I'd be quite interested if you'd actually be able to find flaws in this, since the only responses seem to be ad homiem and such, with no concern for theory backed by observations. (Hopefully thanks in advance)
Venus' temperature is caused *only* by ~92 atmosphere of pressure.
Derivation:
The adiabatic lapse rate = dT/dz = -Mg/R*(y-1)/y = ~7.82K/km (I was lazy and used 100% CO2 for this, also y = gamma) which isn't too far off from the ALR calculated from measurements using least squares = ~7.74K/km.
Furthermore:
T(z) = Tsurface - ALR*z, by definition (~= 735 - 7.82z).
The barometric equation is P = Psurface*e^(-Mgz/RT).
Solving for z = -RT/Mg*ln(P/Psurface),
and plugging into T(z), we get T(P) = Tsurface - (y-1)/y*Mg/R*RT/Mg*ln(Psurface/P)
= T = Tsurface - (y-1)/y*T*ln(Psurface/P),
rearranging, T(P)*(1+(y-1)/y*(ln(Psurface)-ln(P))) = Tsurface
Thereforce T(P) = Tsurface/(1+(y-1)/y*(ln(Psurface)-ln(P)))
Something you may be interested in, though water vapor makes the calculation much more complex so this is for Venus.
Derivation:
The adiabatic lapse rate = dT/dz = -Mg/R*(y-1)/y = ~7.82K/km (I was lazy and used 100% CO2 for this, also y = gamma) which isn't too far off from the ALR calculated from measurements using least squares = ~7.74K/km.
T(z) = Tsurface - ALR*z, by definition (~= 735 - 7.82z).
The barometric equation is P = Psurface*e^(-Mgz/RT).
Solving for z = -RT/Mg*ln(P/Psurface),
and plugging into T(z), we get T(P) = Tsurface - (y-1)/y*Mg/R*RT/Mg*ln(Psurface/P)
= T = Tsurface - (y-1)/y*T*ln(Psurface/P),
rearranging, T(P)*(1+(y-1)/y*(ln(Psurface)-ln(P))) = Tsurface
Thereforce T(P) = Tsurface/(1+(y-1)/y*(ln(Psurface)-ln(P)))
The one day you'd sell your soul for something, souls are a glut.