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» Economics » Thermodynamics » Topics begins with I » Ideal gas

Page modified: Wednesday, July 13, 2011 12:26:13

Ideal gas one calls the idealized model conception of a gas. Although it represents strong simplification, many thermodynamic processes can be already understood about gases and described mathematically with this model.

Model of the ideal gas

In the model of the ideal gas all gas particles are accepted as expansionless grounds, which freely by them the available the volume to move to be able itself. Also freely it is meant that the particles do not feel any forces. However the particles may push among themselves and at the wall of the volume. A gas particle moves thus straight-lined with a constant speed, until an impact in another direction steer it and to accelerate or can brake.

The acceptance of impacts with expansionless particles is absurd in the reason, represents however a formal necessity. If one would not permit impacts, then one could lock up the gas on the one hand not into a volume, since it did not notice the wall, and on the other hand would keep each gas particle for all times its initial speed. The latter would prevent that the energy of the gas could distribute itself on the average evenly on all particles. Such a system cannot be however in the thermodynamic equilibrium, which is a compelling condition for applicability of the thermodynamic main clauses.

See also: Kinetic gas theory



| -! Symbol!! Meaning | - | colspan= " 2 " align= " centers " | variables of state | - | p || pressure | - | V || volumes | - | N || particle number | - | T || absolute temperature | - | n || amount of material | - | U || internal energy | - | colspan= " 2 " align= " centers " | constants | - | k_ \ mathrm {B} || Boltzmann constant | - | R || universal gas constant | - | h || Planck quantum of action |} 

Equations of state

The thermal equation of state for the description of an ideal gas is called general Gasgleichung. It was deduced first from different individual empirical gas laws. Later the Boltzmann statistics permitted a direct reason on the basis of the microscopic description of the system from individual gas particle.

The general Gasgleichung describes dependence of the variables of state of the ideal gas from each other. In the literature it is usually indicated in one of the following forms:

test specification = nRT \ qquad test specification = Nk_ \ mathrm {B} T

whereby R = 8.314472 {\ rm J/mol K} the gas constant designates. Assistance of this equation and the main clauses of thermodynamics can be described the thermodynamic processes of ideal gases mathematically.

Beside the thermal there is the kalorische equation of state in thermodynamics still. This reads for the ideal gas:

U = \ frac32nRT \ qquad U= \ frac32Nk_ \ mathrm {B} T

However are because of the second main clause of thermodynamics thermal and kalorische equation of state from each other dependent.

Characteristics of ideal gases

Ideal a gas has a set of special characteristics, which can be concluded all from the general Gasgleichung and the main clauses of thermodynamics. The general Gasgleichung is the compact summary of a set of laws:

Sentence of Avogadro

Equivalent volumes ideal gases contain many molecules at equivalent pressure and equivalent temperature directly.

The amount of material n as measure for the number of particles (atoms or molecules) is measured in the international unit mol.

  • 1 {\ rm mol} \ quad corresponds \ quad to 6.022 \ cdot 10^ {23} \; {\ rm particles}.

The mol is thus a multiple of the unit, comparable with the dozen.

The volume of an ideal gas with an amount of material n=1 {\ rm mol} with standard conditions (p = 1 \; {\ rm at} = 1.01325 \ cdot 10^5 {\ rm Pa} and T = 0 ^ {\ rm o} {\ rm C} = 273.15 {\ rm K}) results from the general Gasgleichung too:

\ upsilon = \ frac {1 {\ rm mol} \ cdot 8.314472 {\ rm J/mol K} \ cdot 273.15 {\ rm K}} {1.01325 \ cdot 10^5 {\ rm Pa}} = 0.022414 {\ rm m^3} = 22.414 {\ rm litres}

The molecular mass M (mass of 1 mol) corresponds thus to the mass of a mass of gas, which is bar} in a volume contained of 1 {\ rm at by 22,414 litres with 0 "°C and} = 1.01325 {\ rm (measurably from the deficiency in weight of a gas-filled and an evacuated piston).

  • Law of Boyle Mariotte
At constant temperature the pressure is in reverse proportional to the volume: p \ sim V^ {- 1} \ qquad (T = {\ rm const})
  • Law of Amontons
With constant volume the pressure rises like the absolute temperature: p \ sim T \ qquad (V = {\ rm const})

This law is the basis for the gas thermometer of Jolly.

  • Law of Gay Lussac
With constant pressure the volume rises like the absolute temperature: V \ sim T \ qquad (p= {\ rm const})

Thermodynamic sizes

Generally applies to ideal a gas:

  • Change of entropy: \ Delta S= \ nu \ left (C_ {v} \ mathsf {LN} \ left (\ frac {T_ {2}} {T_ {1}} \ right) +R \ mathsf {LN} \ left (\ frac {V_ {2}} {V_ {1}} \ right) \ right)
  • Volumetric expansion coefficient: = 1/T
  • Compressibility: = 1/p
  • Tension coefficient: =

With standard conditions applies to ideal a gas:

  • molecular volume: VM = 0.022414 m3/mol = 22.414 l/mol
  • Volumetric expansion coefficient: = 1/273.15 K-1
  • Compressibility: = 1/101325 Pa-1

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