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. WMDhamnekar

    MHB Maths in Temperature and ideal gas Thermometer

    Hi, I didn't understand the maths involved in the below article in regard to temperature and ideal gas thermometer. If any member knows it, may reply me. If triple point of water is fixed at 273.16 K, and experiments show that freezing point of air-saturated water is 273.15 K at 1 atm...
  2. K

    Finding the Volume of an Ideal Gas

    Hi, I tried to do this question in two different approaches one of them was using the equation PV=mRT where I got the right answer which is 4.305 m**2. However, I tried using this Density = Mass/Volume, where I substituted Denisity= 1.225 and Mass equals 5kg to get the volume as 4.08. Can...
  3. J

    Chemistry Ideal Gas Law and Partial Pressures

    I had already found the Mass of the product (C3H3N) produced by this reaction (theoretical mass at 100% yield) in a previous problem. I did this by finding the Limiting Reagent (C3H6) in the reaction , calculating the number of moles of C3H6 and using the Molar Ratios in the balanced reaction...
  4. A

    Ideal gas: two tanks connected by a cylinder

    I ASSUME THAT THE PRESSES OF THE TWO CONTAINERS WILL BE EQUAL IN THE FINAL (STATIONARY REGIME). SO Pa = Pb naRTa/V = nbRTb/V naTa = nbTb Than , I just need to set up a system My question is , so, will the two pressures at the end be the same? And as for the temperatures, can I also say...
  5. Hiero

    Adiabatic expansion of a piston in a cylinder filled with ideal gas

    I was puzzling over how to solve this and finally peeked at the solution. They used the relevant equation above. I disagree with this though. The problem specifically says “the piston is allowed to slide freely!” This means that we don’t let it happen slowly. So then we are not in...
  6. L

    I When does the ideal gas equation break down?

    P1/V1/T1 = P2 V2 /T2 is derived from the ideal gas equation. However it is stated that this equation breaks down at very high pressures and at very low temperatures. Does anyone know what kind of pressures and temperatures we are talking about here?
  7. E

    B What is the significance of Δx and Δp in the ideal gas entropy equation?

    Up to an undetermined constant ##a## the entropy of an ideal gas goes like$$S = k_B N\ln \left[ a^\frac{3}{2} \left(\frac{V}{N}\right) \left(\frac{E}{N}\right)^{\frac{3}{2}} \right]$$In some notes is written: And then they identify ##\Omega = \left(\frac{\Delta x \Delta p}{w}\right)^{3N}##...
  8. Mahfuz_Saim

    What will be the number of collision per second in a unit area?

    By using PV=nRT formula, I have found the volume of the vessel. As far as I have learned to calculate the number of collision in a unit volume. So, it is being difficult for me to find the right way to solve. I searched on the internet and have got this...
  9. P

    Finding the efficiency of an ideal gas with adiabatic exponent 'γ'

    Here is what I did : work done in going from A to C, W1 = 2nRToln(2) (isothermal process) work done in going from C to B, W1 = pΔV = nRΔT = -nRTo (isobaric process) work done in going from B to A, W3 = 0 (isochoric process) so, total work done = W1 + W2 + W3...
  10. I

    Chemistry What are the partial pressures of each gas in the mixture?

    I've first calculated the partial pressures of each gas: ##N_2: 0.4\times 7.4\times 10^4=3.0\times 10^4 Nm^{-2}\\## ##O_2: 0.35\times 7.4\times 10^4=2.6\times 10^4 Nm^{-2}\\## ##CO_2: 0.25\times 7.4\times 10^4=1.9\times 10^4 Nm^{-2}\\## From here, I do not know how to continue. Could someone...
  11. I

    Question about calculating the minimum temperature in hot air balloons

    First, I tried using the Archimedes principle and calculated the weight of the surrounding air displaced when taking off. ##W = 2500\times 1.29\times 9.81 = 31637.25 N## But then, I got stuck and do not know how to proceed from here on. I don't want the full solution yet but can I get some...
  12. P

    Entropy and the Helmholtz Free Energy of a Mass-Piston System

    Attempt at a Solution: Heat Absorbed By The System By the first law of thermodynamics, dU = dQ + dW The system is of fixed volume and therefore mechanically isolated. dW = 0 Therefore dQ = dU The change of energy of the system equals the change of energy of the gas plus the change of energy...
  13. shadedvertex

    Flaw in alternative approach to determine ideal gas speed distribution

    If we assume the energy of particles in an ideal gas follows a Boltzmann distribution, then the energy distribution function can be defined as below: , where k_B is the Boltzmann constant Since the energy of particles in an ideal gas are assumed to only consist of translational kinetic energy...
  14. Pouyan

    How is entropy affected in a reversible process for an ideal gas?

