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.)

View More On Wikipedia.org
  1. T

    Ideal Gas Problem: Pressure Increase, KE Change?

    Homework Statement An ideal gas is enclosed in a gas syringe. The pressure on the gas is now increased but the temperature of the gas is kept constant. The average kinetic energy of the gas molecules will... A) increase B) remain constant C) decrease D) double Homework Equations...
  2. L

    Thermodynamics - Freely moving piston and rigid cylinder ideal gas problem

    I'm a third year chemical engineering major and this is my first real thermodynamics class, so I'm not entirely sure what I'm doing. Any help is greatly appreciated! Homework Statement A rigid horizontal cylinder contains a freely moving piston. Initially, it divides the cylinder into equal...
  3. S

    Ideal Gas in Piston (Constant Pressure vs Rate of collision)

    A syringe contains ideal gas. The piston is frictionless and no gas escapes. Once heated slowly, the piston moves outwards. The piston stops moving when the temperature is steady. The pressure of the gas after the piston stops moving remains the same (no change in pressure). What can we say...
  4. N

    [fluid dynamics] are they trying to use the ideal gas law for LIQUIDS?

    In my course they're using the equality U = \frac{p}{\alpha \rho} with alpha some constant (U = internal energy per mass, p = pressure, rho = density). They explicitly derive it for an ideal gas yet later apply it to a liquid (in the context of deriving the Navier-Stokes energy equation). Seems...
  5. C

    Reciprocity theorem and ideal gas law

    what is the reciprocity theorem? and does ideal gas law PV=nRT follows the theorem?
  6. B

    Solving Ideal Gas Law Problem: Volume of Rigid Container at 1.20 atm and 60.0°C

    Homework Statement A rigid container holds 2.80 mol of gas at a pressure of 1.20 atm and a temperature of 60.0 degrees Celsius. What is the container's volume? Homework Equations PV=nRT The Attempt at a Solution (2.80*8.31*333)/1.20 = 6457m^3 This answer seems way too big...
  7. K

    MCQ: Ideal Gas Flow Out of Balloon with Temp Increase

    Homework Statement A balloon with a constant volume is in 1000C. The fraction of gas flow out of balloon when temperature increased by 20C is nearly equal to (consider pressure and the gas in balloon is ideal) a. 2/373 b. 2/375 c. 2/100 d. 373/375 e. 100/102 Homework Equations...
  8. G

    Why is the work done by an ideal gas the area under a PV diagram?

    Could someone please prove why the work done by a gas is the area under a PV diagram? That is, I know that dW=P \text{ }dV, but why is that true physically? I realize that W=f \cdot d \text{ and } F=P \cdot A .Thanks.
  9. L

    Solve Perfect Gas Homework: A to B Volume Ratio

    Homework Statement 'A closed cylinder containing a perfect gas at 300K is divided into two parts A and B of equal volume, V0 by a freely moveable close-fitting piston. The gas in B is then heated to 400K but that in A is maintained at 300K. Show that the final volume of the gas in B, Vbf =...
  10. D

    Find temperature of ideal gas, given n, P, Vi, Vf, and Work.

    Homework Statement The previous part of the question: (a) 1 mole of an ideal gas in a container is at 303,000 Pa, volume is 0.005 m^3. What is the work done by the gas if it expands at constant pressure to twice its original volume? (This was easy enough) The part I'm having trouble...
  11. D

    Total Internal Energy of an Ideal Gas

    Homework Statement Argon is stored in a container of volume 2L and a pressure of 5 atmospheres. The amount of gas present is 0.2 moles. Find: (i) The absolute temperature of the gas (ii) The number of atoms of gas in the container (iii) The total mass of the gas (iv) The total internal...
  12. fluidistic

    Fundamental equation and state equations of the ideal gas

    Homework Statement Find the fundamental equation of a monoatomic ideal gas in the Helmholtz potential representation, in the enthalpy representation, and in the Gibbs function representation. Assume the fundamental equation S= \frac{NS_0}{N_0} +NR \ln \left [ \left ( \frac {U}{U_0} \right )...
  13. D

    How Does a Hydro-Pneumatic Shock Absorber Respond to Impact in Thermodynamics?

