Gas Laws

Summary

• The basic gas laws for a constant amount of matter…
  • pressure-volume (constant temperature)
    • The pressure of a gas is inversely proportional to its volume when temperature is constant.
    • The product of pressure and volume is constant when temperature is constant.
    • This relationship is known as Boyle's law or Mariotte's law.
    • A constant temperature process is said to be isothermal.

    P ∝	1	(T constant)
    	V

    P₁V₁ = P₂V₂ = constant

  • volume-temperature (constant pressure)
    • The volume of a gas is directly proportional to its temperature when pressure is constant.
    • The ratio of volume to temperature is constant when pressure is constant.
    • This relationship is known as Charles' law or Gay-Lussac's law.
    • a constant pressure process is said to be isobaric.

    V ∝ T (P constant)

    V1	=	V2	= constant
    T1		T2

  • pressure-temperature (constant volume)
    • The pressure of a gas is directly proportional to its temperature when volume is constant.
    • The ratio of pressure to temperature is constant when volume is constant.
    • This relationship is not associated with any particular scientist.
    • A constant volume process is said to be isochoric.

    P ∝ T (V constant)

    P1	=	P2	= constant
    T1		T2

• Avogadro's hypothesis
  • The number of molecules in a given volume of gas at a given temperature is the same for all gases.
• The ideal gas law (presented two ways)…
  • functional thermodynamics

    PV = nRT

    where…

    P =	absolute pressure
    T =	absolute temperature
    V =	volume

    and…

    n =	number of moles
    R =	gas constant = 8.314 J/mol K

  • statistical thermodynamics

    PV = NkT

    where…

    P =	absolute pressure
    T =	absolute temperature
    V =	volume

    and…

    N =	number of particles
    k =	Boltzmann constant = 1.381 × 10−23J/K

• Thermodynamic changes with special names…
  • An isobaric process is one that takes place without any change in pressure.
  • An isochoric process is one that takes place without any change in volume.
  • An isothermal process is one that takes place without any change in temperature.
    • Isothermal processes are often described as "slow".
    • The pressure of a gas is inversely proportional to its volume only if the change takes place isothermally.
  • An adiabatic process is one that takes place without any exchange of heat.
    • Adiabatic processes are often described as "fast".
    • The pressure of a gas is not inversely proportional to its volume if the change takes place adiabatically.