We study the radiation of thermal photons and dileptons likely to be produced in relativistic heavy ion collisions. We find that the thermal photon multiplicity scales with the charged pion multiplicity as $dN_{ch}/dy)^\alpha$ with $\alpha\sim 1.2$ for a transversely expanding system, contrary to the general belief of a quadratic dependence. The scaling is shown to be valid, both for real and virtual photons. The coefficient of proportionality at a given energy may help us identify the appropriate equation of state of hot hadronic matter produced in such collisions.
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