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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 = - \left.\frac{\partial A}{\partial V} \right\vert_{T,N} = k_BT \left.\frac{\partial \ln Q}{\partial V} \right\vert_{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.


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 10^5Pa 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