You are working in a group to determine how well a proposed water temperature
measurement will work. Answer the following questions relating to this situation.
Calculate the time constant, t, for a mercury thermometer to be used to measure the
temperature of water. Assume that the surface area of the bulb is 1 x 10-4 m², the mass of
mercury in the bulb is 1×10-3 kg, the specific heat of mercury is 139 J kg-1 K-1, and the
coefficient of convective heat transfer is 750 W m 2 K-1. Note that 1 W = 1 J/s.
For one test, the initial temperature of the thermometer is 20 deg C. At time t=0, you place
the thermometer into boiling water (100 deg C). Using the 1st order model we discussed in
class and the value for the time constant from Problem #1, plot the expected change in the
thermometer temperature reading as a function of time. Use Matlab (or similar software) to
plot your results and label the axes.
Calculate how long it will take for the temperature in Problem #2 to reach 95% of the way
to its final value.
A colleague working on the project wants to adapt this work for measuring the temperature
of hot gases (instead of water). Assume that the coefficient of convective heat transfer in this
case is 10 W m-2 K-1. Calculate the time constant in this case. How does this value compare
with that of water?
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