The Physics
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Opus in profectus

# 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
• 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 = 8.315 J/molK
• statistical thermodynamics

PV = NkT

where…  P = absolute pressure T = absolute temperature V = volume
and…  N = number of particles k = Boltzmann constant = 1.382 × 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.