adiabatically isolated system is decreased, allowing it to expand, thus causing it to do work on its surroundings. When the pressure applied on a parcel of gas is reduced, the gas in the parcel is allowed to expand; as the volume increases, the temperature falls as its internal energy decreases. Adiabatic cooling occurs in the Earth's atmosphere with orographic lifting and lee waves, and this can form pilei or lenticular clouds. Due in part to adiabatic cooling in mountainous areas, snowfall infrequently occurs in some parts of the Sahara desert. Adiabatic cooling does not have to involve a fluid. One technique used to reach very low temperatures (thousandths and even millionths of a degree above absolute zero) is via adiabatic demagnetisation, where the change in magnetic field on a magnetic material is used to provide adiabatic cooling. Also, the contents of an expanding universe can be described (to first order) as an adiabatically cooling fluid. (See heat death of the universe.) Rising magma also undergoes adiabatic cooling before eruption, particularly significant in the case of magmas that rise quickly from great depths such as kimberlites. In the Earth's convecting mantle (the asthenosphere) beneath the lithosphere, the mantle temperature is approximately an adiabat. The slight decrease in temperature with shallowing depth is due to the decrease in pressure the shallower the material is in the Earth. Such temperature changes can be quantified using the ideal gas law, or the hydrostatic equation for atmospheric processes. In practice, no process is truly adiabatic. Many processes rely on a large difference in time scales of the process of interest and the rate of heat dissipation across a system boundary, and thus are approximated by using an adiabatic assumption. There is always some heat loss, as no perfect insulators exist. Ideal gas (reversible process) The mathematical equation for an ideal gas undergoing a reversible (i.e., no entropy generation) adiabatic process can be represented by the polytropic process equation where is pressure, is volume, and is the adiabatic index or heat capacity ratio defined as Here is the specific heat for constant pressure, is the specific heat for constant volume, and is the number of degrees of freedom (3 for a monatomic gas, 5 for a diatomic gas or a gas of linear molecules such as carbon dioxide). For a monatomic ideal gas, , and for a diatomic gas (such as nitrogen and oxygen, the main