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

    Ideal gas temperature proportional to absolute temperature

    Homework Statement I[/B] have some difficulties proving that the ideal gas temperature is directly proportional to absolute temperature defined by the second law of thermodynamics. Homework Equations The ideal gas temp. is defined by the ideal gas equation: pV=NkTi(T), where k is Boltzmann's...
  2. G

    Ideal Gas Density: PV=mRT Explained

    Homework Statement in this notes , i was told that the PV=mRT , why ? shouldn't PV= NRT , N=number of moles ? it should be PV = m/M (RT) , right ? Homework EquationsThe Attempt at a Solution
  3. W

    Finding work of adiabatic compressor using ideal gas

    Homework Statement Methane at ## P_1 ## and ## T_1 ## is compressed to a pressure of ## P_2 ## adiabatically at steady-state. Calculate the work done on the compressor and the temperature ## T_2 ## of the discharge gas. Use ideal gas model. Given: ## T_1, P_1, P_2, C_p, \gamma = 1.4 ## ##...
  4. Cora

    Ideal Gas Expansion State Properties & Exergy Balance

    Homework Statement Two well-insulated rigid tanks of equal volume, tank A and tank B, are connected via a valve. Tank A is initially empty. Tank B has 2 kg of Argon at 350 K and 5000 kPa. The valve is opened and the Argon fills both tanks. State 2 is the final equilibrium state. The temperature...
  5. Monsterboy

    Specific Heat of an Ideal Gas: Temperature vs. Molecular Weight and Structure

    Homework Statement Does the specific heat of an ideal gas depend on the temperature only or does it depend on molecular weight and structure ? or both ? Homework Equations PV=mRT , Cp -Cv=R The Attempt at a Solution One of my teachers said it depends only on temperature and the other said...
  6. A

    Entropy Difference of an Unknown Gas (not an ideal gas)

    Homework Statement Temperature, pressure and volume measurements performed on 1 kg of a simple compressible substance in three stable equilibrium states yield the following results. State 1 (T1=400 C , V1= 0,10 m3, P1=3 MPa) State 2 (T1=400 C , V1= 0,08 m3, P1=3,5 MPa) State 3 (T1=500 C , V1=...
  7. W

    Does Increasing Molecules in a Constant Temperature Container Affect Pressure?

    Homework Statement If number of molecules in a closed container increases and it is kept at a constant tempurature, what happens to the pressure? I was confused because I thought if you add molecules the temputature would go up so keeping temputature a constant would have no affect on the...
  8. jdawg

    Ideal Gas Entropy Equation Conceptual Question

    Homework Statement I'm having a little trouble knowing when to use the ideal gas equations for entropy vs just the ones like this: (T2/T1)=(p2/p1)^((k-1)/k). I've noticed a pattern in the solutions for my homework( where you're finding isentropic efficiency of turbines and compressors) they...
  9. S

    Internal Energy of 1 mole of Ideal Gas

    Homework Statement One litre cylinder contains 1 mole of the ideal gas molecules having the average kinetic energy of 0.1eV. What is the total energy of this gas? Homework Equations W = K + U The Attempt at a Solution I figured because the cylinder is closed, no stated temperature change, or...
  10. Searay330

    Change In Internal Energy Of An Ideal Gas

    An ideal gas is compressed from a volume of Vi = 4.50 L to a volume of Vf = 3.00 L while in thermal contact with a heat reservoir at T = 295 K as in the figure below. During the compression process, the piston moves down a distance of d = 0.120 m under the action of an average external force of...
  11. B

    Temperature of ideal gas in a cylinder

    Qn : https://www.dropbox.com/s/dpcws9q4bjpzvtp/20151123_112037.jpg?dl=0 Why is option A and C wrong or correct? My attempted answer : A :A is plausible as if the piston is suddenly moved inwards, the gas molecules bounce off the piston at higher speeds Since Temp proportional to rms speed...
  12. K

    Ideal gas volume work expression (adiabatic)

    Homework Statement I have the following task: Homework EquationsThe Attempt at a Solution But I don't understand how to solve it. Can somebody help me?[/B]
  13. C

    Information stored in the initial condition of an ideal gas

    Homework Statement 1 mm3 of gas at normal pressure and temperature contains about 1015 particles. Considering the particles as point-like and classical, provide a rough, conservative estimate for how many hard drives would be necessary to store the initial conditions of all gas particles. (As...
  14. ptownbro

    Ideal Gas Law: What is the new pressure based on factors?

