a) twice that for container A (b) the same as that for...
  27. L

    What is the Effect of Isothermal Movement on Internal Energy of a Gas?

    Homework Statement The dot in Fig. 19-18b represents the initial state of a gas, and the isotherm through the dot divides the p-V diagram into regions 1 and 2. For the following processes, determine whether the change Eint in the internal energy of the gas is positive, negative, or zero: (a)...
  28. Const@ntine

    Molecular Specific Heat of an Ideal Gas: Computations

    Homework Statement A cylinder with a heavy ram/piston contains air at T = 300 K. Pi = 2.00 * 105 Pa, Vi = 0.350 m3, Mr = 28.9 g/mol & Cv = 5R/2 (a) What's the Molecular Specific Heat of an Ideal Gas, with a constant volume, computed at J/KgC ? (Cv) (b) What's the mass of the air inside the...
  29. G

    Two gases separated by a piston

    Homework Statement [/B] Two ideal gases are contained adiabatically and separated by an insulating, fixed piston that blocks the molecules of gas 2 but allows the molecules of gas 1 through(in both directions). The initial pressures, volumes, temperatures and number of molecules on each side is...
  30. PainterGuy

    Pressure exerted by an ideal gas

    Hi Please have a look on the attachment. Suppose that a 0.1 kg rubber ball having velocity of 60 m/s is moving between two walls A and B, and the distance between the walls is 1 m. It is having elastic collisions with the walls. Let's focus on what is happening at wall B. The ball is moving...
  31. A

    Statistical Physics: Quantum ideal gas

    Homework Statement I'm reading the book about Statistical Physics from W. Nolting, specifically the chapter about quantum gas. In the case of a classical ideal gas, we can get the state functions with the partition functions of the three ensembles (microcanonical, canonical and grand...
  32. psuedoben

    Measure the volume of a lighter than air balloon

    hello, i am trying to calculate the volume of a balloon (which is quite large). It has been filled with helium via a valve connecting helium storage tanks to the balloon. The knowns I have are the volume of the storage tanks, the intital pressure in the tanks, and the final pressure in the tanks...
  33. U

    Pressure dependence of the equilibrium constant for an ideal gas

    I read in some scripts that equilibrium constant for an ideal gas is not a function of pressure: But that is not generally true! Since: $$\left (\frac{\partial \Delta_{R} G}{\partial p} \right )_{T,\vec{n}}=\Delta_{R} V$$ and $$\Delta_{R} G^{0}=-RT\cdot \ln K$$ it should be: $$\left...
  34. Amaterasu21

    Kinetic theory of gases: rebound speed and force questions

    Hi everyone, I remember years ago at school memorising the derivation of the formula for pressure in the kinetic theory of gases, as explained in this Youtube video: Thinking a little more deeply about this derivation there are two things I don't get: 1) At 0:53, the video says the molecule...
  35. SciencyBoi

    Internal Energy of an Ideal gas related to Molar specific heat

    Homework Statement Please look at the below images which is the derivation of the relation between the internal energy of an ideal gas and the molar specific heat at constant volume. (Snaps taken from Fundamentals of Physics Textbook by David Halliday, Jearl Walker, and Robert Resnick) As...
  36. P

    Ideal Gas Law -- Isobaric Epansion followed by....

    Homework Statement An ideal gas with Cv = 5/2R, and γ = 1.4 starts at a volume of 1.5m3 , a pressure of 2.0×105Pa, and a temperature of 300K. It undergoes an isobaric expansion until the volume is V , then undergoes an adiabatic expansion until the volume is 6.0m3 , and finally undergoes an...
  37. M

    Internal Energy of virial expansion

    Hello, I have some trouble understanding the virial expansion of the ideal gas. 1. Homework Statement I have given the state equation: $$ pV = N k_b T \left(1+\frac{A\left(T\right)}{V}\right) $$Homework Equations [/B] and a hint how to calculate the caloric equation of state $$...
  38. H Psi equal E Psi