    Homework Statement A buffer at the end of a rail track consists of a hydro-pneumatic shock absorber. The gas chamber of the absorber has an cylindrical geometry consisting of a length of 800mm and 0.5 m diameter and a pressure of 5 bar. Calculate the final pressure and stroke if a 2 tonne...
  14. G

    The temperature change of an ideal gas, Joule Kelvin expansion (const. enthelpy)

    Homework Statement This is the last part of the question. So far have been made to derive: ## \mu _{\text{JK}}=\left(\frac{\partial T}{\partial P}\right)_H=-\frac{1}{C_P}\left(\frac{\partial H}{\partial P}\right)_T ## Then ##\left(\frac{\partial H}{\partial P}\right)_T=V - T...
  15. M

    Ideal gas: total kinetic energy of molecules striking a vessel's wall

    Molecules in an ideal gas contained in a vessel are striking the vessels wall. I am trying to find the total kinetic energy of gas molecules striking a unit area of that well per unit time. The number of collisions per unit area per unit time is derived from the normalized Maxwellian...
  16. M

    Ideal Gas Law with spring, no numbers, closed container

    Homework Statement The closed cylinder of the figure has a tight-fitting but frictionless piston of mass M. the piston is in equilibrium when the left chamber has pressure p0 and length L0 while the spring on the right is compressed by ΔL. a. What is ΔL in terms of p0, L0, A, M, and k...
  17. fluidistic

    Carnot cycle, fundamental equation of ideal gas

    Homework Statement Assuming that the auxiliary system in the Carnot cycle is a monoatomic ideal gas whose fundamental equation is S=\frac{NS_0}{N_0} +NR \ln \left [ \left ( \frac{U}{U_0} \right ) ^{3/2} \left ( \frac{V}{V_0} \right ) \left ( \frac{N}{N_0} \right ) ^{-5/2} \right ]. 1)Find...
  18. V

    Why is this a definition of the partition function?

    Hi everyone, I'm working through an example in my textbook, and it's making very little sense to me. The problem is: Let Z_1(m) be the partition function for a single quantum particle of mass m in a volume V. First, calculate the partition function for two of these particles if they are...
  19. B

    Enthelpy change for an ideal gas

    Homework Statement I'm not able to understand the following equation ΔH = ΔU + (Δn)RT firstly if T is taken to be constant (as the book says), ΔU = 0 if T is not constant then which T i am supposed to put in? initial or final? Homework Equations please help. Thank you. The...
  20. C

    Temperature change in an isentropic flow of an ideal gas

    I am a bit confused by the definition of an isentropic process in the flow of an ideal gas. isentropic implies reversible & adiabatic. for a process to be reversible, there are no losses to friction (viscosity in this case), for a process to be adiabatic, there is no heat transfer with...
  21. J

    Ideal Gas Entropy: Solving Kardar's Equation IV.33

    I'm working through Kardar's Statistical Physics of Particles, and I'm in chapter 4 on the part about the ideal gas. Here's a link to that chapter from the book: http://web.mit.edu/8.333/www/lectures/lec13.pdf I think he has an error in equation IV.33 but I'd like you guys to make sure of it...
  22. fluidistic

    How Does Gas Escape Affect Volume and Mass in Thermodynamics?

    Homework Statement A container contains 1g of O_2 at a pressure of 1 atm and temperature T_i=47°C. At a certain time, due to an escape of gas, the pressure is 5/8 atm and the temperature decreases to 27°C. 1)What is the volume of the container? 2)How much mass of O_2 has escaped...
  23. P

    What fraction of molecules in an ideal gas have velocites between φ1 & φ2 and θ1 & θ2

    Homework Statement Approximately what fraction of molecules of a gas (assumed ideal) have velocities for which the angle φ lies between 29.5° and 30.5°, while θ lies between 44.5° and 45.5°? Homework Equations The Attempt at a Solution What does the question even mean...
  24. U

    Conversion confusion: Rankine in ideal gas constant

    Hi all. I have ran into a problem in converting from imperial to SI units, as follows. The ideal gas constant for air is often given in imperial units as R = 1716 \frac{ft*lbf}{slug*°R} where 1 ft*lbf = 1.356(10^{-3}) kJ 1 slug = 14.59 kg °R = \frac{9}{5}K Thus making these...
  25. V

    Solving a Monatomic Ideal Gas Expansion Problem

    Homework Statement the diagram above of pressure P versus volume V shows the expansion of 2.0 moles of a monatomic ideal gas from state A to state B. As shown in the diagram PA = PB = 600 N/m2 , VA = 3.0 m3 and VB = 9.0 m3. a) i) Calculate the work done by the gas as it expands ii)...
  26. J

