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. J

    Solving for Two Speeds of an Ideal Gas He at a Given Temperature

    Homework Statement For an ideal gas He at T = 328 K find the two speeds v that satisfy the equation 2F(v) = F(v*). m/s (lower speed) m/s (higher speed) Which of the two speeds you found is farther from v*? the lower speed or the upper speed Explain this result. Homework...
  2. S

    Free (mostly) Expansion of an Ideal Gas

    Hey All, Had a problem to solve and wanted to know how others would approach it. Problem is as follows: An insulated container of known volume has an orifice of know size. Container is filled with air and left to rest so that temperature and pressure is that of atmospheric surroundings...
  3. T

    10 moles of an ideal gas has a gauge pressure of 2 atm what is new T? no clue

    10 moles of an ideal gas has a gauge pressure of 2 atm what is new T?? no clue [b]1. Homework Statement [/b 10 moles of an ideal gas has a gauge pressure of 2 atm and a temperature of 200 K. If the volume of the gas is doubled and the pressure dropped to 1 atm., what is the new temperature...
  4. E

    We all know that Cv for a monoatomic ideal gas is 3/2 R and when we

    we all know that Cv for a monoatomic ideal gas is 3/2 R and when we have constant volume Q=deltainternal energy =n Cv delta T. Ive read that in any case delta internal energy = nCvdelta T why?
  5. A

    Ideal Gas Question Please do help I'm befuddled

    There are 2 identical vessels X and Y and they are connected like this by a tube of negligible volume: X==========Y they have a pressure of p and same temperature of T Y is then heated, increasing it's temperature from T to 2T. what is the final total pressure in terms of p...
  6. P

    Desperate Deriving Ideal Gas Formula

    I know how temperature, volume and pressure are related and I think (think because I haven't tried any exercise alone yet) I can apply PV = nRT with no problems. But usually I am not able to apply a formula until I understand how I got to it, what it means. I'd like to start from the beginning...
  7. A

    Thermodynamics problem - Find the kinetic energy of ideal gas, given P and V

    Homework Statement Find the Kinetic Energy of the ideal gas \overline{Ek}=? if its volume is 10 liters (10-2 m3) and it is under the pressure of p=5·105. Homework Equations p·V = N·k·T (where p-pressure, V-volume, N-number of particles (molecules), k- Boltzmann constant, T-absolute...
  8. B

    Ideal Gas Behavior: Choose the Right Diagram

    Hi guys, Can someone explain me please how to find the following question? Which diagram represents the behavior of an ideal gas the most? I know it's C but I don't know why. They all seem to represent the behavior of a ideal gas. But why C mor than the others? Thanks
  9. S

    s there a way to calculate this using the thermodynamic identity?

    Homework Statement A liter of air, initially at room temperature and atmospheric pressure, is heated at constant pressure until it doubles in volume. Calculate the increase in its entropy during this process. Is there a way to calculate this using the thermodynamic identity (ie. without the...
  10. T

    Solving Ideal Gas Problems: ΔE, ΔS, W & P0V0

    Homework Statement 1.0 mol of a monatomic ideal gas is taken through the cycle in the figure below. http://s1142.photobucket.com/albums/n603/bdoneski/?action=view&current=20-26.gif" a) What is the following as the gas goes from state a to state c along path abc? W0/P0V0 (b) What...
  11. T

    Isobaric Process: Finding Work Done by Ideal Gas

    Homework Statement When 23.3 J was added as heat to a particular ideal gas, the volume of the gas changed from 54.7 cm3 to 100 cm3 while the pressure remained at 1.00 atm. (a) By how much did the internal energy of the gas increase? J (b) If the quantity of gas present was 2.00 10-3...
  12. N

    Calculate Work Done by Ideal Gas

    Homework Statement 1 mole of an ideal gas is at 9 atm pressure, occupies 1 L and has an internal energy of 474 J. The gas is first cooled at constant volume until its pressure is 1 atm. It is then allowed to expand at constant pressure until its volume is 7 L with an internal energy of 766...
  13. E

    How Is Net Work Calculated in a Cyclic Ideal Gas Process?