    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...
  39. DevonZA

    Change of internal energy of an ideal gas

    Homework Statement Homework Equations Δu = ∫ [(a-Ru)+bT+cT^2+dT^3]dT The Attempt at a Solution The answer of 6447kJ/kmol is given but I am struggling to get to this answer after integrating the above formula and inserting the given values. Firstly would the integral of...
  40. R

    Partition function for ideal gas for "medium" temperature

    Looking for the heat capacity of ideal gas due to rotational degrees of freedom. If the temperature of the gas is much higher than the temperature corresponding to the energy differential between states,the partition function can be written as the integral over the density of states. If the...
  41. E

    Ideal gas in a cylinder with a piston

    Homework Statement A vertical cylinder of radius r contains an ideal gas and is fitted with a piston of mass m that is free to move. The piston and the walls of the cylinder are frictionless, and the entire cylinder is placed in a constant-temperature bath. The outside air pressure is p0. In...
  42. C

    Calculating Entropy Change for an Ideal Gas Expansion

    MENTOR NOTE: NO TEMPLATE BECAUSE SUMITTED TO WRONG FORUM. 3.1) A quantity of 0.10 mol of an ideal gas A initially at 22.2 degrees C is expanded from 0.200 dm3 to 2.42 dm3 . Calculate the values of work (w), heat (q), internal energy change (delta U), entropy change of the system (deltaSsys)...
  43. M

    MHB Which Gas Behaves Closest to an Ideal Gas?

    out of the gasses hydrogen,nitrogen,chlorine, and helium which shows behviour closest to an ideal gas.? ive been told the answer is helium because there is no attractive forces between helium atoms. would there not be van der waal forces though.? also would hydrogen just have as little...
  44. M

    Thermodynamics: Compression of an Adiabatic Gas

    Homework Statement Assume 1.500 mol of a monatomic ideal gas is compressed from 3.00 L to 1.00 L. a. If the initial and final temperature is 10.0 °C, what are the initial and final pressures (in atm)? b. How much work input (in kJ) is required if a reversible isothermal path at 10.0 °C is...
  45. Z

    Pressure Equalization of X & Y Gas Bottles

    Homework Statement X and Y are two gas bottles that are connected by a tube that has negligible volume compared with the volume of each bottle. There is a valve in the tube that is initially closed. X has a volume of 2V and contains hydrogen at a pressure of p, Y has a volume V and contains...
  46. J

    Understanding the Different Forms of the Ideal Gas Law and Their Applications

    Hey I was hoping someone could be me a succinct method of knowing what form of the Ideal gas law I need to use and in particular the different R's associated with each form. Form my Thermodynamics class we use PV = nRT Pv = RT PV = mRT Little v being the specific volume (which changes the R...
  47. L

    Final temperature real gas behaving ideally

    Homework Statement Please consider a mixture of oxygen (1 mole), nitrogen (4 mole), and carbon dioxide (3 mole). The mixture was heated in a well - insulated vessel with 753 kJ. Determine the final temperature if the mixture is composed of real gases behaving ideally as described by Eq. 3.48...
  48. HethensEnd25

    An ideal gas closed system reversible process

    Homework Statement an Ideal gas at T = 70 C and 1 bar undergoes following reversible processes: a: Adiabatically compressed to 150 C b: then, cooled from 150 to 70 C at constant pressure c: finally, expanded isothermally to the original state (T=70 C and P = 1 bar) Homework Equations...
  49. W

    What Is the Highest Temperature Reached in the Ideal Gas Cycle?

    Question (see attached diagram): PV diagram with 7.5 moles of ideal diatomic gas through cycle a, b and c. What is the highest temperature reached by the gas during the cycle? (multiple choice answers 180, 325, 208 and 100 C, i know answer is 208 C but I'm not getting it!) It is a PV diagram...
  50. L

    Thermodynamics Work from pressure

    Homework Statement The tires on a bicycle require an air pressure of 80 psig. When isothermally pumped up the bicycle tires, the volume of the air (that was originally in the atmosphere) is reduced by a factor of 5.7. Please determine the work that must be done on each lbm of air that is pumped...
Back
Top