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An earlier approximate theory proposed by Knuth and Fisher and Miller and Andres for solving the Boltzmann equation to calculate speed ratios and temperatures in free jet expansions has been extended to take account of quantum effects and realistic potentials in the collision integrals. The calculations show that quantum effects lead to a substantial increase in terminal speed ratios in helium but not in heavier gases. For He the speed ratios depend sensitively on the shape of the potential. Despite the approximate nature of the theory the predictions are in reasonable agreement with recent experiments. The theory predicts that the presently highest achieved speed ratio in He of 225 can be increased to 700 if condensation does not occur. At this speed ratio the quasiequilibrium gas phase temperature is roughly 10−3 K.
Toennies et al. (1977) studied this question.