Thermodynamics of the thermomechanical effect of liquid He II

Abstract

It has been found by Allen and Jones (193 8 ) that if two vessels containing liquid He II are connected by a capillary and maintained at different temperatures, the hydrostatic pressure in the warmer vessel rises above that of the colder; By maintaining a temperature gradient along the capillary, it is thus possible to produce a flow of helium against a pressure gradient. An apparatus in which this is done may be called a “helium pump”, and the phenomenon which we shall call the “thermomechanical effect” reveals a new mechanism by which heat can be transformed into mechanical work. In such a “pump” heat is absorbed at the warm end of the capillary and liberated at the cold end; by the Second Law of Thermodynamics such part of this heat as is converted into mechanical work must be absorbed and liberated reversibly. As in the case of thermoelectric phenomena, however, to which, as we shall see, the thermomeehanical effect is closely analogous, we have to deal with a superposition of reversible and irreversible processes, the latter being the ordinary conduction of heat and the resistance to flow in the capillary. Until, therefore, we have some experimental proof that the conditions can be chosen in such a way that the irreversible processes are small, we must assume that the reversible and irreversible effects are independent. The existence of reversible therm al effects accompanying the capillary flow has been predicted by Tisza (1938) from certain kinetic speculations which are based on the idea (F. London 1938) that the phase transition into He 11 might be due to the condensation phenomenon of the Bose-Einstein statistics. The present paper discusses w hat can be said about the effects from purely thermodynamical considerations apart from any special kinetic model. A brief deduction of the thermodynamic relations has already been given by the present author in a letter to Nature (H. London 1938a).