    My daughter has the following homework problem we need assistance in confirming if we've understood and completed correctly. Homework Statement The Volume goes from 2.00 Liters to 7.00 Liters, the temperature changes from 800 kelvin to 150 kelvin, and the number moles of gas is quadrupled on...
  15. R

    Ideal Gas Equation and Polytropic Constant

    Homework Statement I'm given a initial and final pressure and temperature of an ideal gas to solve for the work done after it expans in a polytropic process (n=1.2) Homework Equations W = integral of P*dV PV = nRT PV = RT* PV = mRT PV^n = Constant The Attempt at a Solution I get W = integral...
  16. RaulTheUCSCSlug

    Ideal Gas Law in "alternate" universe

    Homework Statement Assume that in an alternate universe, the laws of physics are very different from ours and that "ideal" gases behave as follows: (i) At constant temperature, pressure is inversely proportional to the square of the volume. (ii) At constant pressure, the volume varies directly...
  17. Z

    Entropy problem -- heating 2 moles of an ideal gas....

    Moderator's Note: THIS HOMEWORK WAS POSTED IN ANOTHER FORUM, SO THERE IS NO TEMPLATE. calculate the change in entropy suffered by 2 moles of an ideal gas on being heated from a volume of 100L at 50C to a volume of 150L at 150C. for the gas Cv=7.88 cal/moleC. I'm really confused in entropy and...
  18. A

    Thermodynamics Problem - Adiabatic Reversible Process....

    Homework Statement A specific type of ideal gas has a specific heat capacity at constant pressure (cp=cv+R) that is a function of temperature T, such that cp=0.5+876T, where cp has units of J/kg/K and T has units of K. The gas, which is initially at T1 = 294 K and P1 = 1x105 Pa, undergoes a...
  19. leafjerky

    [Thermo] One m^3 of an ideal gas expands in an isothermal

    Homework Statement One m3 of an ideal gas expands in an isothermal process from 760 to 350 kPa. Determine the specific work done by the gas. Homework Equations ω=W/m 1W2=mRTln(P1/P2) = P1V1ln(P1/P2) P1V1=P2V2 The Attempt at a Solution P1V1ln(P1/P2) = (760)(1)ln(760/350) = 589.29kJ...
  20. wololo

    Chemistry Compare average distance between molecules to size of N2

    Homework Statement Homework Equations Pv=nRt The Attempt at a Solution I already calculated V for a single molecule = 3.99x10^-23 m^3 and the cubic root of this volume gives 3.42x10^-8 m. However, I don't understand what I should do next. What does it mean to compare the value I obtained to...
  21. E

    Thermodynamics Proof : Cv (non-ideal gas) - Cv (ideal gas)

    Can someone please help me with the following proof ...I'm stuck and not sure if I'm even on the right path. Prove that What I've done so far; if U = f(T,V) dU = (∂U/∂T)v dT + (∂U/∂V)t dV Cv (non ideal) = (∂U/∂T)v Using dU = TdS - PdV and Maxwell relation (∂S/∂V)t =(∂P/∂T)v, (∂U/∂V)t =...
  22. A

    Solving Ideal Gas Law Model Homework

    Homework Statement My problem is with the last line of the derivation. Usually, we take the rate of change of momentum (force) to be change of momentum divided by the impact time. But this slide of pp showed that the traveling time of the particle in the box is used but not the impact time. Why...
  23. L

    How to Solve an Ideal Gas Equation Problem with Changing Tire Pressures?

    Hey guys, I just want to make sure I went about this the right way...your input would be greatly appreciated. Thank you in advance. 1. Homework Statement A tire is checked before a road trip and the gauge pressure reads 220 kPa (gauge) - State 1 The same tire is checked after the trip and the...
  24. A

    Ideal gas process internal energy change

    Homework Statement A sample of an ideal gas goes through the process shown in Figure P20.32. From A to B, the process is adiabatic; from B to C, it is isobaric with 100 kJ of energy entering the system by heat. From C to D, the process is isothermal; from D to A, it is isobaric with 150 kJ of...
  25. C

    First law of thermodynamics at constant volume (ideal gas)

    If c_v is the specific heat at constant volume, authors substitute this into the first law as follows: c_v d\theta + pdv = dq How can one deduce that equation for any case? Since the specific heat at constant volume is used, the equation would be valid only where there is no expansion i.e...
  26. B

    Confused - Pressure in a canister?

