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. P

    Angular Frequency of a Piston with Ideal Gas

    Homework Statement A frictionless piston of mass m is a precise fit in the vertical cylindrical neck of a large container of volume V. The container is filled with an ideal gas and there is a vacuum above the piston. The cross-sectional area of the neck is A. Assuming that the pressure and...
  2. G

    Entropy of ideal gas: Volume it *has* or is *allowed* to have?

    Hi. If an ideal gas of ##N## particles is allowed to expand isothermically to double its initial volume, the entropy increase is $$\Delta S=N\cdot k_B \cdot \log\left(\frac{V_f}{V_i}\right)=N\cdot k_B \cdot \log\left(\frac{2V}{V}\right)=N\cdot k_B \cdot \log\left(2\right)\enspace .$$ This can...
  3. Ian Baughman

    Density of an ideal gas as a function of height

    Homework Statement If air has a density of ρ0 on the surface, calculate its density as a function of the height y for two scenarios: (a) the temperature is constant at T0; (b) the temperature decreases linearly T(y) = T0 − ay. Express your results using the given variables together the...
  4. zrek

    Calculating entropy for a simple scenario

    I'd like to create a simple model that demonstrates the basic values of thermodinamics of an ideal gas. I begin with two rooms, several molecules in them. Every data of every individual molecule is given (position, mass, speed, etc), so I can easily calculate the total energy, pressure...
  5. ashash_ash

    First law of thermodynamics: why some equations can't be used

    Homework Statement A cylinder fitted with a frictionless piston contains 5.0×10-4m3 of an ideal gas at a pressure of 1.0×105 Pa and temperature of 300K. The gas is then (i) heated at constant pressure to 450K, and then (ii) cooled at constant volume to the original temperature of 300K. The...
  6. bluejay27

    I Ideal Gas Equation: Pressure not Proportional to Moles

    how is pressure not proportional to the number of moles?
  7. B

    B Energy of Ideal Gas: Internal E & Kinetic E

    Hi, When calculating the energy of an ideal gas we neglect the potential energy and calculate the kinetic energy using: K.E = 3 /2 n R T My question is why do we not consider the electrostatic energy of the gas? If I am trying to work out the internal energy of 1 mol of Radon, why do I...
  8. Siddharth Rajvanshi

    I Ideal Gas Law and Differentiation

    Is it possible to calculate the rate of change of n with respect to rate of change of Pressure and rate of change of Temperature with V unknown but constant by PV = nRT? Rate of change of Pressure and rate of change of temperature can be measured. R and V are constants.
  9. M

    What are the units for the Universal Gas Constant?

    Homework Statement Hello, I am not asking for the answer to an example, rather how the book got some numbers. The problem is an example from the book and shows me the solution but does not show the steps. Given: The compressed air tank has a volume of .84 ft^3. The temperature is 70 F and the...
  10. N

    Calculating Internal Energy & Temperature Change of Ideal Gas

    Homework Statement What is the change in internal energy (in Joules) of an ideal gas that does 4.675x10^5J of work, while 2.95x10^6J of heat is transferred into the system and 7.95x10^6J of heat is transferred from the system to the environment? Calculate the change in temperature of the two...
  11. O

    Internal Energy of Degenerate Fermi ideal gas to the 4th power

    Homework Statement We are asked to derive the expression for the internal energy of an ideal Fermi degenerate gas using Sommerfeld expansions, writing out terms up to the fourth order in ##(\frac{T}{T_F} )## , that is, we must determine ## \alpha ## in the following expression: $$ U=...
  12. J

    Isobaric vs. isothermal expansion

    We have a piston with ideal gas in it and a weight. The weight is placed on the piston. The gas is heated externally and the gas expands. Will the expansion be isobaric or isothermal? One argument would be: the expansion will be isobaric because the weight is providing constant pressure. The...
  13. S

    Turbine Work - Can I assume ideal gas?

