Jacob number

Physical key figure
Surname	Jacob number
Formula symbol	${\displaystyle {\mathit {Ja}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {Ja}}={\frac {\Delta T\,c_{\mathrm {p} }}{h_{\mathrm {v} }}}}$
${\displaystyle \Delta T}$ Temperature difference ${\displaystyle c_{\mathrm {p} }}$ specific heat capacity at constant pressure ${\displaystyle h_{\mathrm {v} }}$ specific enthalpy of vaporization or condensation
Named after	Max Jakob
scope of application	Phase transitions
See also: Stefan number

The Jakob number (after Max Jakob , 1879–1955) is a dimensionless number of thermodynamics . It is used to describe the heat transfer during phase transitions . So she is z. B. When boiling, the ratio of the sensible heat that is absorbed by the liquid to the latent heat that is absorbed by the gas.

Depending on the temperature difference , the Jakob number can be written as: ${\displaystyle \Delta T}$

${\displaystyle {\mathit {Ja}}={\frac {\Delta T\cdot c_{\mathrm {p} }}{h_{\mathrm {v} }}}}$

It is

• ${\displaystyle c_{\mathrm {p} }}$the specific heat capacity at constant pressure
• ${\displaystyle h_{\mathrm {v} }}$the specific enthalpy of evaporation or condensation , depending on the phase transition.

The Jakob number usually takes on relatively small values. For example, there is a temperature difference of ten Kelvin between liquid water on the surface of an ice block and frozen water inside . ${\displaystyle {\mathit {Ja}}=0{,}058}$

As the equivalent of Jakob-number is for melting or solidifying the generally Stefan number used.

Individual evidence

1. ↑ Ralph Remsburg: Advanced Thermal Design of Electronic Equipment . Springer Science & Business Media, 1998, ISBN 0-412-12271-5 , pp. 444 ( limited preview in Google Book search).
2. ^ Huimin Liu: Science and Engineering of Droplets. Fundamentals and Applications. William Andrew Publishing / Noyes, 2000 (Table 4.22b).