  We study the effect of varying the equation of state on the formation of
stellar clusters in turbulent molecular clouds, using three-dimensional,
smoothed particle hydrodynamics simulations. Our results show that the equation
of state helps determine how strongly self-gravitating gas fragments. The
degree of fragmentation decreases with increasing \new{polytropic exponent}
$\gamma$ in the range $0.2 < \gamma < 1.4$, although the total amount of
\new{mass accreted onto collapsed fragments} appears to remain roughly constant
through that range. Low values of $\gamma$ are expected to lead to the
formation of dense clusters of low-mass stars, while $\gamma>1$ probably
results in the formation of isolated and massive stars. Fragmentation and
collapse ceases entirely for $\gamma > 1.4$ as expected from analytic
arguments. The mass spectrum of overdense gas clumps is roughly log-normal for
{\em non}-self-gravitating turbulent gas, but changes to a power-law under the
action of gravity. The spectrum of collapsed cores, on the other hand, remains
log-normal for $\gamma\le 1$, but flattens markedly for $\gamma >1$. The
density PDFs approach log-normal, with widths that decrease with increasing
$\gamma$. Primordial gas may have effective $\gamma > 1$, in which case these
results could help explain why models of the formation of the first stars tend
to produce isolated, massive objects.
