Ideal gas law Definition and 33 Discussions

The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form:


{\displaystyle PV=nRT}


{\displaystyle P}


{\displaystyle V}


{\displaystyle T}
are the pressure, volume and temperature;


{\displaystyle n}
is the amount of substance; and


{\displaystyle R}
is the ideal gas constant. It is the same for all gases.
It can also be derived from the microscopic kinetic theory, as was achieved (apparently independently) by August Krönig in 1856 and Rudolf Clausius in 1857.

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  1. T

    Total force from air spring model (double acting piston)

    Hi everyone, I'm an electrical engineer working on making a linear model for a power take-off system. I've gotten inertial, friction, and hydraulic/electric components done, but what is really confusing me is the gas system; I haven't taken ANY thermodynamics. To simplify it, it is modeled as a...
  2. ContrapuntoBrowniano

    B Ideal gas formula not working?

    Hi! I wanted to do some basic calculations for temperature T on a water-filled pot. I noticed something strange on my calculations, and couldn’t figure out what was wrong... So here it is: The ideal gas formula: k=PV The actual formula Relates equally the product PV with the a constant...
  3. Seibtsantos

    Pressure in a bomb calorimeter at the moment of combustion

    First, I calculated the number of moles of glucose. n = m / M n = 1.8 / 180 n = 0.01 moles of glucose So I checked the combustion reaction. 1 C6H12O6 + 6 O2 -> 6 CO2 + 6 H20 1 + 6 -> 6 + 6 0.01 + 0.06 -> 0.06 + 0.06 I considered the number of moles at the end of the reaction. I subtracted...
  4. K

    Proof question related to the Ideal Gas Law

    A cylinder contains an initial volume V1 = 1m^^3 of a perfect gas at initial pressure p1 = 1 bar, confined by a piston that is held in place by a spring. The gas is heated until its volume is doubled and the final pressure is 5 bar. Assuming that the mass of the piston is negligible and that the...
  5. 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...
  6. WhiteWolf98

    Triple Product Rule Equivalency

    ##p=\frac {RT} v;~p=p(T,v)~...1## ##v=\frac {RT} p;~v=v(T,p)~...2## ##T=\frac {pv} R;~T=T(p,v)~...3## ##Considering~eq.~1:## ##p=\frac {RT} v \Rightarrow (\frac {\partial p} {\partial v})_T=-\frac {RT} {v^2}## ##Considering~eq.~2:## ##v=\frac {RT} p \Rightarrow (\frac {\partial v}...
  7. ArcHorizon

    Physics Modeling of a Gas

    This was the equation that they showed me. I thought P was for pressure, V for Volume, T for Temperature, R for Gas Constant, and n for the number of moles. Was I correct for the initials?
  8. T

    Simple thermo question: Is the pressure inside the balloon the same as the outside pressure?

    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.
  9. S

    Ideal Gas Law and pressure

    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...
  10. 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...
  11. J

    I Application of the ideal gas law

    Hi, I want to calculate the amount of liquid nitrogen (at boiling temp.) needed to build a pressure of 10.1 bar in a vessel of volume 66 m3. The liquid will be poured slowly into the vessel, boil off and fill the volume with gas at the specified pressure. I make the assumption that the process...
  12. negative

    Relation between boltsmann/gas constant and temperature

    so i have been trying to calculate boltsmann constant by assuming the fact that for an ideal gas the equation : PV=nRT is true. i assume that for containing each molecule the wall needs to apply a force. now here is where it get's a little weird. each molocule should be only deflected in the...
  13. E

    How do I calculate the gauge pressure?

