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R13.6 Adiabatic Operation of Batch Reactors

		For adiabatic operationand when the work done by the stirrer can be neglected
			(13-13)
		whereAn analytical solution relating X and T can be found for the case of constant or mean heat capacity.
			(13-15)
		multiplying by dt, separating variables and integrating between the initial conditions, X = 0 and T =T0, and later conditions X =X and T =T, yields
		Taking the antilog, we have
		solving for X yields
		Then
			(13-16)
		This form is the same as the equation relating X and T derived for flow reactors. Rearranging yields
Temperature conversion relationship for an adiabatic batch reactor			(13-17)