    Hi all, I need to estimate the mechanical work I can recover from expanding hot air through a gas turbine. So far I am using the equation below, where Wrev is my ideal isentropic work, s the number of stages, n = k = ratio of specific heats, R gas constant, T1 is the inlet Temperature, Pin the...
  14. Isomorphism

    Heat absorbed by an ideal gas in a cycle

    Homework Statement Homework Equations and the attempt at a solution:[/B] AC is adiabatic and AB is isothermal. Heat absorbed during process AC = 0 (adiabatic). Heat absorbed during process CB = C_p \triangle T=-\frac{\gamma}{\gamma -1} (P_2V_3 - P_2V_2) Heat absorbed during process BA =...
  15. curiosity colour

    Is the Book's Answer to Ideal Gas Behavior Conditions Incorrect?

    Ideal gas behavior condition is high temperature and low pressure, right? so is the book's answer to 10(a) ii wrong? https://scontent-kul1-1.xx.fbcdn.net/v/t34.0-12/14996536_1455768127770250_1228715611_n.jpg?oh=750e2555f8229aa9a4eeb17e3e80b1fb&oe=5829A2EE...
  16. Ron Burgundypants

    Thermodynamics Ideal gas problem

    Homework Statement An isolated box contains two chambers separated by a thermally insulating but moveable partition. Both chambers contain dilute gas (same kind) at different densities and temperatures. The left chamber contains 1.0 x 10^22 particles at 25 degrees celsius and the right chamber...
  17. Ryaners

    Thermo: isothermal, reversible expansion of ideal gas

    Homework Statement Two moles of a monatomic ideal gas are at a temperature of 300K. The gas expands reversibly and isothermally to twice its original volume. Calculate the work done by the gas, the heat supplied and the change in internal energy. So: T = 300K; ΔT = 0 n = 2; R = 8.314 J K-1...
  18. J

    Question about the derivation of the Ideal Gas Law

    I'm an undergraduate taking a physical chemistry course, and I got to a part in my reading about the derivation of the ideal gas law. The passage is linked below...
  19. I

    Partition function, Ideal gas, Entropy

    Homework Statement For a diatomic gas near room temperature, the internal partion function is simply the rotational partition function multiplied by degeneracy ##Z_e## of the electronic ground state. Show that the entropy in this case is ## S = Nk\left[ \ln \left(...
  20. P

    Finding the number of moles of an ideal gas in a capillary

    Homework Statement The temperature across the capillary with constant cross-sectional area and length L is given by ##T=T_0e^{-kx}##. Assuming an ideal gas and constant pressure show the number of moles to be: $$n=\frac{PV(e^{kL} - 1)}{RkLT_0}$$ Homework Equations ##PV=nRT## The Attempt at a...
  21. sliperyfrog

    Ideal gas law, Find the Temperature of the container?

    Homework Statement [/B] There is a lid on a .25m diameter, .30m tall cylindrical container enclosing .021kg of air. The lid is held in place solely by atmospheric pressure. It take 220N of force to pull of the lid at an atmospheric pressure of 101kPa. What is the Temperature of the enclosed...
  22. Elvis 123456789

    Change in entropy of an ideal gas during thermodynamic cycle

    Homework Statement An ideal gas with adiabatic index γ is taken around a complete thermodynamic cycle consisting of three steps. Starting at point A, the pressure is increased at constant volume V1 from P1 to P2 at point B. From point B to point C, the gas is allowed to expand adiabatically...
  23. KDS4

    Rearranging variables Van Der Waals EoS into new variables

    The question I'm stuck on is: P = NKBT/(V-Nb) - aN2/(V2) -----> (1) Re-arrange variables in the Van Der Waals equation of state, Eq. (1), so that V always appears in the equation as V/(3Nb) and P appears as 27b2P/a. Then T should appear in the combination 27b kBT/(8a). Call these...
  24. jdawg

    Deriving hydrostatic pressure equation for an ideal gas

    Assume: Hydrostatic Situation, ideal gas Use empirical formula T = T0 - Bz I have rechecked my work several times and can't seem to find a mistake. The answer is supposed to be: p2 = p1((T0 - Bz)/T0)(g/Bz) dp/dz = -ρg Now substitute ideal gas equation for ρ dp = -(p/RT)g dz ∫(1/p) dp...
  25. Elvis 123456789

    Adiabatic expansion of an ideal gas

    Homework Statement An ideal monatomic gas has initial pressure Po and occupies initial volume Vo. The gas undergoes an adiabatic expansion in which the volume is doubled. Calculate in terms of Po and Vo a) the final pressure of the gas b) the change in its enthalpy during the...
  26. T

