tag:blogger.com,1999:blog-937701726196626615.post8967796302992058604..comments2014-05-03T14:46:52.307-07:00Comments on A Skeptic's Guide to the Greenhouse Effect: Derivation of the "isothermal" column Andershttp://www.blogger.com/profile/15294862989593516422noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-937701726196626615.post-33754751319966733502013-05-20T13:19:06.926-07:002013-05-20T13:19:06.926-07:00First of all, we are not (necessarily) talking abo...First of all, we are not (necessarily) talking about the actual atmosphere but a gas assumed to be in equilibrium. <br /><br />I don't think I assume a constant "kinetic" temperature with height by introducing the first formula. There need to be some constant playing the role of T, but if you don't like it we can just change its name to € or something else. Without it the entire enterprise of Gibbs thermodynamics becomes meaningless and the entropy argument would fall with it anyway.Andershttp://www.blogger.com/profile/15294862989593516422noreply@blogger.comtag:blogger.com,1999:blog-937701726196626615.post-74734971099045683892013-05-20T13:03:10.407-07:002013-05-20T13:03:10.407-07:00"there already exists a temperature T pertain..."there already exists a temperature T pertaining to the system as a whole"<br /><br />It looks to me like you've just ASSUMED a constant temperature T (in eqn. 1 above) throughout the gas.<br /><br />Reif's "Fundamentals of Statistical and Thermal Physics" (1965), page 211 says,<br /><br />"...P(z) = P(0) exp(-mgz/kT) 6.3.20<br /><br />i.e., the probability of finding a molecule at height z decreases exponentially with the height. The result (6.3.20) is sometimes called the 'law of atmospheres,' since it would describe the density variation of the air near the surface of the earth if the atmosphere were at a constant temperature (which it is NOT)."Harry Dale Huffmanhttp://www.blogger.com/profile/03210275295826050501noreply@blogger.com