The mercury thermometer in Chap. 4 was considered to hav
Question and Solution
The mercury thermometer in Chap. 4 was considered to have all its resistance in the convective film surrounding the bulb
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The mercury thermometer in Chap. 4 was considered to have all its resistance in the convective film surrounding the bulb and all its capacitance in the mercury. A more detailed analysis would consider both the convective resistance surrounding the bulb and that between the bulb and the mercury. In addition, the capacitance of the glass bulb would be included. Let Ai inside area of bulb, for heat transfer to mercury A o outside area of bulb, for heat transfer from surrounding fl uid m mass of mercury in bulb mb mass of glass bulb C heat capacity of mercury Cb heat capacity of glass bulb hi convective coeffi cient between bulb and mercury h o convective coeffi cient between bulb and surrounding fl uid T temperature of mercury Tb temperature of glass bulb Tf temperature of surrounding fl uid Determine the transfer function between Tf and T. What is the effect of the bulb resistance and capacitance on the thermometer response? Note that the inclusion of the bulb results in a pair of interacting systems, which give an overall transfer function somewhat different from that of Eq. (6.24).
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