    Homework Statement An ideal gas follows the three-part process shown in the figure. At the completion of one full cycle, find the net work done by the system. Homework Equations W=P*deltaV; Total Work = Wab+Wbc+Wca A=1/2bh The Attempt at a Solution Work done from C to A is zero, because...
  14. P

    Ideal Gas law Partial derivative

    This is a question from my calculus book that i thought was interesting, its not homework but I am curious to how you go about showing it. Show T (∂P/∂T)(∂V/∂T)=NR We know PV=NRT so if we take a partial how does the T end up on the other side?
  15. A

    Entropy of a contained ideal gas mixture

    If an ideal gas mixture is heated inside of a container which does not expand then does the entropy increase? Outside the container I know it would but inside the container the gases can't really become more disordered.
  16. R

    Classical Ideal Gas: Pathria's Insight on Non-Interacting Particles

    In the book of Pathria(p.16), he mentioned that If (i) the mutual interactions among particles are negligible and (ii) the wave packets of individual particles do not significantly overlap, then there does not exist any spatial correlations among the particles in the system composed of...
  17. D

    Where Does the Second Term in the Pressure Equation for an Ideal Gas Come From?

    The following is a direct quote from Cramer's Essentials of Computational Chemistry: Assuming ideal gas statistical mechanics and pairwise additive forces, pressure P can be computed as P(t)=\frac{1}{V(t)}N(kb)(T(t))+(1/3)\sum\sumFF f(ij)r(ij) My question is: I've always been taught P=NkT/V...
  18. B

    Ideal gas undergoes cycle process

    Hi, An amount of ideal gas undergoes the folowing cycle process in the following graph: This process can be presented by the following PV-graph : The answer has to be the upper graph but why can't it be the lower graph ? Thank you!
  19. C

    Chemical potential of an ideal gas

    hi, How can I show that the chemical potential of an ideal gas µ(T,V ) can be given by: \mu(T , V , N )=k_{b}T\left(a+1+ln(\frac{Nv_{0}}{V})\right)
  20. Y

    Proving the Ideal Gas Equation of State

    Homework Statement Show that the equation of state of an ideal gas with N molecules in a container of volume V at temperature T is P=NkT. Use the result derived earlier. The result is A=-NkTlnZ, where Z is the partition function and A is the Helmholtz free energy. Homework Equations The...
  21. S

    Chemistry Ideal gas law, concentrations, mole fractions

    I haven't been able to try all parts of this question yet as I've been running into problems fairly near the start. I've asked for help with it but have just been told 'use the ideal gas law' which is what I tried to do but can't seem to get it right. We have been given answers to parts a, b...
  22. L

    Absolute Temperature and the Ideal Gas Law

    Homework Statement A cylinder in a car engine takes Vi = 4.50 x 10^-2 m^3 of air into the chamber at 30°C and at atmospheric pressure. The piston then compresses the air to one-ninth of the original volume (0.111Vi) and to 20.0 times the original pressure (20.0 Pi). What is the new...
  23. L

    Kinetic Theory of the Ideal Gas

    Homework Statement Find the rms speed in air at 0.0°C and 1.00 atm of (a) the N2 molecules (b) the O2 molecules, and (c) the CO2 molecules. Homework Equations vrms = square root of 3kT/m The Attempt at a Solution (a). 28.0u x (1.66 x 10^-27) = 4.68 x 10^-26 1.5 x (1.38 x 10-23...
  24. T

    Ideal gas and dimensionless entropy.

    Hi, I'm trying to solve the attached exercise, but I'm not sure I'm in the right direction. What I've been trying to do is using the relation: dU=TdS-pdV Dividing it by T and adding dT so the relation will be (dU/T)dT=(ds/dT)-pT(dVdT), but I don’t think it’s the right way to solve it...
  25. K

    Ideal Gas Law Change Rate Problem

    Homework Statement The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at a certain instant, P = 9.0 atm and is...
  26. P

    How does the ideal gas law work?

