Big Bottle RAD H2O
Analysis
Simplistically, all the radon in the water is transferred to the
closed air loop;
Cw * Vw = Ca * Va
Cw = Ca * Va / Vw
but some radon is left in the water. At equilibrium, the water to
air concentration ratios will be 𝛂, given by
𝛂 = 0.105 + 0.405 * exp(-0.0502*T)
where T is the temperature in ℃ (Weigel, 1978).
We can therefore add an air equivalent volume 𝛂Vw to Va.
Cw * Vw = Ca * (Va + 𝛂Vw)
A head space must be left in the bottle to prevent
it exploding if the water heats up, so we correct for
that:
Cw * (Vw - Vh/𝛂) = Ca * (Va + 𝛂Vw)
or
Cw = Ca * (Va + 𝛂Vw) / (Vw - Vh/𝛂)
Thanks