This is an updated and revised file that was posted earlier. (Sorry, I wish I could figure out how to delete old files and upload a revised file, making this post unnecessary.) 

When light, a stream of photons with energy E = hf, shines on the surface of a metal, it produces electrons with a maximum kinetic energy K, given by K = E – W = hf – W where h is the Planck constant, f is the frequency of light and W is the work function of the metal upon which light is shining. W represents the energy that must be given up to bring the electron out of the metal. This is the photoelectric law conceived by Einstein in 1905. 

Likewise, when the sun rises and shines upon the earth, the solar energy flux (also called the solar irradiance, energy per unit time per unit surface area, measured in Watts per square meter) causes the temperature T to start rising. According to the kinetic theory of gases, the temperature T of an ideal gas is directly proportional to the average kinetic energy of the atoms or molecules of the gas. Thus, the observed annual global average temperature can be taken as an accurate measure of the energy that has been transferred to the earth from the sun. 

I found something interesting about the temperature-time relationship over the last few weeks, by studying both the climate (and weather) data at various levels, at the local level of single city, at the national level of a  single country, and also at the global level. The law can be shown to be a simple linear law of the type T = A + Bt where the nonzero intercept A, in my opinion, is exactly similar to the work function conceived by Einstein to explain photoelectricity.

I have been testing the universal applicability of this law since it became obvious to me, recently, during the bitterly cold spell that we have been experiencing in the USA, which got me interested in studying the weather and/or climate data at various levels. The temperature-time data for both Detroit, MI and London, UK, for the full month of December 2013 and (the to-date) January 2014 can be shown to follow this simple law. The global average temperature data, from 1880-2013, can also be shown to obey the same law. As with the photoelectricity experiment, where the K-f graph yields a family of parallels (for different metals, each with its own work function W), the T-t graph is also a family of parallels, with a fixed slope B and a nonzero intercept A, which can be compared to Einstein’s work function. I have deduced the equations for these parallels by considering several (x, y) pairs in the datasets at various levels. It should be noted that Millikan arrives at the absolute magnitude q of the electrical charge on a single electron (in his famous oil drop experiments) and then the numerical value of the Planck constant h from the photoelectric measurements, by using exactly the method just described. He considers various (x, y) pairs in his dataset to show the constancy of q. He does the same with the K-f measurements, where K = qVo with Vo being the stopping potential measured by Millikan (for two metals lithium and sodium). 

I have uploaded a pdf file with some figures discussing these findings on my Facebook page, see the group Global Warming for the Layman, https://www.facebook.com/groups/GWforlayman/


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