    So here's what has me all confuzzled about the relationship between temperature and pressure: Temperature is proportionate to average kinetic energy... but why does expanding a container lower the KEavg of the container's gaseous contents? Shouldn't the conservation of momentum keep all the...
  27. A

    The Science Behind Ideal Gases: Understanding Charles's Law vs. Boyle's Law

    Why it is not necessary for an ideal gas to obey Charles's law, but Boyle's only?
  28. R

    What is the Correct Calculation for Pressure in Boyle's Ideal Gas Law Problem?

    Homework Statement A 3-Litre Vessal gas at a pressure of 200 kPa. 5-Litres of gas at the same pressure if forced into the vessal. Calculate the new Pressure Homework Equations P1V1+P2V2 The Attempt at a Solution P1=200*V1=3 / V2=5 = P2 120 kPa New Pressure = 120 kPa I am...
  29. T

    Isothermal expansion of an ideal gas

    Homework Statement One mole of monatomic ideal gas is taken from an initial pressure(P) and volume(V) to a final pressure(2P) and volume(2V). It goes from pressure=P and volume=V to pressure=P/2 and volume=2V through isothermal expansion and from there volume stays constant but the pressure...
  30. E

    Heat and Ideal Gas Homework: Point 3 Pressure Calculation

    Homework Statement Look at picture The Attempt at a Solution For V at point 3 I got 4.52 x 10^(-2) For V at point 2 I assumed it was the same as Point 1, but this is where it gets confusing because if I assume that, then does point 3 have the same pressure as point 1? This was...
  31. J

    1st Law of Thermo Calculation (Ideal Gas)

    Hydrogen behaves as an ideal gas at temperatures greater than 200 K and at pressures less than 50 atm. Suppose 6.00 mol hydrogen is initially contained in a 100-L vessel at a pressure of 2.00 atm. The average molar heat capacity of hydrogen at constant pressure, cp, is 29.3 J/K/mol in the...
  32. A

    Reversible Adiabatic Expansion for an Ideal Gas

    Homework Statement 1 mole of a monoatomic gas undergoes reversible expansion from 30 L and 400K to 60 L. The molar heat capacity in this situation is (3/2)R, independent of temperature. Calculate the final pressure and temperature of this process if it is adiabatic. Homework...
  33. C

    Chemical potential in ideal gas (does it have meaning ?)

    While useful and unique for reactions or phase transforms, I fail to see how chemical potential brings anything new to ideal gas systems. For example, if chemical potential is described as the quantity the same for 2 systems in diffusive equilibrium, then for ideal gas systems (think 2 boxes...
  34. D

    Adiabatic, Ideal gas, changing heat capacity, work calculation

    1. Propane vapour (1kmol) at a pressure of 40 bar and 230 C expands adiabatically to 0.25 bar and 95 C. Determine a)W, b)Delta S, c)The amount of work obtained if the expansion were done reversibly from the same initial conditions to the final pressure of 0.25bar 2. I am not sure how to...
  35. K

    Does a Thermometer Truly Reflect Air Temperature in Kinetic Theory?

    Let’s take an ordinary household thermometer and expose it to the air. The molecules of the air impact on the surface of the thermometer and transfer kinetic impulses. The thermometer transfers kinetic impulses to the impacting molecules as well. Eventually, thermal equilibrium is reached and...
  36. M

    What is the Ideal Gas Equation for Calculating Gas Properties?

    Homework Statement Considering a container of 3*10-2m3 filled with an unknown gas such that the pression is 15MPA (or 1.5*107Pa) and the temperature is 25°C. Determine the volume occupied by one atom of the gas and determine the average distance between its particles. Homework...
  37. S

    Ideal Gas Carnot engine refrigeration

    Homework Statement What is the relationship between the heat absorbed and rejected by the reservoirs and their temperature. If a heat pump is used to transfer heat what is the rate at which heat is added to the hot reservoir in terms of the temperatures of the reservoir and the work done by...
  38. J

    Finding Number of Moles with Ideal Gas Equation

    I want to find the number of moles and I have the ideal gas equation as : n = PV/RT However I think I'm using the wrong units to find it, I want the answers in moles. n = (1 Pa * 1 m^3) /(8.314 JK^-1 mol^-1 * 1K) so would this give the answer x mol^-1?? I can't see how that would...
  39. D

    What is the Internal Energy of an Ideal Gas at Given Conditions?

