Homework Help: Mathematical Model of Thermometer

1. Nov 5, 2008

Mehta29

1. The problem statement, all variables and given/known data

Find height of Hg column in a thermometer as a function of temperature and time

2. Relevant equations

Supposed to derive my own in this case...using the engineering methodology with conservation and accounting equations.

Total Energy in + Total Energy Out + Work done on the system + Heat = Change in energy of the system

3. The attempt at a solution

I have made the following assumptions
-Closed system - No reactions occur -No work done on the system -No mass transfer - Thermometer is cylindrical
-Dynamic - Heat transfer is uniform - Thermometer stem is adiabatic (given) - No change in KE or PE - Temperatures of System and the surroundings are uniform

The problem is due tomorrow morning so I have been thinking that there would be a first order differential equation involved but not exactly sure where to start (seeing as that is the problem statement to derive said equation)

Thanks for any ideas on where to go with this...

Last edited: Nov 5, 2008