  In the present work we study the main physical properties of a gas of
$\kappa$-deformed bosons described through the statistical distribution
function $f_\kappa=Z^{-1}[\exp_\kappa (\beta({1/2}m v^2-\mu))-1]^{-1}$. The
deformed $\kappa$-exponential $\exp_\kappa(x)$, recently proposed in Ref.
[G.Kaniadakis, Physica A {\bf 296}, 405, (2001)], reduces to the standard
exponential as the deformation parameter $\kappa \to 0$, so that $f_0$
reproduces the Bose-Einstein distribution. The condensation temperature
$T_c^\kappa$ of this gas decreases with increasing $\kappa$ value, and
approaches the $^{4}He(I)-^{4}He(II)$ transition temperature
$T_{\lambda}=2.17K$, improving the result obtained in the standard case
($\kappa=0$). The heat capacity $C_V^\kappa(T)$ is a continuous function and
behaves as $B_\kappa T^{3/2}$ for $T<T_c^\kappa$, while for $T>T_c^\kappa$, in
contrast with the standard case $\kappa=0$, it is always increasing.
  Pacs: 05.30.Jp, 05.70.-a Keywords: Generalized entropy; Boson gas; Phase
transition.
