What is Ideal gases: Definition and 82 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. chocopanda

    Mixing two ideal gases with different V, T at constant pressure

    To be honest, thermodynamics is really not my strong suit and I get confused when and how to apply formulas. My thought process is as follows: - there are two ideal gases (ideal gas law applies) - the pressure remains constant (isobaric process), so p1= p2 = p - I imagine there being two...
  2. C

    Ratio of atomic masses of two ideal gases

    For part(b) The solution is, ##1:10##, however, is the wording correct? I don't see how to find the ratio of atomic mass, however, I can solve for the ratio of the molar mass. ##n_A = n_B## from part(a) by setting the internal energy equation for each ideal gas equal ##\frac{M_A}{m_A} =...
  3. V

    B Collision time interval of a gas molecule with wall of container

    I have been trying to make sense of the derivation of pressure under Kinetic Theory of Gases chapter, but it's not making sense to me when the impulse momentum equation is used for the collision between a gas molecule and the wall of the container. The book says that for the elastic collision...
  4. G

    Understanding the Equipartition Theorem for Ideal Gases

    Hi, I am unfortunately stuck with the following task I started once with the hint that at very low temperatures the diatomic ideal gas behaves like monatomic gas and has only three degrees of freedom of translation ##f=3##. If you then excite the gas by increasing the temperature, you add two...
  5. V

    How could the discrepancy be reduced between the two readings?

    I am able to solve part (a) using the relationship ##\frac {P_1} {T_1} = \frac {P_2} {T_1}##, where ##T_1 = 273.16## since its the triple point of water and ##T_2 =T_s## ##(T_s = ## melting point of sulphur). I use the two readings for thermometer A to get ##P_1## and ##P_2## as mentioned in the...
  6. P

    B Confusion when considering pV=nRT in Two Balloon experiment

    This is the Two-Balloon Experiment: https://en.wikipedia.org/wiki/Two-balloon_experiment#cite_note-MW78-1 The claim on Wikipedia which I am a little confused over is that when 2 balloons (at the 2 red points) are connected via a tube, the smaller balloon at a higher pressure would push air...
  7. E

    Cyclic Process for Ideal Gases

    Hello there, is my solution for part d logically correct? Here is my attempt at the solution : Part a : where : P1 = 3P2 Part b : Since P1=3P2, therefore, T1=3T, where T=300K. Thus, T1=900K Part c : Because the final pressure at the end of the cycle is exactly the same as the pressure at...
  8. Uchida

    I Question regarding dh, du, cp, cv for ideal gases

    Hi, Considering the question bellow from a government work selection process:Check the FALSE alternative on the use of thermodynamic properties. In a cylinder-piston type system, the variation of the enthalpy property (Δh) is usually applied to determine the heat (per kilogram) exchanged with...
  9. P

    Piston Between Two Ideal Gases

    Attempted Solution: Gas Entropy This system is isothermal: the energy of each gas remains constant. $$dU = 0$$ By the combined statement of the first and second laws, $$dU = TdS - PdV$$ Therefore, $$0 = TdS - PdV$$ $$dS = \frac {PdV}{T}$$ Therefore, $$dS_1 = \frac {P_1 dV_1}{T} = \frac {P_1...
  10. nineteen

    Why do we study or learn about ideal gases?

    We are learning the lesson about gases/gaseous states at our school and I couldn't help but wonder, why learn about IDEAL GASES... How do ideal gases help us to analyze about real gases?
  11. T

    Mean free path of ideal gases

    I have a box with a wall in mid dividing it in 2 sections, and the wall has a hole of diameter d. There is ideal gas in both sections at 150 K in one section and at 300 K in another. How am I supposed to calculate ratio of mean free paths in 2 sections. My attempt: L ~ Volume / Number of...
  12. 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...
  13. L

    Do ideal gases move at the same speed?

    I've learned that ideal gases have the same average kinetic energy, but this doesn't necessarily mean that they have the same speeds within a container..Instead, is it right to say that (according to kinetic molecular theory) that the speed of molecules at an instance is a wide range of speeds?
  14. F

    Gas Laws -- why calculate the mean square speed at 273K?

