Dr. Robert Holmes has converted the ideal gas law to T = P M / (ρ R) in this paper: (Molar Mass Version of the Ideal Gas Law Points to a Very Low Climate Sensitivity) with T = temperature P = near-surface pressure R = gas constant ρ = near-surface density M = near-surface atmospheric mean molar mass.

It seems to work on a planet that has an atmosphere > 10 kPa to accurately determine its surface temperature regardless of the atmosphere's composition.

If planetary surface temperature can be determined by pressure, density and mean moles, what does this say to the IPCC claim that temperature will raise by up 5 deg C with a doubling of CO2.

  • $\begingroup$ What? Source in a peer-reviewed journal please. $\endgroup$ Sep 14 '19 at 0:57
  • 1
    $\begingroup$ @Malawby The equation is the ideal gas law. It's more or less valid for low pressure (P → 0 Pa) and "high" temparature gases. Since the IGL is an equation of state the only conclusion you can draw is: if T (for whatever reason) raises (isobaric; which is a good approx. for Earth's atmosphere), the volume of the atmosphere will be increased (which roughly means that the "TOA" is at a higher level). The further claims made by Holmes are physical BS. $\endgroup$
    – klanomath
    Sep 14 '19 at 3:46
  • $\begingroup$ This is an updated paper from the same author: pdfs.semanticscholar.org/c258/… $\endgroup$
    – Malawby
    Sep 14 '19 at 4:28
  • 1
    $\begingroup$ @Malawby: Then getting some basic physics education before insulting people over the ideal gas law is probably prudent. Fortunately klanomath doesn't have to show you any superior reputation, because the derivation and validity of the ideal gas law can be looked up in any statistical mechanics book. $\endgroup$ Sep 14 '19 at 9:32
  • 1
    $\begingroup$ This journal's publisher is alleged by multiple sites to be a predatory one (see eg flakyj.blogspot.com/2017/01/…). In 2014 they published an article that claimed to be a mathematical proof of the law of Karma. $\endgroup$ Sep 14 '19 at 18:58

There is no such thing as the 'Holmes' equation.

Comment: Holmes is the person that formulated this equation I has every right to name it as I please. Could someone please validate the Holmes equation

There is no such thing as the 'Holmes' equation. To the ideal gas law $$T=\frac{P\mu}{R\rho}$$ if P, ρ and μ

are known in order to 'predict' a temperature is

  1. Trivial
  2. Not a predicition, but a statement of state variables.

The ideal gas law, is an Equation of State, not a predictive equation (I don't see any ∂T/∂t in it). As such, it connects the quantities in it at any given point in time, but it cannot be used to compute a time-evolution. Therefore, that Holmes can 'predict' the correct surface temperatures, given the input data P, ρ and μ is a no-brainer in any sufficiently dense gas.
It's actually embarassing for the journal that would publish this. It's either intentionally misleading (climate change denier journal) or they're just garbage scientists. The science involved in predicting where temperatures will evolve is more difficult than stating an equation of state, and at an absolute minimum requires solving evolution equations for P and ρ.
Any evolution for P or T will necessarily be coupled to the radiative balance of the atmosphere, which is what the whole Greenhouse issue is about, and what has been completely ignored by this publication.

  • 1
    $\begingroup$ Ah, beat me too it! But I'm not sure I agree that d/dt is necessary for a model to be predictive, especially as we're talking about an equilibrium state. It's more about what predictors/predictands are in the model and what inferences are made. In this case the radiative/convective effects of the atmosphere are implicitly contained in the input surface pressure and density, so T is just diagnostic. $\endgroup$
    – Deditos
    Sep 14 '19 at 10:27
  • $\begingroup$ @Deditos: Well, physics would disagree. A predictive equation must have hyperbolic structure, even if the propagation of eigenvectors becomes very fast, i.e. $dQ/dt \approx 0$, giving equilibrium for some quantity $Q$, the actual physical equation remains hyperbolic, and thus predictive. $\endgroup$ Sep 14 '19 at 16:58
  • $\begingroup$ Has someone been explaining here that if it gets cooler when you climb, it is actually because of less CO2 traces trapping heat ? $\endgroup$
    – Malawby
    Sep 15 '19 at 8:27

Not the answer you're looking for? Browse other questions tagged or ask your own question.