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.)

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  1. B

    How Does Compressing an Ideal Gas Affect Its Temperature?

    Homework Statement A cylinder fitted with a movable piston contains ideal gas at 27C, pressure .5 x 10^5 Pa, and volume 1.25 m^3. What will be the final temperature if the gas is compressed to .8 m^3 and the pressure rises to .82 x 10^5 Pa. A) 125 C B) 154 C C) 246 C D) 67.7 C E) 41.8...
  2. B

    What is the temperature of the freezer based on the Ideal Gas Law?

    Homework Statement Here is the problem: You are worried that your -80C freezer is on the fritz. Unfortunately you do not have a thermometer. You do have a balloon. so, you blow up the balloon and measure that it has a diameter of 10cm when at 25C. you put it in the freezer, let it come to...
  3. K

    Please help - An ideal gas problem involving work on a mass

    Please help -- An ideal gas problem involving work on a mass 1. An ideal gas has a heat capacity of 20 J/(mol*K). One mole of the gas is in a cylinder and absorbs 1000 J of heat and lifts a 10 kg mass a vertical distance of 2 m while expanding. If the initial temperature of the gas is 300 K...
  4. C

    Thermodynamics - Ideal gas expansion

    Homework Statement 2.1E5 J of heat enters an ideal gas as it expands at a constant T = 77°C to four times its initial volume. How many moles of gas are there? T=350K, Q=2.1E5 J, Vi=x, Vf=4x Homework Equations ΔU=Q-W W=\intpdV U=nCvT The Attempt at a Solution I'm not sure if I'm even on the...
  5. gfd43tg

    Partial molar volume of ideal gas and Gibb's theorem

    Hello, I am working on the derivation that proves that the partial molar volume of an ideal gas is equal to the molar volume of an ideal gas. I am following up to the point in the textbook where they set (∂n/∂ni)nj = 1 where ni is the number of of moles of species i, and nj is the...
  6. Telemachus

    Ideal gas subject to central potential [Statistical Mech]

    The problem says: Consider an ideal gas of N particles in a spherical vessel of radius R. A force acts directly over the molecules and is directly proportional to the distance to the center of the sphere ##V(r)=\alpha r##. Calculate the pressure of the gas, and the density of particles at the...
  7. A

    Work done by ideal gas processes

    Hello all, In my physics textbook they discuss work done by ideal gas processes. The equation they give is Wgas = pΔV. I'm trying to figure it out if this is work done ON the gas by the surroundings, or work done BY the gas on surroundings. From a previous chapter, they presented the...
  8. W

    Damping Force in a piston: Ideal Gas versus a Fluid

    I was in my physics of the human body class and we got on the topic of pistons. It was given to me that the dampening force pertaining to such a piston filled with a gas is proportional to the square of the velocity of the piston; however, for fluids it was given as simply proportional to the...
  9. D

    Classical/quantum transition for an ideal gas in 1m^3 box

    Homework Statement Hey guys, So I have to estimate the temperature at which the classical / quantum transition happens for a 1m^3 box of air. This is done by comparing the de Broglie wavelength with the average distance between the particles - so basically the transition happens when they...
  10. G

    The ideal gas law for an adiabatic process

    Homework Statement Hi can someone please have a look at this question and let me know if I am on the right track, thanks. A diesel engine requires no spark plug; instead the air in the cylinder is compresses so highly the fuel ignites spontaneously on injection to the cylinder. Q. If the air...
  11. Mordred

    Ideal gas laws in cosmology usage

    The ideal gas has the following requirements. 1) there are no intermolecular forces between the molecules. 2) the volume of the gas is negligible compared to the volume of the container they occupy. 3) the interactions between the particles and the container is perfectly elastic (total kinetic...
  12. A

    Entropy Change of Ideal Gas Upon Inserting Wall

    To preface my question, I know it is related to the Gibbs paradox, but I've read the wikipedia page on it and am still confused about how to resolve the question in the particular form I state below. Suppose a completely isolated ideal gas consisting of identical particles is confined to a...
  13. S

    How Is Enthalpy Change Calculated for Heated Argon at Constant Volume?

