  We consider Kaluza-Klein models with background matter in the form of a
multicomponent perfect fluid. This matter provides spherical compactification
of the internal space with an arbitrary number of dimensions. The gravitating
source has the dust-like equation of state in the external/our space and an
arbitrary equation of state (with the parameter $\Omega$) in the internal
space. In the single-component case, tension ($\Omega=-1/2$) is the necessary
condition to satisfy both the gravitational tests in the solar system and the
thermodynamical observations. In the multicomponent case, we propose two models
satisfying both of these observations. One of them also requires tension
$\Omega=-1/2$, but the second one is of special interest because is free of
tension, i.e. $\Omega=0$. To get this result, we need to impose certain
conditions.