    Estimating the final pressure of a transformation

    Homework Statement If the Helmholtz Free Energy remains constant, estimate the final pressure of 1.0mol of an ideal gas in the following transformation: (1.0atm, 300k) → (pfinal, 600k). Given Sgas = R. Homework Equations A = U - TS dA = -SdT - pdV The Attempt at a Solution If the Helmholtz...
  27. MexChemE

    Modeling ideal gas flow using Bernoulli's equation

    Hello, PF! I'm currently brushing up my fluid mechanics and came across some questions while studying the compressible flow of an ideal gas using Bernoulli's equation. First, consider incompressible flow in the following system Neglecting any changes in elevation, the Bernoulli equation for...
  28. D

    How Is Heat Calculated for an Ideal Gas at Constant Volume?

    Homework Statement An ideal gass is at constant volume risen to a new pressure level of ##P_f##. Find te expression for the total heat brought to the system. Homework Equations 3. The Attempt at a Solution [/B] So ##PV=nRT## and ##E=Q## ##Q=C_v(T_f-T_i)## so i just have to find...
  29. Firye Stanly

    Identify Gas Based on Specific Heat Formula and Universal Gas Constant R

    Homework Statement For some gas specific heats for constant pressure and constant volume are calculated. Universal gas constant is R. Find the formula the helps identify the gas. Include only constants and given information. Homework Equations 3. The Attempt at a Solution [/B] Molar specific...
  30. G

    Sound in a gas of non-interacting particles?

    Hi. In some statistical approaches (e.g. canonical ensemble), the particles of an ideal gas are non-interacting. Still, it's possible to derive the ideal gas law and other thermodynamic relations. Wikipedia gives an equation for the speed of sound in an ideal gas. How can there be waves in a...
  31. E

    Isothermal Compression of a Ideal Gas and Distance

    Homework Statement The figure at the bottom shows a cylindrical tank of diameter D with a moveable 3.00-kg circular disk sitting on top. The disk seals in the gas inside but is able to move without friction. The gas inside is at temperature T. The height of the disk is initially at h = 4.00 m...
  32. E

    Small pipe break for an ideal gas

    Homework Statement A large tube filled with an ideal gas at pressure p1 and temperature T1 has a small break in it towards an envirronement at p2, with p1 much larger than p2. What is the flow rate through the hole to the outside of the tube. Homework Equations pv=rT Δh+Δc2/2=δq-δl h1 + c12 =...
  33. B

    Ideal gas through Isobaric process

    Homework Statement This is probably a real easy task for most, but I simply CANNOT manage to calculate it, even given the correct answer. I will translate it as best I can and hope I don't phrase it in a way that causes misunderstandings: 12 Moles of an ideal gas go through an Isobaric...
  34. Tardis Traveller

    Ideal Gas Expansion: Finding Depth of Tank

    Homework Statement A bubble comes from the bottom of the tank of water to the surface and triples in its volume. If the temperature of the tank of water doesn't deppend on the depth what is the depth of the tank that the bubble was at? Homework Equations ##PV=nRT## The Attempt at a Solution...
  35. James Ray

    Solve Ideal Gas Problem: Gamma = 1.4, VA=4.33m^3, PA

    Homework Statement A gas undergoes a cyclic process as shown in the figure above. The gas has gamma = 1.4. In the diagram A has volume V_A = 4.33 m^3, pressure P_A Homework Equations The Attempt at a Solution [/B]
  36. M

    I Ideal Gas Law - Real Life Question?

    Hi Guys and Gals, As I was pumping up a flat bike tyre, a weird thought occurred to me about the application of the ideal gas law. Once the tyre essentially finds its physical dimension limitations (i.e. is shaped like a bike tyre and no longer changing shapes) and starts putting in reasonable...
  37. A

    Heat transferred into a closed system

    So i am making a simple demonstration of ideal gas law using a cylinder piston system, heating the system so the piston is pushed up, i wanted to calculate the heat transferred into the system, will it be Cp(Tf-Ti) or Cp(Tf-Ti)+ work done by the system ?
  38. S

    Why work done on a system causes heat to flow out of it?

