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. T

    Derive the ideal gas law from Charles', Boyle's, and Avogadro's, how?

    What is the trick to derive the ideal gas law and gas constant from the "combination" of Charles', Boyle's, and Avogado's laws? The general chemistry books I have seen tell me this is how they derived the ideal gas law and constant but they do not show how that is achieved. I tried to go about...
  2. Z

    Compression of monatomic ideal gas

    a monatomic ideal gas initially at 17°C is suddenly compressed to one-tenth its original volume. What is the tmeperature after copression? make the same calculations for a diatomic gas.
  3. P

    Ideal Gas and finding final pressure

    Homework Statement I'm trying to understand algebraically how the solution was arrived at for the following problem. Automobile tire at normal atmosphere at 10 deg C. Inflating the tire to 28% of original volume with an increase in temp to 40 deg C What is the pressure? Homework...
  4. A

    Chemical potential of an ideal gas problem

    Hey everyone. I hope someone can help. I'm off on this by several factors so I'm wondering what I may be inferring incorrectly. Homework Statement Express the chemical potential of an ideal gas in termps of T and V: \mu = c_{P}T - c_{V}T\ln T - RT\ln V - s_{0}T + const Homework...
  5. B

    Why does the ideal gas state equation fail at high pressures for real gases?

    Why does the ideal gas state equation fail at high pressures for real gases? I think it has something to do with the forces between the molecules in the gas, but I'm not sure the exact reason
  6. K

    What is the Ideal Gas Law in Space?

    Homework Statement A nebula-a region of the galaxy where new stars are forming-contains a very tenuous gas with 100 atoms/cm^3. This gas is heated to 7500 K by ultraviolet radiation from nearby stars. Put the answer in atmospheres. Homework Equations pV=nRT R=8.31 n=N/NA NA =...
  7. D

    Why is rotational energy not included in the Hamiltonian for an ideal gas?

    When using the equipartition theorem to derive the heat capacity of an ideal gas, you have \left\langle H \right\rangle=\left\langle \frac{1}{2}m\left(v^{2}_{x}+v^{2}_{y}+v^{2}_{z} \right) \right\rangle and each degree of freedom contributes 1/2 kT to the total energy and 1/2 k to the total...
  8. A

    Hot air balloon - Ideal gas law

    Homework Statement Estimate the required temperature of the air inside a (rigid) balloon in order for it to achieve lift off. Volume 2000m3 \summass, mtot=920kg Homework Equations pV=NkT p=\frac{Force}{Area} \rho=\frac{m}{V} The Attempt at a Solution We require Fup>(mair+mtot)g (assume...
  9. F

    Ideal gas law problem in outer space

    Homework Statement In outer space, the density of matter is about one atom per cm^3, mainly hydrogen atoms, and the temperature is about 3.4K. Calculate the average speed of the hydrogen atoms, and the pressure (in atmospheres) M_H = 1.0079au = 1.67 X 10^-27 Kg 1 Hydrogen atom per cm^3...
  10. K

    Show that the Internal Energy of an Ideal gas is a Function of T only

    Homework Statement Show that internal energy U = U(T) only for an ideal gas who'se equation of state is: P(V-b) = RT (the claussius equation for n moles of gas) Homework Equations Thermodynamic Equation of state: \left(\frac{\partial U}{\partial V}\right)_T =...
  11. O

    Find work done on an ideal gas and a copper block.

    1. Homework Statement An Ideal gas and a block of copper have equal volumes V and at the same temperature T and atmosphere pressure P. The pressure on both substances is increased reversibly and isothermally to 5P. a) Find the work done on the ideal gas if V = 0.5 m and T= 300 K P =...
  12. O

    Need help with finding the work done on an ideal gas and copper block

    Homework Statement An Ideal gas and a block of copper have equal volumes V and at the same temperature T and atmosphere pressure P. The pressure on both substances is increased reversibly and isothermally to 5P. a) Find the work done on the ideal gas if V = 0.5 m and T= 300 K P =...
  13. K

    Heating an Ideal Gas: Why Burning Fuel is Equivalent to Reversible Heating

    Homework Statement I'm struggling to explain why for an ideal gas at constant pressure heating by burning fuel is equivalent to reversible heating. I know that all forms of work on a ideal gas are eqivalent but don't know why. Homework Equations The Attempt at a Solution
  14. D

    Specific heats relating to ideal gas properties?

