Why a Lie?
Every formula, every constant, every temperature ratio is an approximation.
Why, Because the whole field of science is nuts. So nuts, that universities, even MIT have to dumb it down. We need simpler rules to make sense of it all.
Also, when thermo dynamics started it was literally the smart words for heat engine. It evolved into the science of energy.
We eventually came to realize, heat is just motion. So technically, there is no field of thermodynamics, its just Dynamics. But no scientist in the field was dumb enough to point this out, hence losing their job as thermodynamics expert.
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Pack of Lies
Where do we start. First, universities almost always teach students to always use the gamma "constant" for ideal gas, which is based on the ratio of 100/140 or the amount of work it takes to expand 1 liter with 1 Bar pressure, to the amount of heat stored in 1 liter of Helium at STP. This gives beta of .7 so gamma of 1.7. But the ratio for air is 100/250 or .4, so the calculations are massively wrong for air.
So why do that? See nature of heat, introduction chapter. Gamma for air isn't a constant, so the work and heat curve for air are not exponential curves, they are exponential curves with a variable exponent. Hurts the brain.
How about temperature ratios? Same thing, basically they never make sense except for vapors, because state changes have huge discontinuities for heat to change temperature 1 degree. But even for vapor temperature ratios, they are still wrong. Every vapor except helium stores more energy as the temperature rises, per degree. At room temperature air stores about 5/6 of a joule per degree per Liter at STP (based on specific heat, but recall 1 liter of air is 1.4 grams), but at 1500 degrees the same liter requires about 1.1 Joules to increase 1 degree. Because the specific heat constants are not right, the ratios of temperature are not ratios of heat.
So no constants are right, no ratios are right, and so no formulas using constants or ratios are right.
You have been told, so for the rest of the site we will pretend Beta is a constant and temperature ratios mean something, its just to keep things simple. Remember they are all approximations.
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