Editing Lapse rate (section)

== Lapse rate in an isolated column of gas ==

A question has sometimes arisen as to whether a temperature gradient will arise in a column of still air in a gravitational field without external energy flows. This issue was addressed by [[James Clerk Maxwell]], who established in 1868 that if any temperature gradient forms, then that temperature gradient must be universal (i.e., the gradient must be same for all materials) or the [[second law of thermodynamics]] would be violated. Maxwell also concluded that the universal result must be one in which the temperature is uniform, i.e., the lapse rate is zero.<ref>{{cite journal|last=Maxwell|first=J Clerk|title=XXII. On the dynamical theory of gases|journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science|volume=35|issue=236|year=1868|pages=185-217}}</ref>

Santiago and Visser (2019) confirm the correctness of Maxwell's conclusion (zero lapse rate) provided relativistic effects are neglected. When [[General relativity|relativity]] is taken into account, gravity gives rise to an extremely small lapse rate, the Tolman gradient (derived by R. C. Tolman in 1930). At Earth's surface, the Tolman gradient would be about <math>\Gamma_t = T_s \times (10^{-16}</math>m<math>^{-1})</math>, where <math>T_s</math> is the temperature of the gas at the elevation of Earth's surface. Santiago and Visser remark that "gravity is the only force capable of creating temperature gradients in thermal equilibrium states without violating the laws of thermodynamics" and "the existence of Tolman's temperature gradient is not at all controversial (at least not within the general relativity community)."<ref name="SantiagoVisser19">{{cite journal |last1=Santiago |first1=Jessica |last2=Visser |first2=Matt |title=Tolman temperature gradients in a gravitational field |journal=European Journal of Physics |date=2019 |volume=40 |issue=25604 |page=025604 |doi=10.1088/1361-6404/aaff1c |arxiv=1803.04106 |bibcode=2019EJPh...40b5604S }}</ref><ref name="Tolman1930">{{cite journal |last1=Tolman |first1=R. C. |title=On the weight of heat and thermal equilibrium in general relativity |journal=Phys. Rev. |date=1930 |volume=35 |issue=8 |page=904|doi=10.1103/PhysRev.35.904 |bibcode=1930PhRv...35..904T }}</ref>