    Homework Statement An automobile tire is pumped up to a gauge pressure of ##2.0 \times 10^5 ## Pa when the temperature is 27◦ C. What is its gauge pressure after the car has been running on a hot day so that the tire temperature is 77◦ C? Assume that the volume remains fixed and take...
  14. H

    Heat and work when temperature increases by 1 degree

    Homework Statement Kinetic energy per mol is 3/2KT Homework Equations Q = nC##\Delta##T U = Q + W W = -P##\Delta##V The Attempt at a Solution 1) internal energy = 3/2NKT 2) heat needed to increase temperature of 1 mol ideal gas by 1 degree at constant volume? Since constant volume, W = 0 Q...
  15. J

    Ideal gas law question

    1. Two equal glass bulbs are connected by a narrow tube and the whole is initially filled with a gas at a temperature of T0 and pressure of P0. Then, one of the bulbs is immersed in a bath at a temperature, T1 and the other in a bath at a different temperature, T2. Show that in this problem, the...
  16. Baritone

    Power in a Sound Wave

    Homework Statement Suppose a tube is filled with helium gas at a pressure of 0.11MPa and a temperature of 297K. If a piston of area of 400mm2 at one end of the tube creates sound by moving sinusoidally with a frequency of 60Hz, creating a wave with amplitude of 3.8mm, what power goes into (I'm...
  17. H

    How to find added thermal heat in monoatomic gas?

    Homework Statement for number 3,4,5 I'm still trying Homework Equations PV/T = PV/T q = ΔU + W W = P ΔV The Attempt at a Solution (3) I used PV/T = PV/T to find the ΔT for each process for A→B I find PV/TA = P3V/TB ----- TB = 3TA (T increase) for B→C I find P3V/TB = 4P3V/TC -----...
  18. J

    Forms of the Ideal gas law

    Hey I was hoping someone could be me a succinct method of knowing what form of the Ideal gas law I need to use and in particular the different R's associated with each form. Form my Thermodynamics class we use PV = nRT Pv = RT PV = mRT Little v being the specific volume (which changes the R...
  19. Ian Baughman

    Density of an ideal gas as a function of height

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  20. Ian Baughman

    Physics of a Hot Air Balloon

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  21. ashash_ash

    First law of thermodynamics: why some equations can't be used

    Homework Statement A cylinder fitted with a frictionless piston contains 5.0×10-4m3 of an ideal gas at a pressure of 1.0×105 Pa and temperature of 300K. The gas is then (i) heated at constant pressure to 450K, and then (ii) cooled at constant volume to the original temperature of 300K. The...
  22. N

    Ideal Gas Law

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  23. KDS4

    Rearranging variables Van Der Waals EoS into new variables

    The question I'm stuck on is: P = NKBT/(V-Nb) - aN2/(V2) -----> (1) Re-arrange variables in the Van Der Waals equation of state, Eq. (1), so that V always appears in the equation as V/(3Nb) and P appears as 27b2P/a. Then T should appear in the combination 27b kBT/(8a). Call these...
  24. marcophys

    Calc L/min air compression to different pressures & temps in my compressor

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  25. astrocytosis

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  26. Tardis Traveller

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  27. S

    Derivation of 1/3nMc^2 = nRT

    In the derivation the first step used F=Δmv/t and for t, they used t=2L/v where L is the distance between one end to the other end of the wall. But I don't understand why we use 2L as the distance. Isn't the force exerted by that molecule only for the very short period where the molecule is in...
  28. C

    Thermodynamics - Two gases in a container

    Homework Statement Two kilograms of air at 5 bar, 350 K, and 5 kg of carbon monoxide, initially at 4 bar, 450 K, are confined to opposite sides of a rigid, well-insulated container by a partition. The partition is free to move and allows conduction from one gas to the other without energy...
  29. S

    Calculate the change of temperature in terms of T

    Two Thermally insulated cylinders, A and B, of equal volume, both equipped with pistons, are connected by a valve. Initially A has its piston fully withdrawn and contains a perfect monatomic gas at temperature T, while B has its piston fully inserted, and the valve is closed. Calculate the final...
  30. EliotBry

    What is the total mass of the atmosphere?

    Homework Statement Problem from the book "Engines, Energy and Entropy", Page 55, question 7 has me stumped. It doesn't feel like their is sufficient information to work out the mass of the air. They've given us density (as seen in the picture, if the upload works) , which is mass over volume...
  31. M

    Filling Balloons

    Homework Statement A clown at a birthday party has brought along a helium cylinder, with which he intends to fill balloons. When full, each balloon contains 0.00260 m3 of helium at an absolute pressure of 1.10 x 105 Pa. The cylinder contains helium at an absolute pressure of 1.80 x 105 Pa and...
  32. 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...
  33. B

    Physics: pressure of mixing gases

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