    Partition separates two gases in a rigid well-insulated container. Q=0, W=0. State 1: Air: m=1kg P=500kPa T=350K CO_2: m=3kg P=200kPa T=450K Assume constant specific heats. Assume kinetic and potential energy changes are negligible. Assume the partition between the two gases...
  15. mishima

    Can gas pressure and density be reduced without changing temperature?

    I'm curious from a lab sort of perspective, how does one keep a gas at a constant temperature yet decrease both pressure and density? Like how could I reduce the pressure of argon gas with the gas kept at room temperature? Put it in a vacuum larger than the space it normally occupies or...
  16. M

    Ideal Gas: Non-Uniform Conditions Explained

    Hi, If I have a container with fixed volume, and fill it entirely with a known quantity of CO2, and then heat the edges, I should be right in saying I have under my control the temperature, volume and molecule number, and the pressure is fixed by the ideal gas equation (assuming the assumptions...
  17. W

    Ideal Gas law and a hot air balloon problem

    My physics problem is as following, Estimate the average temperature of the air inside a hot air balloon. Assume that the total mass of the unfilled balloon and payload is 500kg. what is the mass of the air inside the balloon? we are told to use a radius of 15m Equations needed density = m/V...
  18. P

    What is the Formula for Calculating the Temperature of an Ideal Gas?

    Homework Statement see attachment. I've asked this question before but no one replied. not sure what formula I should use. already tried lambda (max and med) = C*m*K but neither of them worked. I need some help with this pretty quick if anyone can, thanks. Homework Equations The...
  19. X

    Solving a Relativistic Ideal Gas Momentum Probability Distribution

    Homework Statement For a relativistic ideal gas, the momentum probability distribution is given by where http://latex.codecogs.com/gif.latex?\epsilon_p=\sqrt[]{m^2c^4+c^2p^2}. Determine A Homework Equations The Attempt at a Solution I know that...
  20. E

    Which unit of pressure is used in the ideal gas law?

    The ideal gas law states that pressure (P) is equal to the product of density (N), the ideal gas constant (R) and temperature (T): P = N x R x T I can't figure out which unit the pressure is actually in, although it does seems to work out as the figure I'm supposed to get with a 11706.85°...
  21. J

    Adiabatic process in a monatomic ideal gas

    Homework Statement In a quasistaic adiabatic process in a monatomic ideal gas PV^5/3 = constant [DO NOT PROVE]. A monatomic ideal gas initially has a pressure of P0 and a volume of V0. It undergoes a quasistatic adiabatic compression to half its initial volume. Show that the work done on...
  22. Q

    Mixture of ideal gas (a tricky one?)

    Homework Statement ethylene is stored in 5.6 liter spherical vessel at 260degC and 2750 kPa. To protect against explosion the vessel is enclosed in another spherical vessel with volume of 56L and filled with nitrogen at 260degC and 10.1Mpa. The entire assembly is maintained at 260degC in a...
  23. D

    Which process results in greater work done for the expansion of an ideal gas?

    1. Consider an I.G. expanding from a given state to a fixed final volume at either an isobaric or isothermal process. For which case is the work done greater? 2.Energy balance: \sumEin - \sumEout = (Win - Wout) + (Qin - Qout) = \DeltaU; W = \int Fds Where Q represents heat, W represents work...
  24. D

    Ideal Gas Equation: Calculating R in PV=nRT

    Homework Statement The ideal gas equation, PV=nRT, may have the following units: P is given in bar (bar) V is given in m3 (cubic meters) N is given in mol (moles) T is given in K (kelvin) Which value of R would you use for the calculation if you were using the above units for the...
  25. N

    Bernouilli (ideal gas) method on Photongas? Components of light?