    Homework Statement Why is the formula ##p = \frac{1}{3}\rho<c^2>## used to calculate the mean square speed at 273K? Why 273K?
  15. T

    Thermodynamics - Ideal Gases

    Hello everyone. I stumbled across a problem while studying for my exam that I cannot confidently answer. Can we assume nitrogen at the temperature of 27˚C and the pressure of 100 kPa an ideal gas? Justify your answer. The definition of an ideal gas is "...a gas whose molecules are spaced far...
  16. R

    Ideal gases and pressure

    I read from a website that Most gases behave like ideal gases at many temperatures and pressures. and we have learned that the gases behave like ideal one only in high temperature and low pressure . so which one is true .
  17. A

    Two monatomic ideal gases are in thermal equilibrium with ea

    Homework Statement Two monatomic ideal gases are in thermal equilibrium with each other. Gas A is composed of molecules with mass m while gas B is composed of molecules with mass 4m. The ratio of the average translational kinetic energies KA/KB is: Homework Equations KE=0.5xmxVavarage^2...
  18. M

    I Ideal Gases: O2 & H2 - Kinetic Energy Comparison

    Hello, I want to make sure I understand the following considering ideal gases. Assuming I have two different types of gases, say, O2 and H2 (each at thermal equilibrium), is it correct to say that the kinetic energy of the O2 gas equals to the kinetic energy of the H2 gas since they're both...
  19. Elena14

    Dalton's law for ideal gases at different temperatures

    How would Dalton's law be affected when there are two ideal gases in a container at different temperatures? Let the gas with higher temperature be gas A and the gas with lower temperature be gas B. Then heat will be transferred from gas A to gas B due to which kinetic energy of the molecules of...
  20. M

    Calc Vol of 1 Mol Steam @ 100°C, 1 atm: Ideal Gas Eqn

    Homework Statement Calculate the volume of 1 mol of steam at 100°C and a pressure of 1 atm assuming that it is an ideal gas. Homework Equations PV=nRT The Attempt at a Solution Well, if I am honest I was just going to re arrange the above equation for V and plug the numbers in but that seems...
  21. O

    Helmholtz potential for mixture of simple ideal gases

    Homework Statement Two subsystems within a 20 l cylinder are separated by an internal piston. Each of them is initially composed of 1 mole of component 1 and one mole of component 2, both of which will be treated as a monatomic ideal gas. The cylinder has diathermal walls and is in contact...
  22. J

    Finding volume ratio between 2 vessels using ideal gases

    Homework Statement I have been tasked with designing a feasible experiment to determine the ration between 2 vessels. I think i have a way that works on paper. Homework Equations pV = nRT and the conservation of mass. The Attempt at a Solution 1.Start with 2 vessels of unknown volume x and y...
  23. J

    Statements on ideal gases

    Homework Statement Homework EquationsThe Attempt at a Solution I chose 1&2, but all three are correct. I thought for a constant pressure, if temperature is doubled, then the volume would doubled too? As P=V/T ?
  24. L

    Delta(U) = Cvdelta(T) for Ideal Gases?

    I don't understand how Delta(U) = Cvdelta(T) is always true for Ideal Gases...Shouldn't this only be true for constant volume processes? Yet it seems to be used even when a gas is expanding or being compressed... Any ideas...Thanks in advance.
  25. H

    Modeling index of refraction of dilute gases

    I'm interested in predicting the index of refraction of atmospheric air and several nonpolar gases at room temperature for pressures of 1 atm - 0 atm. I'm not really sure where to get started. I have found the relation n=\sqrt{1+\frac{3AP}{RT}} but I don't really get where it comes from. Well...
  26. S

    Ideal gases do not possess potential energy

    Is it that ideal gases do not possesses potential energy because there are no intermolecular forces. But, real gases do have potential energy and its potential energy is the highest among the different phases. ( Potential Energy of Gas>Liquid>Solid ). I need someone to make these things clear to...
  27. E

