372
EXTENSION OF THERMODYNAMIC COMPUTATIONS
Illustrations of the Use of Erroneous Densities
In order to illustrate the amount of divergence between
p a and p, we have for this balloon ascension—
TABLE 83
The Difference Between p (Non-adiabatic) and p a (Adiabatic)
Density
z
P
Pa
50000
0.0000
0.0000
45000
0.0035
0.0033
40000
0.0180
0.0057
35000
0.0324
0.0099
30000
0.0551
0.0203
25000
0.0929
0.0426
20000
0.1586
0.0935
15000
0.2754
0.2073
10000
0.4760
0.4190
5000
0.7730
0.7151
surface
1.1485
1.1485
Since p is greater than p a it follows that,
, v Pi- Po. „ , Pi- Po
(782) — is smaller than
P10
PaO
and this is compensated in the gravity equation by the terms
for the circulation and radiation. It has been tested by numerous
Pi — Po
computations that g (zi — z 0 ) = — Cp a (Ta — T 0 ) — — '
PaO
without important residuals from the surface to the vanish
ing plane, and that — Cpw (T a — T 0 ) ^ holds true
throughout the atmosphere. No system of meteorology
k
founded on R a = ^P a = constant is applicable in prac
tical studies of atmospheric conditions.
There is another important matter in which erroneous den
sities have been introduced into studies of radiation phenomena.