    What do I see in my solution is : ΔW + ΔQ = W_pv + W' + ΔQ (A little difficult to perceive the useful work ) Work on the environment : -p0*(-ΔV) (WHY negative sign?, Is this the work ON the gas?) ΔV=nR (T0/p0 -T/p) By TdS = dQ ΔS + ΔS0 =0 Reversible case: ΔU= -T0ΔS - (-p0(-ΔV)) + W' (WHY...
  15. greg_rack

    Speed of sound in an ideal gas

    First of all I thought it was necessary to calculate the temperature(the only data missing for the formula) using the ideal gas equation(since I've already been given 'p' and 'V'), and plug it in the 'v' formula, but the problem immediately occurred when i tried to find out the number of...
  16. D

    Accounting for Liquid Water Density in Ideal Gas Pressure Calculations

    First calculate the total pressure, but that gives me p2=p1*t2/t1 = 2,86 bar and partial pressure of 0,87 bar which is wrong. any tips?
  17. CptXray

    Ideal gas in a cylindrical container

    It looks more like a computational obstacle, but here we go. Plugging all of these to the partition function: $$Q = \frac{1}{N! h^{3N}} \int -\exp(\frac{1}{2m}(p^2_{r}+p^2_{\phi}/r^2+p^2_{z})+gz)d\Gamma=$$ $$= \frac{1}{N! h^{3N}} \int \exp{(\frac{-1}{2m}p^2_{r})}dp_{r_{1}}...dp_{r_{N}}...
  18. F

    Moving an adiabatic partition in an adiabatic container

    The actual data for the problem and my (and my friend's) attempt at a solution are in the attached file. In a nutshell, this is what happened. I obtained a solution based on the fact that the system is isolated. Thus the initially hot gas moves the partition doing work onto the initially cold...
  19. ContagiousKnowledge

    General solution of the spherical wave equation

    Since the spherical wave equation is linear, the general solution is a summation of all normal modes. To find the particular solution for a given value of i, we can try using the method of separation of variables. $$ ψ(r,t)=R(r)T(t)ψ(r,t)=R(r)T(t) $$ Plug this separable solution into the...
  20. Zifan Wang

    Ideal Gas Law: Question about a compressor exam question

    This is a question in my midterm. I calculated for the answer as c) 11.7 atm by the Ideal Gas Law. The professor states that "all the air is originally at 1 atm" in the prompt indicates an idea of "both 70 L of air and existing 6 L of air in the tank are at 1 atm", and he grades d) 12.7 atm as...
  21. B

    Ideal gas: Temperture at 1 atm

    Summary: U=3/2*n*R*T Can some of you help me with this The total internal energy of an ideal gas is 3770 J. If there are 3 moles of the gas at 1 atm, what is the temperature of the gas? I use U=3/2*n*R*T but get the wrong answer, (101 K) but it should be 303 K [Moderator's note: Moved from...
  22. M

    Chemistry Ideal Gas Problem | Get Help Now!

    Hello guys. I really try to understand the problem, can you please help.
  23. N

    Ideal Gas Law in Two Dimensions

    I am creating a two-dimensional model of an ideal gas, and I was wondering how I should determine initial velocity. Ideally, I would like for the simulation to reach a point where the velocity distribution resembles that of the maxwell-boltzmann curve — will this be achieved if I, say, assign...
  24. S

    Changing the Air Temperature with a hair dryer

    Hi, so I found this on another old "AP" High School Finals Exam. I think I may be super lost. Because the only way that I can think about is KE = 3/2kT. And then that the difference of the Kinetic Energy of the air Particles is the Q supplied by the heater inside the air dryer. So ## \frac...
  25. ArcHorizon

    Calculations using the Ideal Gas Law

    2.1 * 10^-4m/3 Temperature 310K Pressure: 5.3 * 105 Pa So the Ideal gas formula is PV = nRT 2.1*10^-4m^3 Times 5.3*105Pa = n * Gas Constant * Temperature 2.1*10^-4m^3 (*) 5.3*105Pa = # of moles * I'm not sure what I was doing, but the whole equation stuff got hard and I stopped. I left...
  26. J

    I How Do You Calculate Initial Pressure and Final Volume in Adiabatic Expansion?