    Hello, A friend of mine (we're both first-years) has just done his herexam of Thermodynamics & Intr. to Statistical Mechanics. He had to get a relationship between pressure P and energy density E/V for a photongas. As a simplification E = \sum |p| c was given. He couldn't do it with the...
  26. K

    Calculating Heat & Work for 1 Mole of Ideal Gas

    Homework Statement 1 mole of monatomic ideal gas. P1 = 2 atm V1 = 44.8 L T1 = 1092 K. The path to P2 = 1 atm V2 = 22.4 L and T2 = 273K is P = 6.643E-4 * V^2 + 2/3. Calculate the heat and work. Homework Equations q = nCpΔT w = PΔVThe Attempt at a Solution I attempted to directly plug in the...
  27. H

    Calculate Pressure of Interstellar Hydrogen Gas at 3K

    Homework Statement Some regions of interstellar space is made of lone hydrogen atoms with a density of 1 particle / cm3, at a temperature of around 3 K. Calculate the pressure due to these particles. Homework Equations P = nkbT, where P is the pressure, n is the number density and T is...
  28. J

    Ideal Gas Theory: Calculate N, V from P, T

    Homework Statement a) An ideal gas has a pressure of 1atm, volume of 0.5m^3m temperature of 300k. Find the number of moles. b) Three moles of an ideal gas is at a pressure of 1x10^2 Nm^-2 and a temperature of 263K. Calculate the volume. Homework Equations 1) PV = NRT 2) PV=NKbT...
  29. J

    Calculating Mass of Air in an Ideal Gas Tire for Beginners

    I have no clue how to start this problem can someone help? Problem: An automobile tire that has V= 0.6 m3 is inflated to a gage pressure of 200 kPA. Calculate the mass of air in the tire if the temperature is 20 Degree Celsius. Suggestion from my teacher: Air is assumed to be an ideal...
  30. H

    Deriving mean free path of ideal gas

    Homework Statement The mean free path for an ideal collisional gas can be calculated as shown on thishttp://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/menfre.html" . I understand the derivation, except for one thing. Homework Equations The Attempt at a Solution The molecule is...
  31. V

    How Accurate Is the Pressure Calculation for Argon in a Cubic Container?

    Can I please check if I've converted these units right? I'm doing a question and got the answer a few order of magnitudes out. Question: Argon has a collision cross section of 0.36nm^2. At what pressure is the mean free path of argon atoms equal to the length of the side of a 1cm^3 cubic...
  32. Q

    Solving Enthalpy for Ideal Gas: Finding H as a Function of S and P

    Hello. I'm having troubles solving the enthalpy for an ideal gas. From the equation H=U+PV, i could find H substituting PV=NRT = U/c, but then i need the energy as a function of S and P, so i'd get H as a function of its proper variables (S and P).. I can't find such an expression. It's just...
  33. T

    Pressure Cooker-Involving Ideal Gas law and Total Pressure

    Homework Statement A cook puts 9.00g of water in a 2.00L pressure cooker and warms it to 500 degree celcius. What is the pressure inside the container.Homework Equations P_{total} = P_{1} + P_{2} +... (eqn1) PV = nRT (eqn2) \frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{1}} (eqn3) The Attempt at a...
  34. K

    How Does Water Pressure Affect Piston Position in an Ideal Gas Cylinder?

    Homework Statement An upright cylinder 1.00m tall and closed at it's lower end is fitted with a light piston that is free to slide up and down. Initially the piston is in the centre. Above the piston, the cylinder forms a cup-like cavity which water is poured into until it is full. Assuming...
  35. K

    Why diatomic molecules (ideal gas) are 1-d oscillators.

    I think I did understand this once but now I am confused. If we choose the center-of-mass frame for a diatomic molecule, it also obeys the force law F=-kr, where r=(x,y,z), so why isn't it a 3-d harmonic oscillator, like an atom in solid? I know it may have something to do with the fact that gas...
  36. A

    Ideal gas law practical application

    Homework Statement To measure how far below the ocean surface a bird dives to catch a fish, a scientist uses a method originated by Lord Kelvin. He dusts the interiors of plastic tubes with powdered sugar and then seals one end of each tube. He captures the bird at nighttime in its nest and...
  37. L

    Ideal Gas Law Problem - Environmental Physics

    Homework Statement 1. Consider ideal gas in a rigid cylinder of 2 litres, at pressure of 3 Bar. The gas is connected through a thin capillary to a free expanding bag, which contains ideal gas at pressure 1Bar and volume of 1 litre. A valve in the capillary initially prevents the gases to mix...
  38. G

