The Stefan number (St or Ste) is defined as the ratio of
sensible heat
Sensible heat is heat exchanged by a body or thermodynamic system in which the exchange of heat changes the temperature of the body or system, and some macroscopic variables of the body or system, but leaves unchanged certain other macroscopic vari ...
to
latent heat
Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a first-order phase transition.
Latent heat can be underst ...
. It is given by the formula
where
* ''c
p'' is the
specific heat
In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
,
** c
p is the
specific heat
In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
of solid phase in the
freezing
Freezing is a phase transition where a liquid turns into a solid when its temperature is lowered below its freezing point. In accordance with the internationally established definition, freezing means the solidification phase change of a liquid ...
process while c
p is the
specific heat
In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
of liquid phase in the
melting
Melting, or fusion, is a physical process that results in the phase transition of a substance from a solid to a liquid. This occurs when the internal energy of the solid increases, typically by the application of heat or pressure, which inc ...
process.
* ∆''T'' is the
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer.
Thermometers are calibrated in various Conversion of units of temperature, temp ...
difference between phases,
* ''L'' is the latent heat of melting.
It is a
dimensionless
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
parameter that is useful in analyzing a
Stefan problem
In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem is a particular kind of boundary value problem for a system of partial differential equations (PDE), in which the boundary between the phases can m ...
. The parameter was developed from
Josef Stefan
Josef Stefan ( sl, Jožef Štefan; 24 March 1835 – 7 January 1893) was an ethnic Carinthian Slovene physicist, mathematician, and poet of the Austrian Empire.
Life and work
Stefan was born in an outskirt village of St. Peter (Slovene: ; to ...
's calculations of the rate of
phase change
In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic State of ...
of
water
Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...
into
ice
Ice is water frozen into a solid state, typically forming at or below temperatures of 0 degrees Celsius or Depending on the presence of impurities such as particles of soil or bubbles of air, it can appear transparent or a more or less opaqu ...
on the
polar ice caps
A polar ice cap or polar cap is a high-latitude region of a planet, dwarf planet, or natural satellite that is covered in ice.
There are no requirements with respect to size or composition for a body of ice to be termed a polar ice cap, nor a ...
and coined by G.S.H. Lock in 1969. The problems origination is fully described by Vuik and further commentary on its place in
Josef Stefan
Josef Stefan ( sl, Jožef Štefan; 24 March 1835 – 7 January 1893) was an ethnic Carinthian Slovene physicist, mathematician, and poet of the Austrian Empire.
Life and work
Stefan was born in an outskirt village of St. Peter (Slovene: ; to ...
's larger career can be found in
[Crepeau, J. (2007). Josef stefan: His life and legacy in the thermal sciences. Experimental Thermal and Fluid Science, 31(7), 795-803. doi:https://doi.org/10.1016/j.expthermflusci.2006.08.005]
Notes
{{DEFAULTSORT:Stefan Number
Dimensionless numbers of thermodynamics