    I have a compressed pure gas at a specific temperature and volume. (T1, V1) It suddenly (adiabatically) expands until it's at ambient pressure and a specific temperature. (P2, T2). Given: T1, V1, T2, and P2, I want to find P1 and V2. There's a great example in wikipedia which is almost...
  27. DaTario

    I KT in systems other than ideal gas

    Hi All, When dealing with the kinetic theory of gases in thermodynamics, we obtain the result that the mean kinetic energy per atom is (3/2) kT. In considering different samples like 200g of liquid water or a solid cube of lead with one cubic meter, does kT still play an important role in...
  28. Catstranaughts

    Find Vol 2 in Ideal Gas Law Problem with V1 and V2 Open and V3 Shut

    Please refer to diagram. V1 is open initially then V2 is open for 5 minutes for pressure to equalize. V1 and V2 are then shut. V3 is opened. What is Vol 2 ? P(final)*V(final) = n(final)* R*T => (Vol1 + Vol2) = n(final)*R*25C/ 0.070 Torr where n(final) = n(Vol1) + n(Vol2) If I shut V3, I...
  29. Philip Koeck

    Can the isothermal expansion of an ideal gas be irreversible?

    For the reversible expansion of an ideal gas the heat flowing out of the surroundings and into the system is equal to the work done by the system. Since both system and surroundings have the same constant temperature the entropy increase of the system is equal to the entropy decrease of the...
  30. Clara Chung

    Ideal gas problem after constraint removed

    Attempt: P_1 (initial pressure on the left section) P_2(initial pressure on the right section) T_f, P_f (final pressure for both sections) P_1 (V/3) = N/2 k (3T/2) P_2 (2V/3) = N/2 k (T/2) P_f V/2 = N/2 k T_f Resulting in 4 unknowns and 3 equations... Not enough to find T_f...
  31. R

    Thermodynamics and ideal gas law concepts

    I'm having trouble wrapping my head around some thermodynamics and ideal gas law concepts. I don't have a specific textbook question but Just a concept I'm having trouble with. What I'm struggling with is understanding some of the relations between pressure, volume and temperature...
  32. WhiteWolf98

    Fluid Dynamics - Mass Conservation, State Equation for an Ideal Gas

    I understand that ##\dot m=\rho Q## and ##{\dot m}_{in}= {\dot m}_{out}## . So one can say that ##\rho Q_1 = \rho Q_2##. But I'm not sure if that equation is correct. I don't know if the density remains constant, or the volume flow rate. And then how I'm also supposed to tie a state equation in...
  33. T

    Internal energy in ideal gas

    I have the definition of change in internal energy. $$ \Delta U = Q - W $$ I can get the work by $$ W = \int_{V_1}^{V_2} p dV = p \Delta V $$ however the pressure isn't constant so this won't do. ## W ## is work done by the gas and ## Q ## is amount of heat energy brought into the system. I'm...
  34. L

    B Confused about the ideal gas law

    Ok, i am struggling to figure something out. I don't know why math is so much easier than physics haha. ok, here is my struggle. I have two states, state 1 and 2, which i will call just 1 and 2. 1: T=298kelvin V=0.025m(cubed) P=310Kpa Mass1=Mass2 R=0.2870 2: T=323kelvin V=0.025m(cubed) P=...
  35. hnnhcmmngs

    Minimum heat removed from gas to restore its state

    Homework Statement After a free expansion to quadruple its volume, a mole of ideal diatomic gas is compressed back to its original volume isobarically and then cooled down to its original temperature. What is the minimum heat removed from the gas in the final step to restoring its state...
  36. T

    Exploring the Ideal Gas Law: A Balloon Problem

    Homework Statement Homework Equations Ideal gas law The Attempt at a Solution The solution to this problem assumes the pressure inside the balloon is the same as the outside pressure, i.e. atmospheric pressure. Is this a valid assumption? I would guess otherwise.
  37. Lolaamaigatti04

    What would be a real-life example of the ideal gas law?