    Help with Ideal gas equation of state

    I am reading through my thermodynamics book. Going over a air-standard otto cycle example problem. For reference the example problem is as follows: The temperature at the beginning of the compression process of an air-standard Otto cycle with a compression ratio of 8 is 5408R, the pressure...
  27. fluidistic

    Thermodynamics, ideal gas relation

    Homework Statement Find the relation P=P(V) for a transformation dQ=0 in an ideal gas (PV=nRT and U=CnRT).Homework Equations dU=dQ-PdV.The Attempt at a Solution If I assume that C and R are constant I get dU=CR \left [ \frac{\partial (nT)}{\partial n} dn + \frac{\partial (nT)}{\partial T } dT...
  28. A

    Why Is Heat Capacity at Constant Pressure Independent of Pressure?

    Hi, with the ideal gas law we have: cp = CV + (∂V/∂T) * P = CV + Nk (constant P) can someone explain why it intuitively most be so that, the heat capacity at constant pressure is independent of pressure? I mean surely a gas at high pressure wants to expand more?
  29. J

    Ideal Gas Law/Estimate of Cooling Power

    Oh you who are wise in the ways of Physics, I beg a moment of your time. I've poked around wikipedia and found my way to PV=nRT and Thermal Mass and some other basics, and Googled "compressed air" "ice" "expansion" and similar, but can't quite find anything that helps me answer my question...
  30. alemsalem

    Can internal energy levels of atoms affect chemical potential of ideal gas?

    μ/T represents the change in entropy if we change the number of particles,, so according to the fundamental assumption of statistical mechanics μ/T should tell us about the tendency of two systems to exchange particles... but I am having a hard time imagining how rotational or vibrational...
  31. A

    Thermodynamics - Ideal Gas Model

    I've been working on this problem for a couple of hours, and I can't seem to crack it. I feel like just a tip on how to get started would get me up over the hump. Homework Statement Two pistons in two different cylinders are connected by a rigid rod. A pin used to fix the pistons in place...
  32. P

    Thermodynamics-how to tell if a gas is an ideal gas?

    I know a gas is ideal if it has a higher T or low P relative to its CP. A probably stated that nitrogen is at 300kPa and 227 deg C. The solutions says its an ideal gas, but how does it know? Is it just same to assume that or is there an actual table that has gas's and their CPs?
  33. J

    Ideal Gas Law and pressure in a holder

    Homework Statement What is the pressure inside a $50.0$ L container holding $105.0$ kg of argon gas at $20^\circ$ C?Homework Equations Ideal Gas Law: PV=nRTThe Attempt at a Solution From the ideal gas law, I get P=\frac{nRT}{V}=\frac{\frac{105.0\times 10^3g}{36g/mol}\times 0.08214\frac{L\cdot...
  34. A

    Why Does External Pressure Not Affect Work Done on Compressed Gas?

    I really need help on this question, I've tried asking several people but I still don't quite get it. The formula for the work done on compressing/expanding an ideal gas is \int-pdV. Now first of all - p denotes the internal pressure of the gas right? If so, good so far. Let us now assume...
  35. B

    How much steam is needed to open a relief valve using the ideal gas law?

    I am trying to solve a problem but I am not sure if I am going about it the right way. I am using the ideal gas law to find out the amount of steam it will take to open a relief valve. Using the law I have calculated the amount of steam that will be in a volume but I am not sure if that is also...
  36. C

    Ideal Gas law and mole conversions

    Homework Statement You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds 0.900L . The pressure of the gas inside the balloon equals air pressure (1.00 atm). The air inside the balloon has a constant temperature of 22 C. How many...
  37. C

    What Are the Temperatures of an Ideal Gas During an Adiabatic Expansion?

    Homework Statement A 4.15 mol sample of a diatomic ideal gas (γ = 1.4) expands slowly and adiabatically from a pressure of 5.60 atm and a volume of 13.5 L to a final volume of 34.5 L. Find initial+final temperatures Homework Equations pV/T (all initial) = pV/T (all final) The...
  38. Telemachus

    Silly doubt: ideal gas eq. of state entropic representation

    Hi there. I have a silly doubt about the entropy of mixing for ideal gases The entropy of mixing is this (Eq. [1]): S_{mix}=\sum_j N_j s_{j0}+\left (\sum_j N_j c_j \right) R \ln{\frac{T}{T_0}}+\sum_j N_j R \ln {\frac{V}{N_jv_0}} Now I don't know what identity the book uses to rewrite this on...
  39. C

    How Does Temperature Constancy Affect Atmospheric Pressure with Altitude?

