In a certain experiment, it is necessary to be able to move a small radioactive source at selected, extremely slow speeds. This is accomplished by fastening the source to one end of an aluminum rod and heating the central section of the rod in a controlled way. If the effective heated section of the rod is 3.1 cm long, at what constant rate must the temperature of the rod be changed if the source is to move at a constant speed of 26 nm/s?

Answer 1

the formula for thermal expansion is:

[Delta Length]/[initial Length]=k[delta T] so the 1st derivative with respect to time is:

d/dt (L/L0)= k d/dt(T) so
d/dt(T) = L/(L0 k) where k is the expansion coefficient of aluminum.

k = 22.2 m/m Kx10^-6