    Homework Statement What is a real-life example of the ideal gas law? Homework Equations PV = nRT (Pressure x volume = number of moles x the gas constant x temperature in Kelvin) The Attempt at a Solution https://www.reference.com/science/ideal-gas-law-used-everyday-life-3dacbd6ebd3b5949...
  38. A

    I Free expansion of an ideal gas

    If considering the free expansion of an ideal gas adibatically such that the final volume is double of the initial volume. Since dU=0 for free expansion ,which implies Ti=Tf for ideal gas...(1) From adiabatic relation , TiViγ-1=TfVfγ-1, to satisfy (1) ,γ-1=0 and for ideal gas Cp-Cv=nR or...
  39. S

    Ideal Gas Law and Pressure at 80°C

    Homework Statement An ideal gas has a molar mass of 40 g and a density of 1.2 kg m-3 at 80°C. What is its pressure at that temperature? Homework Equations PV=nRT R constant= 8.314 n= number of moles T= tempreture in kelvin density=Mass/ Volume The Attempt at a Solution i simply solved it like...
  40. relatively-uncertain

    Universal Gas Equation problem

    Hi everyone, I'd really appreciate any help with this problem: A helium cylinder for the inflation of party balloons hold s 25.0L of gas and is filled to a pressure of 16500kPa at 15 degrees celsius. How many balloons can be inflated from a single cylinder at 30 degrees celsius if the volume of...
  41. A

    Specific heat at constt. volume of an ideal gas

    The ans comes out (c) if I take specific heat at constt volume to be independent of temp. Whether the specific heat is always temp. independent for an ideal gas??
  42. T

    Thermodynamics of a Single-Component Ideal Gas

    Homework Statement In all calculations, take R = 8.31 J/m-K. Use the Sackur-Tetrode equation with N replaced by n and K replaced by R to calculate the changes in entropy. Also, assume that these processes are quasi-static so that the ideal gas law and the first law apply at all times. Consider...
  43. Death eater

    I What is the difference between a perfect gas and an ideal gas?

    What is difference between perfect gas and ideal gas?
  44. R

    I Density of states in the ideal gas

    The MB energy distribution is: MB_PDF(E, T) = 2*sqrt(E/pi) * 1/(kB*T)^(3/2) * e^(-E/(kB*T)) How do I arrive at the density of states which hides inside the expression 2*sqrt(E/pi) * 1/(kB*T)^(3/2) ? I've only seen DOS that have "h" in them.. I want it to contain only E, pi, kB and T.. This is...
  45. jamiebean

    Basic physics units problems involving the Ideal Gas Law

    Homework Statement The following is the equation of ideal gas law, where p is pressure (Force/Area), V is volume, n is number of moles and T is temperature in Kelvin. What is the fundamental unit of R? pV = nRT A. kg^−1 · m^−2 · s^ 2 · K · mol B. kg^−1 · m^−4 · s ^2 · K · mol C. kg · m^4 · s...
  46. T

    Confusion about the work done by an ideal gas

    When an ideal gas,in a piston kind of system and whose equilibrium state is mentioned, is allowed to expand (piston is allowed to move and not gas leaking )against a constant external pressure very quickly, then, is the work done by gas zero or not zero ? The argument for work being zero is...
  47. S

    Canonical partition function of an ideal gas (unit analysis)

    Homework Statement Basically the units of the Canonical Partition Function within the logarithms should be zero Homework Equations The Attempt at a Solution N here is a number so we ignore the left logarithms, applying a "Unit function " for the terms within the logarithm...
  48. G

    Using Ideal Gas Law to Calculate Vertical Pressure Gradient

    Homework Statement Consider a cylindrical parcel of air of area A and infinitesimal height dz. If this air parcel is to remain stationary, the difference between the total pressure forces exerted on its top and bottom faces must be equal to its weight. Use this information and the ideal gas...
  49. Q

    Calculating Mercury Column Height in J-Shaped Tube: Manometry Homework Solution

    Homework Statement A J-shaped tube has an uniform cross section and it contains air to atmosphere pression of 75 cmo of Hg. It is pours mercury in the right arm, this Compress the closed air in the left arm. Which is the heigh of the mercury's column in left arm when the right arm is full of...
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