    Compressing ideal gas isothermally, calc work

    Homework Statement 10 moles of an ideal gas are compressed isothermally and reversibly from 1 to 10 atmospheres at 300K. Determine the work done ON the gas.Homework Equations dw=-PdV PV=nRT The Attempt at a Solution dT=0 T=300K dP=10atm calc dV from ideal gas law = 2.27e10 m^3 so now we...
  39. M

    Entropy of Ideal Gas N2 at 350 K, 2.0 bar

    Homework Statement what is the entropy of 1.0 litre of gasoues n2 at Ta=350 K and Pa=2.0 bar given that So = 191.61 J/(K gmol) at To = 298.15 K and Po = 1 bar? Homework Equations I think : S(at 350) - So = NC_p ln (Ta/To) - NR ln(Pa/po) The Attempt at a Solution My problem is, C_p...
  40. T

    Monatomic ideal gas thermodyanmics

    Suppose 1.0 mol of a monatomic ideal gas initially at 10 L and 338 K is heated at constant volume to 676 K, allowed to expand isothermally to its initial pressure, and finally compressed at constant pressure to its original volume, pressure, and temperature. (a) What is the net energy entering...
  41. V

    Kinetic Energy in relation to the ideal gas law

    I'm trying to fit this together. For monotomic molecules, the avg kinetic energy is 3/2 k_b T for diatomic, it is 5/2 k_b T PV = n_particles * k_b T Why is there no factor of 3/2 or 5/2 in the ideal gas law? How is it factored out?
  42. P

    Entropy of an ideal gas using statistical thermodynamics

    I cam across a question that asks for the entropy of an ideal gas of N molecules in which the energy of each molecule can assume 2 and only 2 distinct values 0 and E. It gives occupation numbers to represent the energy levels respectively with a fixed total energy. Now I know S=kln(omega) =...
  43. X

    Calculating Work Done by an Ideal Gas: Part A & B

    Homework Statement A monatomic ideal gas has pressure p_1 and temperature T_1. It is contained in a cylinder of volume V_1 with a movable piston, so that it can do work on the outside world. Consider the following three-step transformation of the gas: 1. The gas is heated at...
  44. A

    Solve Air Heated @Constant Vol: Find 1Q2

    Homework Statement Air is heated from 300 to 350K at constant volume, Find 1Q2. Homework Equations 1Q2 = m(u2-u1)+1W2 u2-u1 = cv(t2-t1) The Attempt at a Solution The PV diagram of the process is straight up, so the area under the curve is 0, so the work done is zero. Cv is .717...
  45. J

    .Work Done by an Ideal Gas - Derivation and Implications

    The expression for the work done by an ideal gas is: \int_{V_i}^{V_f} P dV But what if V_f \prec V_i ? If W \prec 0 does that mean 1) work is done on the gas or 2)on this case, W= - \int_{V_i}^{V_f} P dV so that W \succ 0 and W still means the work done by the gas? Note: The...
  46. W

    Ideal Gas Compression Homework: T(cylinder) = 298K

    Homework Statement A compressed cylinder holds nitrogen gas at room temperature. How cold is the gas that is escaping from the cylinder? T(cylinder) = 298 K P(cylinder) = 1.034e7 Pa n = 1 Homework Equations PV = nRT The Attempt at a Solution So since I was not given either the volume of...
  47. H

    Can Air Be Treated as an Ideal Gas in Absolute Zero Calculations?

    Homework Statement Calculate your experimental value of absolute zero , how does your experimental value compare to the theoretical value -273C? Homework Equations T_abs=(S1*T2-S2*T1)/(S1-S2) The Attempt at a Solution This is all part of a lab. I'm not asking people to do any...
  48. M

    Calculate the work done by an ideal gas.

    Homework Statement 1 mole of an ideal gas is at 7 atm pressure, occupies 6L and has an internal energy of 508 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 8L with an internal energy of 814 J...
  49. P

    A diatomic ideal gas such as air..

    A diatomic ideal gas such as air, for which γ = 1.4, expands adiabatically to 40 times its original volume. (a) By what factor does the temperature change? (b) By what factor does the pressure change? I'm not sure how to attempt/approach this one. If anyone has any suggestions, it would be...
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