### Abstract:

In this project work, quantum theory of the thermodynamic properties of an ideal Bose gas
is presented using quantum statistics. First a calculation is performed to obtain
expressions for partition function and for distribution function of bosons in the system.
Next, internal energy of an ideal Bose gas is calculated using Bose Einstein functions at a
higher and lower temperature. The occurrence of Bose Einstein condensation also has
been taken in to account. It is one of the most interesting phenomena predicted by quantum
statistical mechanics. It starts to occur when the temperature of the Bose gas is less than
the critical (condensation) temperature. If the temperature lowers to zero at zero
momentum state, all particles occupy the single- particle energy state and they form a
condensate. This phenomenon is called BE condensation and it is purely a quantum effect.
Specific heat capacity at a constant volume of the system is mainly presented and
calculated in this work using Euler’s gamma and Riemann’s zeta functions. At zero
temperature of the gas its specific heat lowers to zero, but at the critical temperature
it reaches its maximum value which is greater than the classical one. It shows that it is a
quantum effect of an ideal Bose gas .But it becomes lower and lower to the classical value
when the temperature gets higher at normal phase ( ). Finally, the entropy of the
system also has been calculated .In general, at a sufficiently low temperature, T=0, the
specific heat, internal energy and entropy of an ideal Bose gas have no contribution at zero momentum state (condensed phase).