    A manufacturer quotes a standard CO2 canister contains 16g of CO2 at a volume of 20cm^3. So I need to calculate the pressure in the canister... Using ideal gas law P = nRT/V n = 0.364mol (16 of co2) R = 8.314 J/Kmol (universal gas constant) T = 294k (gas is at room temp 21 deg C) V = 20cm3...
  27. 0

    Ideal Gas Law Equilibrium Requirements

    It is well known that the ideal gas law applies only to an ideal gas, one consisting of particles infinitesimal in size and exhibits no interactions between the particles. Considering an ideal gas, is the ideal gas law valid under non-equilibrium conditions? For example, does the ideal gas law...
  28. @PinkGeology

    Ideal gas law: can you use it to find P during exsolution?

    If you shake up a bottle of soda and it gets slightly larger because the disturbed gas in solution is trying to expand but cannot, could you use the difference in (THE SMALL AMOUNT THE BOTTLE ACTUALLY SWELLED) and the (POTENTIAL AMOUNT THE GAS WOULD SWELL IF NOT CONTAINED) to determine the...
  29. P

    Calculating Pressure Loss in Compressible Fluid Flow: A Case Study

    I have a quick question regarding compressible fluid flow, specifically: for a given amount of time, how much pressure is lost when attaching a balloon valve to a small air tank. I decided to model my solution after the following problem (from an old fluid mechanics textbook of mine), Air is...
  30. Walteholic

    Will absolute zero change with pressure?

    Say we are talking about an ideal gas. According to ideal gas law (PV=nRT), assuming the gas is now at absolute zero, if we further decrease the pressure of the environment, while keeping the container volume constant, will the gas goes under absolute zero? I wasn't an expert in Physics so...
  31. J

    Solving Ideal Gas Problem: Find # of Balloons Filled

    Homework Statement A gas cylinder contains 4x10^4 cm cubed of hydrogen at a pressure of 2.5x10^7 Pa and a temperature of 290 K. The cylinder is used to foll balloons. Each balloon contains 7.24x10^3 cm cubed of hydrogen at a pressure of 1.85x10^5 and a temp of 290K when full. Find the number...
  32. S

    Average kinetic energy of particles of an ideal gas

    Homework Statement So first the task: Determine the average value of the kinetic energy of the particles of an ideal gas at 0.0 C and at 100 C (b) What is the kinetic energy per mole of an Ideal gas at these temperatures. I took the above right out of the pdf we got from our professor. I know...
  33. goonking

    Ideal gas law in terms of density

    Homework Statement Homework Equations PV=nRT The Attempt at a Solution not sure if this is the right approach plugging into -ρg gives us -PMg/RT = dP/dy now we have to integrate both sides to find P?
  34. D

    Compressing ideal gas, show no heat exchange

    Homework Statement An ideal monatomic gas is contained in a cubic container of size ##L^3##. When ##L## is halved by reversibly applying pressure, the root mean square ##x##-component of the velocity is doubled. Show that no heat enters of leaves the system.Homework Equations ##dU = dQ -pdV##...
  35. S

    Question about compressibility factor

    At low temperatures, z falls below 1 and the reason for that is because the intermolecular interactions cause the pressure exerted to be lesser than expected. PVm/RT=z and since P is less than expected z drops below 1. However, as the pressure increases z increases to be above 1 because as P...
  36. R

    What is the Ideal Gas Force on a Container at Temperature T?

    Homework Statement In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as Tq. A good estimate for q is: A. 2 B. 1 C. 1/2 D. 1/4 Homework Equations PV= nRT I think, Volume of container and moles are constant. So P ∝ T The...
  37. D

    Deriving S(T,V) for an ideal gas

    Homework Statement Given: Ideal gas equations: Find S(T,V) for an ideal gas Homework Equations Ideal gas equations: \begin{array}{l} {\rm{}}\\ U = \frac{3}{2}N{k_B}{\left( {\frac{N}{V}} \right)^{2/3}}\exp \left[ {\frac{S}{{\left( {3/2} \right)N{k_B}}} - {s_0}} \right]{\rm{ }}\\ T = {\left(...
  38. E

    Ideal Gas Law - Adding additional gas & additional question

    Hello, I know this has been fairly discussed to death, but I've had relative trouble finding a response that specifically addresses the n, in PV= nRT, the ideal gas law. Out of relatively common sense, by adding additional moles of gas, the pressure in the gas should increase as there are more...
  39. Rumo

