  We present estimates of the energy input from supernovae (SNe) into the
intergalactic medium using (i) recent measurements of Si and Fe abundances in
the intracluster medium (ICM) and (ii) self-consistent gasdynamical galaxy
formation simulations that include processes of cooling, star formation, SNe
feedback, and a multi-phase model of the interstellar medium. We estimate the
energy input from observed abundances using two different assumptions: (i)
spatial uniformity of metal abundances in the ICM and (ii) radial abundance
gradients. We show that these two cases lead to energy input estimates which
are different by an order of magnitude, highlighting a need for observational
data on large-scale abundance gradients in clusters. Analysis of galaxy
formation results and estimates from observed Fe and Si abundances indicates
that the SNe energy input can be important for heating of the entire ICM
(providing energy of ~1 keV per particle) only if the ICM abundances are
uniform and the efficiency of gas heating by SN explosions is close to 100%
(implying that all of the initial kinetic energy of the explosion goes into
heating of the ICM). We conclude that unless these most favorable conditions
are met, SNe alone are unlikely to provide sufficient energy input to heat all
of the cluster ICM and may need to be supplemented or even substituted by some
other heating process(es). (Abridged)
