170
8.
ÈLËCTRICÏTŸ THROUGH GASES
In computing & from the line, the current values may be expressed
in either amperes, milliamperes or other units, since log il — log {2
:
log i1’/i2 and the ratio i1/z'2 is not altered by a change of units.
Dividing [7 values by 300 to convert from volts to electro-static
units and using e = 4.8 X 10”10 and k = 1.37 X 10"16 gives
11600
T = —’—
,
degrees absolute.
(8—5)
'
5
If common logarithms are used, the constant will be 5040 instead
of 11,600; i.e., : in this and in subsequent equations must be multiplied by 2.303. T_he
“
partial
”
or electron temperatures so found,
range from tens of thousands to a few hundreds of thousands of
degrees absolute.
If the velocities are distributed according to the Maxwellian
law, as evidenced by a straight line in the-logarithmic plot, then.
the electrons may be treated. as a perfect gas, according to the
usual developments of the Kinetic Theory.11
From this, and from
the established relation between electron volts (K,) and the average
kinetic energy (6‘; in ergs) , it can be seen that
"
,
‘
=
lm02 = â/%T = ——e
8—6
2
2
300
’
(
)”
.
where Ve is the equivalent energy of the electrons in volts,
mean
of the squared values of their thermal velocities, 6 is the
electronic charge in e,s.u. and m is the mass of the electron. It
'
a130 knoWn that the average Velocity 5 = (8v2/37r) %. ThiS, With
,
the known constants and equations 8—5 and 8—6 permits the fol—
__
'
lowing quantities to be evaluated:
‘
…
_
,
_
V
:
—,
volts
.‘8—7r
(Vç_=0651S/3,1fcommon l'ogarithms are used), and
‘
,
:
_
= —V———
>Cm-/SeC-,
’
(8—8)
aSWellas
,
‘
Ë=———
ergs
’
_
(8—9)