Pressure

Pressure ($p$) is the force per unit area applied on a surface, in a direction perpendicular to that surface, i.e. the scalar part of the stress tensor. In thermodynamics the pressure is given by

$p=-{\frac{\partial A}{\partial V}|}_{T,N}=k_{B}T{\frac{\partial \ln Q}{\partial V}|}_{T,N}$

where $A$ is the Helmholtz energy function, $V$ is the volume, $k_B$ is the Boltzmann constant, $T$ is the temperature and $Q(N,V,T)$ is the canonical ensemble partition function.

Units

The SI units for pressure are Pascals (Pa), 1 Pa being 1N/m$2^{}$, or 1J/m$3^{}$. Other usual units are bars and millibars (mbar); 1mbar=100Pa=1hPa, 1 hectopascal. 1 bar is $10^5$Pa by definition. This is very close to the standard atmosphere (atm), approximately equal to typical air pressure at earth mean sea level:

atm, standard atmosphere = 101325 Pa = 101.325 kPa = 1013.25 hPa = 1.01325 bar

See also

• Pressure equation
• Virial pressure
• Test volume method