http://www.pdas.com/atmosTable2SI.html below 10 km; fits

pressure vs altitude (10km)
An analysis of data submitted by computer: on 15-SEP-2018 at 11:54 indicates that a function of the form:
--Exponential-- y=A exp(Bx)
can fit the 22 data points with a reduced chi-squared of 0.11E+07

                FIT
 PARAMETER     VALUE        ERROR
   A =         0.1034E+06   0.62E+03
   B =        -0.1331       0.11E-02
 
 NO x-errors
 NO y-errors


scale height =-1/B = 7.513 km
---

temperature vs altitude (10km)
An analysis of data submitted by computer: on 15-SEP-2018 at 11:56 indicates that a function of the form:
--Linear-- y=A+Bx
can fit the 22 data points with a reduced chi-squared of 0.11E-02

                FIT
 PARAMETER     VALUE        ERROR
   A =          288.1       0.13E-01
   B =         -6.490       0.22E-02

Lapse Rate = 6.5 K/km

---
pressure vs altitude (86km)

An analysis of data submitted by computer: on 15-SEP-2018 at 12:00 indicates that a function of the form:
--Exponential-- y=A exp(Bx)
can fit the 45 data points with a reduced chi-squared of 0.31E+07

                FIT
 PARAMETER     VALUE        ERROR
   A =         0.9887E+05   0.31E+04
   B =        -0.1426       0.64E-03

scale height = -1/B = 7.013 km

---
to me all of these plots look "pretty good"

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Swihart chapter 5 #8

law of Dulong & Petit says molar specific heat of solids is about 3 R
assume a rock density of about 3 g/cm^3 = 3000 kg/m^3
the energy loss seems to be assuming sigma T^4 per area from the ground, 
but more realistically the atmosphere would also heat the ground
this heat loss is made up with a Delta T=10 of some moles or mass of ground

rate of energy loss per area: sigma T^4 for 12*3600 seconds = 
* ? sigma*295^4*12*3600
    18551668.66420149    (J/m^2 = 10^3 erg/cm^2, energy lost over 12 hours per m^2)
Q=n C (Delta T) = n 3 R 10 = above

*  ? res/(3*R*10)
    74375.12066666526    !(moles)
* ? 74375.*.025          !(mole weight= 25 g)
    1859.375000000000    !(kg of rock)
* ? res/3000             !(density of rock =3000 kg/m^3)
    .6197916666666666    !(m)