THE ASYMPTOTIC FEATURES OF THE UNSTEADY EXPANSION OF AN IDEAL-GAS INTO A VACUUM

Further developing the results obtained in [1], where the asymptotic f orm of the one-dimensional expansion of an ideal gas with adiabatic in dex kappa> 1 was investigated, the features of the unsteady expansion of an ideal gas (non-viscous and non-heat-conducting) into a vacuum ar e investigated. If t is the time and x is a coordinate measured from t he plane, axis or centre of symmetry, the formulas obtained in [1], wh ich take into account the effect of the vanishing pressure on the iner tial expansion of the gas, hold in the region of the plane xt, elongat ed in the direction of the t axis. The approach used below is free fro m this limitation, and the relations obtained hold everywhere far from the origin of coordinates. In addition to this, asymptotic formulae a re obtained which describe the spherically symmetric inertial expansio n of a gravitating gas, and an asymptotic analysis is carried out for an ideal gas with kappa=1. The corrections for gravitation, like the f ormulae for the inertial expansion of a gas into a vacuum, are indepen dent of its thermodynamic properties. The results obtained hold for ti mes t for which, as a result of the expansion, the volume occupied by the gas considerably exceeds its initial value.