    Molar Ratio of Two Ideal Gases

    Homework Statement A mixture of two gases, A and B, exists at pressure p1, volume V, and temperature T1. Gas A is subsequently removed from the mixture in a constant-volume process. The remaining gas B is found to have a pressure p2, volume V, and temperature T2. Express the ratio of the...
  28. J

    Vapor Pressure and non ideal gases

    Hi, I understand that vapor pressure is independent of initial pressure, and depends only on temperature. However, is this true of a non ideal gas at high pressures? (I am specifically interested in the vapor pressure of a meg/water mixture at approx. 100 bar), Thanks
  29. R

    Question about u and h and Its Differential Changes for Ideal Gases

    Hello 1. I was wondering why internal energy is usually expressed as a function of temperature and specific volume and enthalpy a function of temperature and pressure (ie why is u(T,v) and h(T,p)) and some other set of two properties? 2. For du = \frac{∂u}{∂T}dT + \frac{∂u}{∂v}dv and dh =...
  30. J

    Ideal Gases dealing with scientific notation

    I am not sure how to properly use the scientific notation in this problem. I have attempted to solve it several different ways to no avail. A house has a volume of 1.45 x 10(4)m(3). At 20.0° C and 740 mm Hg, the air fills the house. If the temperature and pressure increase to 35.0°C and...
  31. S

    Statistical thermodynamics- ideal gases mixture (Reif 3.6)

    A glass bulb contains air at room temperature and at a pressure of 1 atmosphere. It is placed in a chamber filled with helium gas at 1 atmosphere and at a room temperature. A few months later, the experimenter happens to read in a journal article that the particular glass of which the bulb is...
  32. W

    Ideal Gases and Kinetics

    This might be a stupid question, but I am confused about the ideal gas theory. I know that we assume high temperatures and low pressures, and that the volume is negligible when we compare it to a container, but my textbook is very confusing about this point. It says assume zero/negligible...
  33. S

    Effects of decreasing volume and temperature for ideal gases

    How does decreasing the volume increase the temperature of the gases? I was doing an experiment today and when i decreased the volume of the gas from 65ml at 1atm to 20ml the temperature detected an increase of 0.5°C. However, in Boyle's Law temperature is a constant. So would this mean...
  34. S

    Ideal gases and partial volume

    What does it mean by 21% oxygen and 79% nitrogen by volume? Because won't the oxygen and nitrogen have the same volume which is the volume of the whole container? nTRT/VT=nO2RT/VT+nN2RT/VT so why would we say oxygen is 21% by volume since the volume of the oxygen and nitrogen is the same...
  35. Q

    Ideal gases physics help here?

    Homework Statement A moster of a gas has 4 moles and first is in the temperature 300 K and pressure 10 atmosphere.After a change of state, ∆T= -50 K and ∆V=10 liter.Find the final temperature ,volume and pressure of the gas. Homework Equations P*v=n*R*T The Attempt at a Solution...
  36. F

    Two questions on ideal gases and heat

    Homework Statement A horizontal cilindre with a piston of mass M = 0.5 kg is filled with air (the specific heat of air is Cp = 1000 Joule/Grad*kmole). The heating of the gas results in the piston's accelerated displacement (with constant acceleration) until the velocity v = 1 m/s. Determine...
  37. sunrah

    Thermodyn.: ideal gases in 2 two chambers separated by a sliding barrier

    Homework Statement Two different ideal gases are separated by a sliding barrier that can move vertically. The gas in the upper chamber 1 has n moles of material, whilst the gas in the lower chamber 2 has 3n moles of material. At T0 the weight of the barrier is such that the volumes of the two...
  38. H

    Heat capacities of ideal gases

    Homework Statement A cylinder contains 0.2mol of Helium at 30 degrees C and is heated different ways. How much heat is needed to raise the temperature to 70C while keeping thevolume constant? Homework Equations dQ=dU+dT nCpdT=nCvdT+nRdT The Attempt at a Solution What I am...
  39. A

