A company is considering building a continuous sterilisation unit for the sterilisation of medium. In the...

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A company is considering building a continuous sterilisation unit for the sterilisation of medium. In the continuous sterilisation unit the medium is heated up rapidly to a high temperature of 140°C by the injection of steam and then held at this temperature as the hot medium flows through the holding section; the sterile medium is then rapidly cooled over an expansion valve and flash tank. The holding section is essentially a long insulated pipe through which the medium flows. The company wants to sterilise medium at a rate of 1 L/min, using pipe with an internal cross sectional area of 1 cm². The company expects there to be less than a chance of 1 in a million (106) that there are still some of the original bacteria left in the medium when the medium leaves the continuous steriliser unit. It has been shown that the sterilisation process can be described by the equation: dN dt = -KN In which N is the number of bacterial cells. k = 15 min-¹. Calculate how long the pipe in the holding section has to be. A company is considering building a continuous sterilisation unit for the sterilisation of medium. In the continuous sterilisation unit the medium is heated up rapidly to a high temperature of 140°C by the injection of steam and then held at this temperature as the hot medium flows through the holding section; the sterile medium is then rapidly cooled over an expansion valve and flash tank. The holding section is essentially a long insulated pipe through which the medium flows. The company wants to sterilise medium at a rate of 1 L/min, using pipe with an internal cross sectional area of 1 cm². The company expects there to be less than a chance of 1 in a million (106) that there are still some of the original bacteria left in the medium when the medium leaves the continuous steriliser unit. It has been shown that the sterilisation process can be described by the equation: dN dt = -KN In which N is the number of bacterial cells. k = 15 min-¹. Calculate how long the pipe in the holding section has to be.

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The given differential equation dNdt kN describes a firstorder exponential decay process where N is ... View the full answer