# 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**P*_{1}*V*_{1}=*P*_{2}*V*_{2}=*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)*V*_{1}= *V*_{2}= *constant**T*_{1}*T*_{2} - 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)*P*_{1}= *P*_{2}= *constant**T*_{1}*T*_{2}

- pressure-volume (constant temperature)
- 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

where…*PV*=*nRT**P*=absolute pressure *T*=absolute temperature *V*=volume *n*=number of moles *R*=gas constant = 8.315 J/molK - statistical thermodynamics

where…*PV*=*NkT**P*=absolute pressure *T*=absolute temperature *V*=volume *N*=number of particles *k*=Boltzmann constant = 1.382 × 10 ^{−23}J/K

- functional thermodynamics
- 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.

- An isobaric process is one that takes place without any change in