( at 20 degrees C, 45% humidity and 29.9 inches of mercury ) That's about 20KV/inch for air variable capacitors used in amateur radio.

  This is just a general rule of thumb value, it is not linear. See Paschen's Law below.

  If we eliminate the antenna, 100 watts of RF into 50 ohms will generate:

   P = E^2 / R   or E = sqrt (P*R)

   So to solve we have:

   E = sqrt (100 watts * 50 ohms)

   E (rms) = 70.7 volts

   E(peak) = 1.4 * 70.7 = 99 volts

The gap necessary to create an arc with 99 volts is:

   99V / 20,000V = 0.005 inches

 The law essentially states that the breakdown characteristics of a gap are a function (generally not linear) of the product of the gas pressure and the gap length, usually written as V= f( pd ), where p is the pressure and d is the gap distance. In actuality, the pressure should be replaced by the gas density.

Paschen's Law reflects the Townsend breakdown mechanism in gases, that is, a cascading of secondary electrons emitted by collisions in the gap. The significant
parameter is pd, the product of the gap distance and the pressure. Typically, the Townsend mechanism (and by extension Paschen's law) apply at pd products less
than 1000 torr cm, or gaps around a centimeter at one atmosphere. Furthermore, some modifications are necessary for highly electronegative gases because they
recombine the secondary electrons very quickly.

In general, an equation for breakdown is derived, and suitable parameters chosen by fitting to empirical data.

Here are three equations:

Breakdown voltage:
Vbreakdown = B * p * d / (C + ln( p * d))

Breakdown field strength:
Ebreakdown = p * ( B / ( C + ln ( p * d)))

where:
C =ln( A / ln ( 1 + 1 / gamma))

where:
gamma is the (poorly known) secondary ionization coefficient.

For air:
A = 15 cm-1Torr -1
B = 365 Vcm-1 Torr-1
and gamma = 10-2
so
C = 1.18

For air, and gaps on the order of a millimeter, the breakdown is roughly a linear function of the gap length: V = 30pd + 1.35 kV,
where d is in centimeters, Vs = volts spark and p is in atmospheres.
 

Air	Vs min	(V)pd at Vs min
		(torr cm)
	327	0.567

 
 
 

Temperature dependence

Paschen's law ( V = f(pd)) should really be stated as V = f( Nd) where N is the density of gas molecules, which is, of course, affected
by the temperature as well as the pressure of the gas ( n/V = p/RT). An empirical formula for air (considering it as an ideal gas) is:
 
 

x = 293 * p * d / (760 * T)
Vbreakdown = 24.22 * x + 6.08 * SQRT(x)

p = pressure in Torr (mm Hg),
d = distance in cm,
T = Temperature in Kelvins
Vbreakdown in kV
 

Humidity dependence

In air, increasing humidity increases the breakdown voltage. The effect is most noticeable in uniform field, and less important
in non uniform gaps (such as sphere gaps where the gap is a large fraction of the sphere diameter, or in rod or needle gaps).