    Homework Statement Argon is heated from T1 to T2. Assume ideal gas behaviour. Calculate the energy input. Assume a constant volume, mass and constant specific heat capacity. Pressure variable T1=523.15 K T2=823.15 K M= 0.03995 kg m=50 kg R=8.31 Cv=0.0125 kJ/(mol.K) Homework Equations...
  14. C

    Ideal gas law and thermodyanimic processes

    Homework Statement An ideal gas is enclosed in a cylinder with a movable piston at the top. The walls of the cylinder are insulated, so no heat can enter or exit. The gas initially occupies volume V1 and has pressure p1 and temperature T1. The piston is then moved very rapidly to a volume of...
  15. M

    Thermodynamics - PV Diagram of an Ideal Gas

    Thermodynamics -- PV Diagram of an Ideal Gas Homework Statement Right, I've got a PV diagram attached to make this easier to explain. The substance is an ideal gas. I need to calculate the heat absorbed along the different paths ACB, ADB and AB. The first two are easy. The red lines in the...
  16. G

    Thermodynamics problem, Enthelpy zero for an ideal gas

    Homework Statement Show that \left(\frac{\partial H}{\partial T}\right)_{T} = 0 for an ideal gas Homework Equations The question required me to first solve \left(\frac{\partial U}{\partial T}\right)_{P}...
  17. A

    How Much Helium Can a 11m Diameter Balloon Hold and What Can It Lift?

    A spherical helium balloon 11 m in diameter is at ambient temperature and pressure, 15 degrees Celsius and 100 kPa. How much helium does it contain? It can list a total mass of balanced atmospheric air. How much mass of the balloon fabric & cage can then be lifted? Here is my work but I'm...
  18. T

    Understanding Mechanical Work: Ideal Gas and Fixed Pressure

    Hi all, I was wondering if I am having a definition problem on mechanical work. Since dW = -PdV (as I was told in class), is it correct to say the pressure is fixed with W = -PV, since dW = d(PV) = -VdP - PdV = -PdV suggests dP = 0? Thanks S.
  19. M

    Deriving Ideal Gas Law through partition function

    Homework Statement The pressure of a non-interacting, indistinguishable system of N particles can be derived from the canonical partition function P = k_BT\frac{∂lnQ}{∂V} Verify that this equation reduces to the ideal gas law. The Attempt at a Solution I have a very poor...
  20. P

    Ideal Gas Equation: Deriving pV=Nm<c>^2/3

    I need a detailed derivation of why pV = \frac{Nm<c>^{2}}{3}for an ideal gas using the example of a gas molecule placed in a cube-shaped container, the derivation in my book isn't that clear.^{}
  21. M

    How Much Nitrogen Gas Escapes from a Compressed Cylinder?

    i) Commercially, nitrogen is sold as compressed gas in cylinders. If a cylinder of volume 116 L is filled with N2 to a pressure of 1.38 x 104 kPa at 298.15K, what mass of N2 does the cylinder contain? Assume ideal gas behaviour. Answer: Mass N2 = 18104 g = 18.1 kg ii) Now, regarding part i), if...
  22. Night-san

    Ideal Gas Law: messing with ratios

    Homework Statement Air is pumped into a bicycle tire. The 43 moles of air initially in the tire have a gauge pressure of 1 atm. How many moles of air must be pumped into the tire in order to raise the gauge pressure to 5 atm? Assume that the volume and temperature of the air inside the tire...
  23. N

    What is the Equation of State for an Ideal Gas?

    Homework Statement Hi Often I bump into the relation p=\rho c_s^2, where p is the pressure, rho the density and cs the speed of sound in the ideal gas. It is apparently called the equation of state for an ideal isothermal gas. I know about pV=NkT, which becomes p=\rho kT, but does this mean...
  24. D

    Internal Energy of an Ideal Gas

    Homework Statement 400. g of oxygen has a volume of .25 m3 and a pressure of 125,000 Pa. What is the internal energy of the gas? What would the internal energy of the gas be if it were compressed to .10 m3 while the pressure was held constant?Homework Equations U = 3/2 PVThe Attempt at a...
  25. G

    Why Is Time Interval Between Gas Particle Collisions Calculated as Δt=2l/v?

