Question

In a certain experiment, a small radioactive source must move at selected, extremely slow speeds. This motion 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 in the figure has length d = 3.80 cm, at what constant rate must the temperature of the rod be changed if the source is to move at a constant speed of 72 nm/s? The linear expansion coefficient of aluminum is 23 x 10-6 1/Cº. Radioactive Electric heater source Clamp

Answer 1

Here the effective length that is changing is d = 3.8 cm

Now, we know from linear expansion that:

L = aL AT

Now, differentiating above equation wrt time:

Substituting values:

72 * 10-9. 23 ж 10-63.8 * 10-2 * д1 at

дт 7.2 = 23 * 3.8 * at

The temperature of the rod should be changed at a rate of 0.08 celsius per second