Note on the sensitive time of a Wilson expansion chamber

Abstract

By “sensitive” time of a cloud chamber is meant the length of time for which the supersaturation in the chamber remains sufficient to cause condensation along the tracks of ionizing particles. If the cooling expansion is made rapidly this sensitive time depends on the rate at which the temperature of the gas in the chamber rises after the expansion. This problem of the warming of a gas in a vessel, after an initial cooling, has been previously considered by Rayleigh (1). To follow the whole history of the warming until the gas reaches the temperature of the vessel requires an elaborate mathematical treatment which can only be carried out for specially shaped vessels. Rayleigh considers two special cases, viz. a gas contained between two parallel infinite planes, and a gas contained in a spherical vessel. The results obtained by Rayleigh for these cases are, however, not very helpful in dealing with the cloud-chamber problem under consideration. This is so, not so much because specially shaped vessels are assumed, but because the treatment does not lend itself to an evaluation of the rate of warming in the early stages of the process. It is this initial warming that we are concerned with here, since a cloud chamber ceases to be sensitive when the average temperature of the gas has risen by only 5% or less of the cooling produced by the expansion. Rayleigh's result for the average rise in temperature of the gas at any instant is represented by an infinite series which converges very slowly when the rise in temperature is small.