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.

Problem #1:

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.

Problem #2:

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.

Problem #3:

Calculate how long it will take for the temperature in Problem #2 to reach 95% of the way

to its final value.

Problem #4:

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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