    Hello everyone, When I was studying about the way to find the RMS speed of an ideal gas by using classical mechanics, I wondered that why the time interval of the collisions can be approached as the time between two collisions, instead of contact-time between particle and wall. remember...
  26. B

    Finding specific heat capacity of a non-monatomic (ideal gas)

    Homework Statement Suppose that 31.4 J of heat is added to an ideal gas. The gas expands at a constant pressure of 1.40x104 Pa while changing its volume from 3.00x104 to 8.00x104 m3. The gas is not monatomic, so the relation CP = 5/2R does not apply. (a) Determine the change in the internal...
  27. A

    MHB Ideal Gas Law: Pressure, Volume, & Temperature Changes

    The ideal gas law states that PV = nRT where P is the pressure in atmospheres, V is the volume in litres, n is the number of moles, R = 8.314 Latm/Kmol is the gas constant, and T is the temperature in Kelvins. Suppose that at a specific instance that two moles of gas is under 5 atmospheres of...
  28. J

    Ideal Gas Simulator: Help Solving Collision Detection Issue

    This one's aimed primarily at the programmers in this forum. I've written a programme in python (Set as a long term project from my A-level physics teacher) which will hopefully end up being a scientifically accurate ideal gas simulator in 2D - I'll set up a bunch of particles with random...
  29. A

    How to Calculate Final Pressure of an Ideal Gas with Changing Conditions?

    Ideal gas laws question.. Help! Homework Statement Volume of 150cm^3 of an ideal gas has an initial temp. Of 20 degrees celcius and an initial pressure of 1 atm. What is the final pressure if the volume is reduced to 100cm^3 and the temp is raised to 40 degrees celcius. Homework...
  30. S

    Is the Ideal Gas Law Applicable to Non-Isothermal Processes? | Homework Question

    Homework Statement Is the ideal gas law, PV = mRT, only applicable to processes which are carried out isothermally? I mean, can it not be applied to a polytropic process, PVn = k.Homework Equations See above.The Attempt at a Solution N.A.
  31. A

    Ideal gas laws dealing with pressure volume and temp.

    Homework Statement An ideal gas has the following initial conditions: Vi = 520 cm3, Pi = 3 atm, and Ti = 100°C. What is its final temperature if the pressure is reduced to 1 atm and the volume expands to 1000 cm3? Homework Equations I used the equation p1 x v1 / t1 = p2 x v2 / t2...
  32. LunaFly

    Polytropic Process for an Ideal Gas

    Hi, I have a general question about polytropic processes when working with an ideal gas. A polytropic process is one for which PV\gamma = constant. What I am wondering is if we assume that n is constant, does that mean that the temperature does not change for the process? I see that...
  33. G

    Gravitational Potential Energy of an Ideal Gas

    I'm trying to find the avarage enerrgy of an ideal gas when it's under a gravitational potential. I know how to obtain the kinectic avarage energy but the potential energy depends upon the position of each molecule. There is a avarage height lo look for in order to determine this potential term?
  34. M

    Pressure distribution of ideal gas under non-uniform temperature

    Suppose there is a square box with an ideal gas inside at standard temperature and pressure. Now one side of the box is heated up while the other opposite side remains at room temperature (assume a large heat sink). It is clear the temperature distribution of the gas inside the chamber will...
  35. Kelsi_Jade

    Partial Derivatives for an Ideal Gas

    The question is: a) Find explicit expressions for an ideal gas for the partial derivatives: (∂P/T)T, (∂V/∂T)P and (∂T/∂P)V b) use the results from a) to evaluate the product (∂P/V)T*(∂V/∂T)P*(∂T/∂P)V c) Express the definitions of V(T,P) KT(T,P)an BT(T,V) in terms of the indicated independent...
  36. J

    Solve Ideal Gas Problem Homework: Compute Work Done by Air

    Homework Statement Air that initially occupies 0.140m3 (V1) at a gauge pressure of 103.0 kPa (p1) is expanded isothermally to a pressure of 101.3 kPa (p2) and then cooled at constant pressure until it reaches its initial volume. Compute the work done by the air. Homework Equations...
  37. Z

    Compression of an ideal gas

    Homework Statement An ideal gas, Cp = (5/2)R, Cv = (3/2)R, is changed from P1 = 1 Bar and V1t = 12m^3 and V2t = 1m^3 by the following mechanically reversible processes: a) Isothermal compression b) Adiabatic compression followed by cooling at constant temperature c) Adiabatic compression...
  38. Chestermiller

    Do Physicists and Engineers Define Ideal Gas Differently?

