Supernova remnants are thought to be the dominant source of Galactic cosmicrays. This requires that at least 5% of the available energy is transferred tocosmic rays, implying a high cosmic-ray pressure downstream of supernovaremnant shocks. Recently, it has been shown that the downstream temperature insome remnants is low compared to the measured shock velocities, implying thatadditional pressure support by accelerated particles is present. Here we use a two-fluid thermodynamic approach to derive the relation betweenpost-shock fractional cosmic-ray pressure and post-shock temperature, assumingno additional heating beyond adiabatic heating in the shock precursor and withall non-adiabatic heating occurring at the subshock. The derived relations showthat a high fractional cosmic-ray pressure is only possible, if a substantialfraction of the incoming energy flux escapes from the system. Recently a shockvelocity and a downstream proton temperature were measured for a shock in thesupernova remnant RCW 86. We apply the two-fluid solutions to thesemeasurements and find that the the downstream fractional cosmic-ray pressure isat least 50% with a cosmic-ray energy flux escape of at least 20%. In general,in order to have 5% of the supernova energy go into accelerating cosmic rays,on average the post-shock cosmic-ray pressure needs to be 30% for an effectivecosmic-ray adiabatic index of 4/3.
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