  Identifying the processes that determine the initial mass function of stars
(IMF) is a fundamental problem in star formation theory. One of the major
uncertainties is the exact chemical state of the star forming gas and its
influence on the dynamical evolution. Most simulations of star forming clusters
use an isothermal equation of state (EOS). However, theoretical predictions and
observations suggest that the effective polytropic exponent gamma in the EOS
varies with density.
  We address these issues and study the effect of a piecewise polytropic EOS on
the formation of stellar clusters in turbulent, self-gravitating molecular
clouds using three-dimensional, smoothed particle hydrodynamics simulations. To
approximate the results of published predictions of the thermal behavior of
collapsing clouds, we increase the polytropic exponent gamma from 0.7 to 1.1 at
some chosen density n_c, which we vary. The change of thermodynamic state at
n_c selects a characteristic mass scale for fragmentation M_ch, which we relate
to the peak of the observed IMF. Our investigation generally supports the idea
that the distribution of stellar masses depends mainly on the thermodynamic
state of the star-forming gas. The thermodynamic state of interstellar gas is a
result of the balance between heating and cooling processes, which in turn are
determined by fundamental atomic and molecular physics and by chemical
abundances. Given the abundances, the derivation of a characteristic stellar
mass can thus be based on universal quantities and constants.