    Ideal Gases under Adiabatic Compression

    I'm having trouble understanding what happens to the internal energy of an ideal gas being compressed adiabatically. If DU = DQ + DW, then as we do work PdV compressing the gas, since in adiabatic processes DQ=0, W the change in internal energy is non-zero, so U must increase. But if...
  40. D

    Blowing up a balloon (thermodynamics and ideal gases)

    1. Homework Statement A balloon behaves such that the pressure is P = CV3 where C = 100 kPa/m3 . The balloon is blown up with air from a starting volume of 1 m3 to a volume of 3 m3 . Find the work done by the air. 2. Homework Equations W=PdV 3. The Attempt at a Solution...
  41. D

    Blowing up a balloon (thermodynamics and maybe ideal gases)

    Homework Statement A balloon behaves such that the pressure is P = CV3 where C = 100 kPa/m3 . The balloon is blown up with air from a starting volume of 1 m3 to a volume of 3 m3 . Find the work done by the air. Homework Equations W=PdV The Attempt at a Solution What I...
  42. G

    Ideal Gases: dU=dW+dQ and dU=3/2RdT

    (I): dU=dW+dQ also (II): dU=\frac{3}{2}RdT if you compress a gas dW in dU is positive from pV=nRT lesser volume could either mean more pressure or more T. If dV gives dp only then dT=0 how can then dU for dW in (I) be equal dU in (II)?
  43. J

    Conditions when real gases behave as ideal gases

    Well i know real gases behave as ideal gas (almost) when pressure is low and temperature is high. I want to understand this - When pressure is low attractive forces in the gas moelcules will be stronger(as compared to high pressure) but the fast movement due to high temperature compensates it...
  44. fluidistic

    Thermodynamics, finding the fundamental equation of ideal gases

    Homework Statement An ideal monoatomic gas is characterized by the two equations PV=NRT and U=\frac{3NRT}{2} in which R is a constant. Find the fundamental equation corresponding to a monoatomic ideal gas. Homework Equations S=\left ( \frac{1}{T} \right ) U+\left ( \frac{P}{T} \right )...
  45. J

    Quick questions about ideal gases

    Homework Statement Hey guys, I am having trouble understanding how the ideal gases behave and I got these 3 questions in homework: If an ideal gas is transferred, at constant temperature, 10 Joules of heat, does the internal energy change? If an ideal gas is transferred, at constant...
  46. Rapier

    Work Done On Ideal Gases

    Homework Statement I want to start by saying that my instructor is a particle physics guy. He loves to talk about particles seems to want to rush through fluids and thermo so he can get to particles and the 'real modern physics.' He is skipping, skimming and not really covering a lot of this...
  47. X

    Ideal gases thermodynamic enthelpy and internal energy change

    Homework Statement See attachment ecxample001. Homework Equations See attachment D11. The Attempt at a Solution In the first equation (Cp/R = a+bT+cT^2...etc.), Cp/R is the constant pressure specific heat. The general formula for enthalpy change is h2-h1 = integral[Cp]dT, so does...
  48. E

    Thermodynamics question - Ideal gases

    A rigid tank with a volume of 0.75 m3 initially contains air at 70 kPa and 25 degrees C. A small hole develops in the tank. The surrounding air at 100 kPa and 25 degrees C slowly leaks into the tank due to the hole. Heat transfer between the surroundings and the tank maintains a constant air...
  49. J

    Thermodynamics specific volume, heat, & ideal gases

    Homework Statement I attached the problems. The first one is D) at the top of the page parts a) and b). The second one is E) at the top of the second attachment. 1) The rigid tanks shown below have volumes of .4m^3 and .004^3 respectively and each contains a water liquid-vapor mixture of...
  50. D

    Entropy of Mixing for Two Ideal Gases at Different Temperatures

    Homework Statement Two monatomic ideal gases are separated in a container by an impermeable wall, with volumes V_{1} and V_{2}, temperatures T_{1} and T_{2}, number of atoms N_{1} and N_{2}, and both are at the same, constant pressure P. The wall is then removed, and the pressure is continued...
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