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  Consider a vessel maintained at a constant temperature , containing a homogeneous reacting mixture. Let the characteristic size of the vessel be . Since the mixture is homogeneous, the density  is constant. During the initial period of ignition, the consumption of reactant concentration is negligible (see  and  below), thus the explosion is governed only by the energy equation. Assuming a one-step global reaction , where  is the amount of heat released per unit mass of fuel consumed, and a reaction rate governed by Arrhenius law, the energy equation becomes
  where