    In another thread, DH and I have been discussing the definition of an ideal gas. DH, who appears to be a physicist, seems to use a definition different from that which we engineers use. I am soliciting responses from both physicists and engineers as to their understanding of the term "ideal...
  39. C

    Final Temperature of Ideal Gas in Constant Pressure and Volume Compression

    Homework Statement A container of gas at 3.90atm pressure and 136 ∘C is compressed at constant temperature until the volume is halved. It is then further compressed at constant pressure until the volume is halved again. What is the final temperature of the gas? Homework Equations PV=nRT...
  40. S

    Thermodynamics, ideal gas, virial coefficient

    Homework Statement So the problem gives you the compressibility factor Z. It gives two equations, one for ideal gas and other one for non-ideal gas. The question states: The second Virial coefficient B(T) depends on the temperature T and is related to the intermolecular potential B(T) =...
  41. M

    Thermodynamics and polytropic ideal gas (very simple theory question)

    hey all! i have a question i was hoping some of you could unravel. specifically, in thermodynamics i understand in a quasi-static situation we can right work as: W=\int PdV where W is work, P is pressure, and V is volume. my book defines polytropic to be PV^n = constant it then...
  42. C

    Using the Ideal Gas temperature scale

    Homework Statement Below is some values of the observed values of pressure P of a gas in a constant volume gas thermometer at an unknown temperature and at the triple point of water as the mass of the gas used is reduced. ##P_{TP}## (torr) | 100 | 200 | 300 | 400 ##P## (torr)...
  43. R

    How Many Moles of NO2 and SO2 Are in the Mixture?

    Homework Statement A sample containing only NO2 and SO2 has a total pressure of 120 torr. Measurements show that the partial pressure of NO2 is 43 torr. If the vessel has a volume of 800.0 ml and the temperature is 22.0°C, how many moles of each gas are present?Homework Equations PV = nRT The...
  44. C

    Ideal Gas HW Problem: Pressure at 11,000 meters?

    Ideal Gas HW Problem!? Homework Statement "At an altitude of 11,000 meters, the air temperature is -50 degrees celsius. The air density is 0.403 kg/m^3. What is the pressure of the atmosphere at that altitude." Homework Equations P = P0exp(- Mgy/RT) The Attempt at a Solution I...
  45. A

    Ideal Gas & Piston Homework: Calculate Distance Moved

    Homework Statement Asshown in the figure below, an enclosed cylindrical container(cross-sectional area : S) is divided into two sections (A,B) by piston P.The length of each section is 10cm.Each section contains a monoatomic gas at temperature 0°C and pressure 1.0×10^5 Pa.(both contain the...
  46. A

    Multi-Species Ideal Gas Law and Mean Molecular Mass

    Hi forums. I have what I think is a simple question but I'm making myself confused. I'm trying to work out the relationship between energy density ( u = energy per unit volume ) and temperature in a multi-species ideal gas (no molecules just different mass ions). The simplest example of...
  47. H

    Derivation of ideal gas law by Hamiltonian mechanics

    Hi! I am trying to understand the statistical mechanics derivation of the ideal gas law shown at: http://en.wikipedia.org/wiki/Ideal_gas_law inder "Derivations". First of all, the statement "Then the time average momentum of the particle is: \langle \mathbf{q} \cdot \mathbf{F} \rangle=...
  48. marellasunny

    Equilibrium reaction ICE method to ideal gas law

    QUESTION: Say I have the following equilibrium reaction CO+\frac{1}{2}O_2\leftrightharpoons CO_2 The stoichiometric mixture of CO and $O_2$ in a closed vessel, initially at 1 atm and 300K, is exploded. Calculate the composition of the products of combustion at 2500K and the gas pressure. Take...
  49. C

    Ideal Gas Heat Capacity Regression Coefficients

    I'm trying to find a comprehensive list of the empirical coefficients to be used in the following equation for calculating ideal gas constant pressure heat capacities: \frac{c^{IG}_P}{R}=A+BT+CT^{2}+DT^{-2}+ET^{3}(Eqn. 1) cPIG is the ideal gas constant pressure specific heat capacity; R is...
  50. fluidistic

    What energy is this? Related to monoatomic ideal gas

    For a monoatomic ideal gas, if ##c_v## is constant then the internal energy is worth ##U=\frac{3nRT}{2}##. This is a state equation. From the fundamental equation ##S(U,V,n)= \frac {nS_0}{n_0}+nR \ln \left [ \left ( \frac {U}{U_0} \right ) ^{3/2} \left ( \frac{V}{V_0} \right ) \left ( \frac...
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