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) α with α ∼ 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.PACS numbers: 25.75. Dw, 12.38.Mh, 24.10.Nz, 25.75.Gz The search for the quark-gluon plasma (QGP), a deconfined state of strongly interacting matter, is entering a decisive phase. Evidence has been mounting for some time now, that such matter is perhaps being produced in collisions involving heavy nuclei at the CERN Super Proton Synchrotron (SPS). If confirmed, this holds out a promise that the QGP likely to be created at the Brookhaven Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC) will occupy a much larger space-time volume, in similar collisions. The plasma thus produced will have to expand and cool, due to large internal pressure. It has also to undergo hadronization, once the temperature drops below the transition temperature. These hadrons may continue to interact for some time before their density gets too low to support frequent collisions. We may also have a mixed phase of quarks, gluons, and hadrons during which the speed of sound may become vanishingly small, if quantum chromodynamics admits a first order phase transition.Many of the observables from the above collisions, like the particle distributions, electromagnetic radiation, the spatial and temporal dimensions of the fireball etc., will be decided by the equation of state of hadronic matter. The transverse expansion of the system which drastically alters the time scales in the system, at least with regard to the mixed and the hadronic phases is also affected by the equation of state [1]. What should be the equation of state of hot hadronic matter which is created in heavy ion collisions? It is expected that if the tran-sition temperature is very close to the pion mass then the hadronic matter could possibly well be determined by pions and only a few low lying mesonic resonances. The hadronic matter is likely to be populated by heavier hadrons once the temperature is higher. Will these hadrons stay in chemical and thermal equilibrium, till the freeze-out? This will be decided by the competition between the collision frequency and the rate of expansion, and if valid, it will be reflected in uniquely determined particle ratios [2]. It is not difficult to imagine that the equation of state or at least the composition of the hadronic matter may be somehow related to the manner in which the hadronization proceeds. This aspect has not yet received enough attention as it involves the non-perturbative realm of quantum chromodynamics.The question of hadronization of the plasm...