Effusion
In physics and chemistry, effusion is the process in which a gas escapes from a container through a hole of diameter considerably smaller than the mean free path of the molecules. Such a hole is often described as a "pinhole" and the escape of the gas is due to the pressure difference between the container and the exterior. Under these conditions, essentially all molecules which arrive at the hole continue and pass through the hole, since collisions between molecules in the region of the hole are negligible. Conversely, when the diameter is larger than the mean free path of  the gas, flow obeys the Sampson flow law. In medical terminology, an effusion refers to accumulation of fluid in an anatomic space, usually without loculation. Specific examples include subdural, mastoid, pericardial and pleural effusions. Etymology. The word effusion derives from the Latin word, effundo, which means "shed, pour forth, pour out, utter, lavish, waste." Effusion into vacuum. Effusion from an equilibrated container into outside vacuum can be calculated based on kinetic theory. If a small area formula_1 on the container is punched to become a small hole, the effusive flow rate will be formula_2 where formula_3 is the molar mass , formula_4 is the Avogadro constant, and formula_5 is the gas constant. The average velocity of effused particles is formula_6 Combined with the effusive flow rate, the recoil/thrust force on the system itself is formula_7 An example is the recoil force on a balloon with a small hole flying in vacuum. Measures of flow rate. According to the kinetic theory of gases, the kinetic energy for a gas at a temperature formula_8 is where formula_10 is the mass of one molecule, formula_11 is the root-mean-square speed of the molecules, and formula_12 is the Boltzmann constant. The average molecular  speed can be calculated from the Maxwell speed distribution as formula_13 (or, equivalently, formula_14). The rate formula_15 at which a gas of molar mass formula_3 effuses (typically expressed as the "number" of molecules passing through the hole per second) is then Here formula_18 is the gas pressure difference across the barrier, formula_1 is the area of the hole, formula_4 is the Avogadro constant, formula_21 is the gas constant and formula_8 is the absolute temperature. Assuming the pressure difference between the two sides of the barrier is much smaller than formula_23, the average absolute pressure in the system ("i.e." formula_24), it  is possible to express effusion flow as a volumetric flow rate as follows: or where formula_27 is the volumetric flow rate of the gas, formula_23 is the average pressure on either side of the orifice, and formula_29 is the hole diameter. Effect of molecular weight. At constant pressure and temperature, the root-mean-square speed and therefore the effusion rate are inversely proportional to the square root of the molecular weight. Gases with a lower molecular weight effuse more rapidly than gases with a higher molecular weight, so that the "number" of lighter molecules passing through the hole per unit  time is greater. Graham's law. Scottish chemist Thomas Graham (1805–1869) found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles. In other words, the ratio of the rates of effusion of two gases at the same temperature and pressure is given by the inverse ratio of the square roots of the masses of the gas particles. where formula_31 and formula_32 represent the molar masses of the gases. This equation is known as Graham's law of effusion. The effusion rate for a gas depends directly on  the average velocity of its particles. Thus, the faster the gas particles are moving, the more likely they are to pass through the effusion orifice. Knudsen effusion cell. The Knudsen effusion cell is used to measure the vapor pressures of a solid with very low vapor pressure. Such a solid forms a vapor at low pressure by sublimation. The vapor slowly effuses through a pinhole, and the loss of mass is proportional to the vapor pressure and can be used to determine this pressure. The heat of sublimation can also be determined by measuring the vapor pressure as a function  of temperature, using the Clausius–Clapeyron relation.