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For a fixed mass of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional. [2] Boyle's law is a gas law, stating that the pressure and volume of a gas have an inverse relationship. If volume increases, then pressure decreases and vice versa, when the temperature is held constant.
The equation to calculate the pressure inside a fluid in equilibrium is: + = where f is the force density exerted by some outer field on the fluid, and σ is the Cauchy stress tensor. In this case the stress tensor is proportional to the identity tensor:
The equation to calculate the pressure inside a fluid in equilibrium is: + = where f is the force density exerted by some outer field on the fluid, and σ is the Cauchy stress tensor. In this case the stress tensor is proportional to the identity tensor:
For a static gas, the density is the same throughout the entire container. Density is therefore a scalar quantity. It can be shown by kinetic theory that the density is inversely proportional to the size of the container in which a fixed mass of gas is confined. In this case of a fixed mass, the density decreases as the volume increases.
Given that the head loss h f expresses the pressure loss Δp as the height of a column of fluid, = where ρ is the density of the fluid. The Darcy–Weisbach equation can also be written in terms of pressure loss:
The pressure and temperature of the gas are directly proportional: As temperature increases, the pressure of the propane gas increases by the same factor. A simple consequence of this proportionality is that on a hot summer day, the propane tank pressure will be elevated, and thus propane tanks must be rated to withstand such increases in pressure.
The number of collisions that are so affected is also proportional to the density. Thus, the pressure is lowered by an amount proportional to ρ 2 {\displaystyle \rho ^{2}} , or inversely proportional to the squared molar volume.
In the same conditions of temperature and pressure, the molar mass is proportional to the mass density. Therefore, the rates of diffusion of different gases are inversely proportional to the square roots of their mass densities: where: ρ is the mass density.