    Speed of sound in an isentropic ideal gas

    Homework Statement \rho_0, c_0 is the mean density, the mean speed of sound in the ideal gas. Is the following correct? c(\rho)=c_0\left(\frac{\rho}{\rho_0}\right)^{\frac{\kappa-1}{2}} Homework Equations p = const * \rho^\kappa, c=\sqrt{\frac{\partial p}{\partial \rho}} The Attempt at...
  40. A

    Question about Ideal gas law and its application

    Homework Statement Estimate partial pressure of nitrogen in atm in a room where you are at this moment. Use an ideal gas approximation and assume that air is composed of only nitrogen and oxygen. Show how you arrive the final answer in detail. Homework Equations pv=RT, while p stands for...
  41. E

    How Is Time Factored Into the Derivation of the Ideal Gas Law?

    Here is a screenshot from a page from a textbook that explains how to derive the ideal gas law: In the third bold line, I don't understand how "time" in force = (change of momentum)/(time) is equal to 2x/u (the time it takes for the particle to travel to the opposite face and back again) -- I...
  42. P

    Change in internal Energy During Expansion of an Ideal Gas

    Homework Statement Derive an expression for the change in internal energy of 1 mol of an ideal gas for expansion from volume V_i to V_f under constant pressure of 1atm where \gamma = \frac{C_p}{C_v}=\frac{5}{3} Homework Equations \Delta U=\frac{3}{2}nR\Delta T PV=nRT The Attempt at a...
  43. A

    Applying the ideal gas law in the Earth's atmosphere

    Hi there, I'm considering how the ideal gas law applies in practice in our planet's atmosphere. In particular, I'm considering this form of the law: P = ρRT (1) where P is pressure, ρ is density, R is the gas constant and T is the temperature. I also know that, to a good approximation, the...
  44. J

    Calculating Volume of Escaped Air Bubble Using Ideal Gas Law | Homework Question

    Homework Statement An air bubble of volume 3.0x10-5m3 escapes from a divers equipment at a depth of 45m where the water temperatures is 5 degrees C. What is its volume as it reaches the surface, where the temperature is 12 degrees C? Atmospheric pressure = 101kPa, density of sea water =...
  45. W

    Work done by monoatomic ideal gas

    Homework Statement The volume of 30.0 moles of a monoatomic ideal gas is reduced at a uniform rate from 0.616m3 to 0.308m3 in 2h. Its temperature is increased at a uniform rate from 27.0◦C to 450◦C. The gas passes through thermodynamic equilibrium states throughout. (a) Write down explicitly...
  46. R

    Deviation of a gas from ideal gas behaviour

    Hi all, I have a question from a tutorial sheet that I'm stuck with. The question is Estimate the pressure at which a gas of argon atoms, at a temperature of 300 K, will begin to show deviations from the ideal gas behaviour due to the finite size of the atoms. Answer: Of order 10^9 Pa. So I...
  47. Seydlitz

    Deriving Ideal Gas using Molecular Flux Equation

    So basically I was wondering whether it's possible to get the expression of ideal gas using molecular flux equation which is ##\phi = \frac{1}{4}\bar{v}n##. The derivation should be straightforward. I need to get the expression of pressure. Because the flux by definition already gives the rate...
  48. Z

    Ideal gas law combined with vapor pressure

    I am working on a DIY project and want to understand the system/mathematical model of a traditional steam espresso machine. How I have started to think about the problem is a closed container with liquid and gas. At room temperature I know the vapor pressure of the water. As I increase the...
  49. L

    Entropy Change for an Ideal Gas

    Homework Statement 10 moles of an ideal gas Cv = 20.8 J/mol at T0 = 300 K and P0 =0.3 MPa occupy the left half of an insulated vessel. At time t=0 a 1 kW electrical heating element is turned on. after 30 s, the partition dividing the vessel ruptures and the heating element is turned off...
  50. G

    How Do I Determine the Change in Entropy of the System?

    Homework Statement Determine ΔSsys when 3.0 mol of an ideal gas at 25°C and 1 atm is heatedd to 125°C and expanded to 5 atm. Rationalize the sign of ΔSsys. Homework Equations State Function: dS = (dU)/T + (PdV)/T State Function for Entropy of Ideal Gas: dS = (CV,mdT)/T + (nRdV)/V Ideal gas...
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