Chemical Potential Of A Binary System Of Helium Isotopes At Tempera Tures Between 0 K And 5 K

ABSTRACT

A study of the two stable isotopes of helium at low temperature was done using statistical

mechanics approach. It was assumed that pairs of ~He - iH e were formed creating a

new particle in the mixture. Such a mixture exhibits quantum effects at temperatures

close to 0 K. A model of pair interaction was used. The partition function of the mixture

was used in establishing the chemical potential of the mixture. The case of a particle in a

cube of known volume was used. An expression of the chemical potential of the pair was

obtained in terms of temperature. The relationship between chemical potential of the pair

and temperature was studied. Also obtained is an expression of chemical potential in

terms of density for a fixed volume of the mixture confined in a ~ubical container. A

computer software mathCAD professional 2000 was used to generate data. The properties

of the mixture over a wide range of densities and temperatures were analyzed. It was

established that an increase in temperature led to decrease in chemical potential

regardless ofthe number of particles in the system. The chemical potential of the pair in a

mixture of fermions and bosons in the region of 0 K and 5 K is positive ranging from

8.972 x W-6 eV to 4.4700 x 10-4 eV. The variatiation of chemical potential with

temperature between 0 K and 5 K was 8.939 x 10-3 eV / K. The study also established

that the chemical potential of the pair did not vary with change in quantum states.