The constant volume explosion of a flammable gas is one of the more common accidental explosions. The explosion pressure at the stoichiometric condition is approximately 50 times greater than the failure pressure of most industrial structures. Observations from accident scenes suggest that some explosions are caused by a quantity of fuel significantly less than the stoichiometric amount required to fill an enclosure. This paper presents a method for analyzing the explosion hazard in an enclosure which is only partially filled with a flammable gas. The method, called the adiabatic mixing model, is based on thermodynamics and can be used to calculate the minimum fuel quantify which will yield a specified explosion pressure. Results are presented for a set of representative fuels and are compared with alternative explosion models. The results demonstrate that catastrophic structural damage can be achieved with a volume of flammable gas which is less than one percent of the enclosure volume. The method can be a useful tool for both hazard analysis and accident investigations.