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Classical Physics
What does the 2.3 constant in e^Q/2.3RT come from?
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[QUOTE="FQVBSina, post: 6246476, member: 553119"] [B]TL;DR Summary:[/B] Many activation energy/temperature dependance equations have the term e^Q/RT and often it is written as Q/(2.3RT). Where did this mysterious 2.3 come from? Ok, I have actually found the answer from [URL]http://www.bristol.ac.uk/phys-pharm-neuro/media/plangton/ugteach/ugindex/m1_index/med_memb/file/Nernst1.htm[/URL]. Basically, a convenient way to analyze these equations is to take the log of both sides. Since e takes the natural log and the equations are usually in log base 10, the conversion factor between natural log and log10 is 2.303, simplified to 2.3. Since I didn't find an explicit question on this and someone else may have the same question, I will leave this post here if you don't mind. Many energy/temperature relationships are given as an exponential term, such as the diffusion equation: $$D(T) = D_0*e^{\frac {-Q_{ID}} {RT}}$$ Where D0 is the initial diffusivity material constant, QID is the activation energy, R is the gas constant, and T is temperature. And often right after this, the book would write it as: $$D(T) = D_0*e^{\frac {-Q} {2.3RT}}$$ Where did this 2.3 come from? Example: This book on page 228: [URL='https://books.google.com/books?id=gCcSBQAAQBAJ&lpg=PA228&ots=tvZtxC9VW5&dq=diffusivity%20Q%2F(2.3RT)%20where%20did%202.3%20come%20from&pg=PA228#v=onepage&q=diffusivity%20Q/(2.3RT)%20where%20did%202.3%20come%20from&f=false']https://books.google.com/books?id=gCcSBQAAQBAJ&lpg=PA228&ots=tvZtxC9VW5&dq=diffusivity Q/(2.3RT) where did 2.3 come from&pg=PA228#v=onepage&q=diffusivity Q/(2.3RT) where did 2.3 come from&f=false[/URL] [/QUOTE]
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What does the 2.3 constant in e^Q/2.3RT come from?
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