The aim of this paper is to calculate the quantum thermodynamic functions until the third
virial coefficient of plasma under the influence of a weak magnetic field. The calculation
is based on the binary Slater sum in the case of a low density plasma, which is exact in a
quadratic order with respect to the magnetic field. The method which was used is based
on the Bloch equation. The second virial coefficient is obtained in the form of a convergent
series expansion in terms of the interaction plasma parameter ξab = eaeb
KTλab
where λab being
the thermal de Broglie wavelength between two particles. We compared our results with
others.