page_title: Surface tension
section_title: Influence of temperature
hierarchical_section_title: Surface tension / Thermodynamics / Thermodynamics of bubbles / Influence of temperature
context_page_description: Surface tension is the tendency of liquid surfaces to shrink into the minimum surface area possible. Surface tension allows insects, usually denser than water, to float and slide on a water surface.
  At liquid–air interfaces, surface tension results from the greater attraction of liquid molecules to each other than to the molecules in the air.
  There are two primary mechanisms in play. One is an inward force on the surface molecules causing the liquid to contract. Second is a tangential force parallel to the surface of the liquid. The net effect is the liquid behaves as if its surface were covered with a stretched elastic membrane.
  Because of the relatively high attraction of water molecules to each other through a web of hydrogen bonds, water has a higher surface tension than most other liquids. Surface tension is an important factor in the phenomenon of capillarity.
  Surface tension has the dimension of force per unit length, or of energy per unit area. The two are equivalent, but when referring to energy per unit of area, it is common to use the term surface energy, which is a more general term in the sense that it applies also to solids.
context_section_description: Surface tension is dependent on temperature. For that reason, when a value is given for the surface tension of an interface, temperature must be explicitly stated. The general trend is that surface tension decreases with the increase of temperature, reaching a value of 0 at the critical temperature. For further details see Eötvös rule. There are only empirical equations to relate surface tension and temperature:
  Eötvös:
  Here V is the molar volume of a substance, TC is the critical temperature and k is a constant valid for almost all substances. A typical value is k = 2.1×10⁻⁷ J K⁻¹ mol-​²⁄³. For water one can further use V = 18 ml/mol and TC = 647 K (374 °C).
  A variant on Eötvös is described by Ramay and Shields:
  where the temperature offset of 6 K provides the formula with a better fit to reality at lower temperatures.
  Guggenheim–Katayama:
  γ° is a constant for each liquid and n is an empirical factor, whose value is  for organic liquids. This equation was also proposed by van der Waals, who further proposed that γ° could be given by the expression
  where K₂ is a universal constant for all liquids, and PC is the critical pressure of the liquid (although later experiments found K₂ to vary to some degree from one liquid to another).
  Both Guggenheim–Katayama and Eötvös take into account the fact that surface tension reaches 0 at the critical temperature, whereas Ramay and Shields fails to match reality at this endpoint.
caption: Temperature dependence of the surface tension between the liquid and vapor phases of pure water