A Ponderomotive Effect associated with the Flow of Heat through Liquid Helium II

Abstract

It has recently been suggested^1,2 that liquid helium II shows a certain similarity with a Knudsen gas, the atoms moving with a very long mean free path. From the formula which is quite general (l is mean free path, χ is thermal conductivity, c_ν is specific heat per gram, Ï is density, ν is velocity of the atoms or quanta performing the heat conduction), one obtains values for l of several millimetres, even if one takes for χ the smallest values measured by Keesom² and assumes for ν either the velocity of sound or a value deduced from the zero point energy (both about 2.5 × 104 cm./sec). Thus, if a Knudsen manometer were immersed in helium II, the moving vane should be repelled from the heater plate with a force of the order of magnitude where Q is the total heat flow striking the vane, provided the separation of plate and vane is less than the mean free path. Expression (2) is also of a very general nature and can only be modified by a factor of the order of magnitude of unity arising from the velocity distribution and the type of the collisions of the atoms with the vane.