Shock phenomena associated with the quark-to-hadron matter phase transition are studied using the concept of adiabats. To allow for an analysis of a medium with vanishing baryon density, the shock and Poisson adiabats are formulated in terms of hydrodynamic fluxes, rather than only thermodynamic variables. The bag-model equation of state is used to describe the phase transition. It is shown that deflagrations from the quark phase above the critical temperature and strong detonations from the supercooled quark phase to the superheated hadron phase are unlikely. Instead the possibility of weak condensation detonations from the supercooled quark phase to a mixed phase is indicated. Strong detonations can occur if the latent energy density of the phase transition is small compared to the energy density of the hadron gas. Simple properties of the adiabats and of the equation of state are employed to derive several analytic results.