    Homework Statement A container of volume 0.72 m^3 contains 1.4 mol of argon gas at 24 degrees C. Assuming argon behaves as an ideal gas, find the total internal energy of this gas. The value of gas constant is 8.31451 J/mol x K. Answer in units of J. Homework Equations PV=nRT...
  40. Saladsamurai

    Ideal Gas Mixtures: Dalton vs Amagat Models

    Hello all! :smile: You know, I thought I knew something about ideal gas mixtures, but now I am not so sure. I am reading through a section of a text that discusses the Dalton and the Agamat models of ideal gas mixtures. I will briefly describe each: Dalton Model: The underlying assumption...
  41. D

    Ideal Gas Pressure: Solve Physics HW

    Homework Statement This is for my physics homework and I haven't done gen chem in a while so I was wondering if this was right: One mole of an ideal gas at 0◦C is held at a constant volume of 94 liter. Find the change in pressure if the temperature increases by 61◦C. Answer in units of atm...
  42. S

    Is Internal Energy of Ideal Gas Really Only Dependent on Temperature?

    We known U=3/2nRT (monatomic ideal gas), just depends on temperature. Most texts assert connecting U and Q with constant volume condition and say"\Delta U = nCv\Delta T for any process because of internal energy only depends on temp". I think that statement is very strange. Deriving...
  43. P

    Ideal Gas Law, Pressure equilibrium

    Ok so I just need help with clarifying in how I should attempt to solve this problem. There's two question involving the same information. I've solved the first question but need help with setting up the second one. Here is the problem: Two containers, A and B are filled with argon. The...
  44. M

    Temperature and Entropy of an ideal gas

    Homework Statement One mole of an ideal gas is confined to a vessel of volume 4L at a temperature of 300°C. The vessel is placed inside a container of volume 200L and the gas is released. (a) What is the final temperature of the gas if it's expansion into the container is adiabatic...
  45. F

    Calculating Heat Needed to Raise Room Temp: An Ideal Gas Approach

    Homework Statement Treating air as an ideal gas of diatomic molecules, calculate how much heat is required to raise the temperature of the air in an 8.3 m by 13 m by 5.0 m room from 24 °C to 27 °C at 101 kPa. Homework Equations PV = nRT ---> n = PV/RT Q = NCpDeltaT The Attempt...
  46. R

    Adiabatic expansion of an ideal gas.

    Problem: One mole of a diatomic ideal gas, initially having pressure P and volume V, expands so as to have pressure 2P and volume 4V. Determine the entropy change of the gas in the process. Attempt: I thought this would just be R ln(V2/V1)... So, I said (8.314)*ln(4) but it's wrong...
  47. P

    How Many Air Molecules are Contained in a Smooth Cylinder at Equilibrium?

    Homework Statement A smooth, well-greased insulated cylindrical container with a metal base has a light (so you can neglect its weight), airtight piston that can frictionlessly move up and down the inside of the container. A mass M = 73 kg sits on top of the piston. The piston has a circular...
  48. L

    Ideal gas law and a bicycle pump

    Homework Statement When you push down on the handle of a bicycle pump, a piston in the pump cylinder compresses the air inside the cylinder. When the pressure in the cylinder is greater than the pressure inside the inner tube to which the pump is attached, air begins to flow from the pump to...
  49. A

    Simple Ideal Gas Law but i keep getting it wrong

    Homework Statement P=1.5 atm; n=2 mols, R=8.314; T=250 K; V=? Homework Equations PV=nRT i converted p into Pa and got 151987.5 Pa. The Attempt at a Solution I plugged in all of the numbers and got V=0.027 L but it keeps saying my answer is wrong. It says answer for 2 sig figs. I...
  50. M

    How Is Volume Affected by Pressure in an Ideal Gas?

    Homework Statement A monatomic ideal gas is held in a thermally insulated container with a volume of 0.0900m 3. The pressure of the gas is 110 kPa, and its temperature is 347 K. To what volume must the gas be compressed to increase its pressure to 150 kPa? To what volume must the gas be...
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