The mercury thermometer in Chap. 5 was considered to have all its resistance in the convective film.

The mercury thermometer in Chap. 5
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 mercury. In addition, the capacitance of the glass bulb would be
included. Let

Ai = inside ama of
bulb, for heat transfer to mercury

A0 = outside ama of
bulb, for heat transfer from surrounding fluid

m = mass of
mercury in bulb

rnb = mass of glass bulb

C = heat capacity of mercury

Cb = heat
The mercury thermometer in Chap. 5
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 mercury. In addition, the capacitance of the glass bulb would be
included. Let

Ai = inside ama of
bulb, for heat transfer to mercury

A0 = outside ama of
bulb, for heat transfer from surrounding fluid

m = mass of
mercury in bulb

rnb = mass of glass bulb

C = heat capacity of mercury

Cb = heat capacity of glass bulb

hi = convective coefficient between bulb
and mercury

h, = convective coefficient between bulb
and surrounding fluid

T = temperature of mercury

Tb = temperature of
glass bulb

Tf = temperature of
surrounding fluid 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. (7.24).

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