    Ideal Gas Law Problem (Please help!) Show that if the temperature in the atmosphere is independent of altitude, then the pressure as a function of altitude y is p=(p initial)e^(-mgt/kT) Where m is the average mass per molecule of air. I really have no idea where to start. Please help...
  40. F

    The Relationship Between Temperature and Pressure of an Ideal Gas

    can temperature be changed without changing pressure as well as number of molecules for an ideal gas?
  41. S

    Filling the wheel with air (ideal gas)

    Homework Statement A wheel has volume 1.2 x 10-3 m3 when being full. A pump has working volume of 9 x 10-5 m3. How many times do you need to push the pump to fill the air to the wheel (initially there is no air in the wheel) until the pressure is 3.0 x 105 Pa? The atmospheric pressure is 1.0 x...
  42. X

    Ideal gas specific heat calculation

    Homework Statement See attachment "problem". Homework Equations See attachment "data" The Attempt at a Solution Can someone tell me what values to plug in for the equation R/M integral (a+bT+cT^2...). The solution doesn't show this step, so I have no idea the numbers they used to...
  43. K

    Partial Pressures of an Ideal Gas Mixture Containing Water Vapor

    Homework Statement A gas mixture of 0.13 mol NH3, 1.27 mol N2, and 0.025 mol H2O vapor is contained at a total pressure of 830 mm Hg and 323 K. Calculate the following: (a) Mole fraction of each component. (b) Partial pressure of each component in mm Hg. (c) Total volume of mixture in m3...
  44. S

    Ideal gas - monatomic or diatomic?

    Homework Statement 5 moles of an idea gas at 300K at a pressure of 1.00 x 10^5 Pa is heated to 500K at constant pressure. The amount of heat transferred is 29.1kJ. Determine whether a gas is monatomic or diatomic through consideration of the values of the molar heat capacity at constant...
  45. M

    Ideal Gas Law Gas in a Piston Problem

    Homework Statement A gas is in a piston which is at 25 degrees celsius with a volume 4.0L is held in a room at atmospheric pressure. If the temperature is increased to 193 degrees celsius, the piston expands to it's maximum volume. If the pressure in the room is then increased to 4.3 atm, what...
  46. M

    How Many Molecules in 1 mL of a Vacuum at 27.0 degrees Celsius?

    Homework Statement A vacuum pump on Earth can produce a vacuum with a pressure as low as 1.00*10^-8 torr. How many molecules are present in each mL at a temperature of 27.0 degrees Celsius? V = 1mL = 10^-3 L <-- How many sig figs should I use here? Should I make it 1.00*10^-3L or keep it...
  47. S

    Thermodynamics, ideal gas, probability distributions

    I need some help with e), but could someone also check to see if the rest is correct? Homework Statement The velocity component v_x of gas particles in the x-direction is measured and the probability distribution for v_x is found to be P \propto e^{-\frac{-m v_x^2}{2 k_B T}} with m the...
  48. R

    Calculating Heat Transfer to Ideal Gas During Isochoric Process

    How to calculate heat transfer to an ideal gas during isochoric process? I only know initial and final pressures and volume. (Do I have to know whole cycle (closed loop)?) Here, no work is done so: dU = dQ n*c*dT=dQ But T and its change is unknown, so what would be the next step?
  49. S

    Pressure and Temperature question: Ideal Gas Laws

    Homework Statement Find the pressure and temperature when given the following data on helium gas: Volume (V) = 0.10 m^3 ** Helium mass (m) = 4.0 amu ** Number of atoms (N) = 3.0 x 10^24 Assuming PV = 1 then P=1/V then Pressure = 1.0 / 0.10m^3 = 10Pa Homework Equations PV = NkT...
  50. M

    Can you write the ideal gas law this way?

    Homework Statement Calculate the work done in an adiabatic process where P1 = 1.2 atm, V1 = 0.2 m^3, P2 = 2.4 atm and V2 = 0.117 m^3 Homework Equations W=-nCvΔT PV=nRT The Attempt at a Solution I tried to group the work formula as follows: W=-(nΔT)Cv and then tried to rewrite...
Back
Top