    I don't understand how compression of a gas causes heat to flow out of the container of that gas... Could someone please help? Thank you in advance!
  39. S

    How Does Intermolecular Potential Energy Behave in Ideal and Real Gases?

    Homework Statement In the kinetic model of an ideal gas, it is assumed that: A. The forces between the gas and the container are zero B. The intermolecular potential energy of the molecules of the gas is constant. C. The kinetic energy of a given gas molecule is constant D. The momentum of a...
  40. N

    Entropy of mixing - Ideal gas. What is x?

    Homework Statement A bottle with volume v containing 1 mole of argon is next to a bottle of volume v with 1 mole of xenon. both are connected with a pipe and tap and are same temp and pressure. the tap is opened and they are allowed to mix. What is the total entropy change of the system? Once...
  41. S

    Calculate the change of temperature in terms of T

    Two Thermally insulated cylinders, A and B, of equal volume, both equipped with pistons, are connected by a valve. Initially A has its piston fully withdrawn and contains a perfect monatomic gas at temperature T, while B has its piston fully inserted, and the valve is closed. Calculate the final...
  42. toforfiltum

    Effect of density on rms speed in ideal gas eqn

    Homework Statement Homework Equations 1) PV = nRT 2 )## P = ⅓ ρ<c^2> ## 3) KE ∝ T The Attempt at a Solution According to the second equation above, density is inversely proportional to root mean square speed at constant pressure, but the answer states that the root mean square speed depends...
  43. Henry Stonebury

    Thermodynamics: Pressure and temperature from turbine

    Homework Statement A turbine is receiving air from a combuster inside of an aircraft engine. At the inlet of the turbine I know that T1 = 1273 K and P1 = 549 KPa, and the velocity of the air is essentially 0. The turbine is assumed to be ideal, so its efficiency is exactly 1. Also: R = 287...
  44. M

    I Internal energy of an ideal gas -- confusion

    We know that internal energy of ideal gas depends only on temperature. Let's say we have 1 mole of ideal gas with pressure P1, volume V1 and temperature T. Let's call this the state 1. Equation of state for ideal gas applies: PV=RT. Now if we expand (or compress gas) isothermally, gas will then...
  45. henrco

    Ideal Gas compressed at constant pressure

    Hi, Could I please get some guidance on my approach and solution, for this particular problem. Any assistance welcome. 1. Homework Statement An ideal gas is compressed at a constant pressure of 1.3 atm from a volume of 20 L to 12 L. During this process it gives off 3.69 kJ of heat. What is...
  46. Ethan Godden

    An ideal gas going through a cycle

    Homework Statement The problem is attached Homework Equations ΔEint=Q+W W=-PΔV The Attempt at a Solution Attempted solution is in the attachment. The problem is I am not getting the same answer as the supposed correct answer. Thank You, Ethan
  47. D

    Thermodynamics First law ideal gas question

    Homework Statement We have 0.0008 Kmol of an ideal gas are expanded from V1 to V2 v2=3V1 process is reversible and T/V=Constant if the work obtained by this expansion is 9.4 KJ find the initial temperature R=8.314 KJ Kmol-1 Homework Equations PV=nRT possibly T/V = T/V The Attempt at a...
  48. Gh. Soleimani

    My Case of Total Translational Kinetic Energy of Ideal Gas

    I have really problem with equation of the root – mean – square (rms) speed of the gas molecules when we use the universal gas constant (R) mentioned in all references. Accordance to all reference books, we have below equation for the total translational kinetic energy: Vrms = (3RT/ M)^0.5...
  49. Z

    Enthalpy and the Ideal Gas Law: Understanding Constant Pressure Reactions

    Hi! I'm new to the forums and currently reading about Chemical Thermodynamics. So here's what I know: ΔE = q - w So for constant volume reactions, no work is done hence: ΔE = q But for constant pressure reactions, heat be may released (for exothermic reactions) and work is done hence: ΔE =...
  50. V

    Do Different Volumes of Helium Affect Molecular Speed in Balloons?

    Homework Statement [/B] Two balloons with Helium gas are filled, first with 10 liters of He and second with 20 liters. Molecules of which balloon will be moving faster as compared to the other? Homework EquationsThe Attempt at a Solution Speed of molecules is directly proportional to...
Back
Top