Alarmists and Physics Deniers don’t actually know what this equation signifies and make themselves look silly by trotting it out as if it somehow supports Alarmist Theory and/or debunks the Gravito-Thermal Effect.
Nothing of the sort. There’s a full explanation and worked example at ChemGuide.co.uk.
Let’s apply it to typical temp, pressure, density at sea level:
Pressure = 101,325 Pa
Volume = 1 m3
Density = 1.227 kg/m3
n = density divided by molecular mass of ‘air’, which is 29g/mole
R = universal gas constant* = 8.31441 J/K/mol
Temp = 288K
Stick in the numbers on the right hand side, 1,227/29 x 8.31441 x 288 = 101,314. Close enough to 101,325!
Now we’ve got the hang of it, what’s the likely temperature at 10 km altitude?
Wiki tells us that pressure up there is 26,300 Pa, density is 416 g/m3.
The left hand side is 26,300 x 1 = 26,300
The right hand side is 416/29 x 8.31441 x T = 119.3 x T
So 119.3 T = 26,300; and T = 26,300/119.3 = 220K
Which is exactly what the blue line on Wiki’s chart – and real life measurement – show. Which is the same as what you’d get if you just start by assuming ever increasing density in a gravitational/acclerating field and working from there (see diagram 5). In fact, you can assume constant density, linearly increasing density, or geometrically increasing density, there would still be a similar profile with increasing pressure and temperature towards the surface. Basic maths. Any other outcome is mathematically impossible unless you assume that density increases with height at an implausible rate (in which case, what happens at the top?).
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