We present results from an inviscid unsteady one-dimensional model of the discharge, from a cylindrical container into vacuum, of initially homogeneous, high-pressure, high-temperature ideal gas. In this study (Part I), the discharge is begun, by displacement of a diaphragm at one end of a cylindrical chamber, only after the burn of the contents is complete; in a companion study (Part II)-published separately, the venting is initiated during dame propagation across the reactive-gas mixture. Of particular interest are the integrals over time of the momentum and the mass discharged from the container exit, and the ratio of the momentum-discharge integral to the mass-discharge integral-this ratio is essentially the specific impulse. We address first the case of simple, nozzleless blowdown, in which the cross-sectional area of the container exit, A*, is equal to the cross-sectional area (V/L) of the plenum of the cylindrical container; we consider the complete time evolution for the case of a massless diaphragm that plays no dynamical role, and just the early-time evolution for the case of a diaphragm with a mass that is finite relative to the mass of the gas initially stored in the container. We also address the case in which the area of the exit A* is significantly less than the cross-sectional area (V/L) of the plenum of the cylinder, say, [(A*/(V/L)] less than or equal to (1/4); for this case, acoustic waves equilibrate the thermodynamic state of the essentially quiescent gas in the plenum of the container, so that a quasisteady treatment suffices and, throughout the plenum, the pressure (upon neglect of acoustic oscillations) is taken to be spatially uniform, though temporally evolving. We suggest that the specific impulse as a function of time for intermediate values of the area ratio, i.e., for (1/4) < [(A*/(V/L)] < 1, may be obtained (for a given value of the isentropic ratio gamma) by interpolation of results between the nozzleless-blowdown case [A*/(V/L) = 1] and quasisteady cases [0 < (A*/(V/L)] less than or equal to 1/4]. Finally, in the context of a propulsion device attached to a payload in orbit, we briefly address tradeoffs (in the kinetic energy derived by the payload from combustion of the propellant of the microthruster) involving the relative mass of the combustion-chamber cap (diaphragm).