If a cadmium rod doubles its length after heating, then what was the temperature change when the coefficient of linear expansion is 41 × 10^-6/K?

Answer 1

We want to know when the length of a rod (L) doubles due to thermal expansion.

Since the coefficient of expansion is 41 * 10^-6, then we know that the change in length for the rod is

L * deltaT * 41 * 10^-6/K.

In order for the rod to double in length, the rod must go from length L to length 2L so the change in length must be 2L - L = L.

Setting the two expressions for the change in length to be equal produces the following

L * deltaT * 41 * 10^-6 = L

We can solve the equation above for deltaT. Notice that we can divide through by L. That means that the original length does not matter. That's great because it was not given to us anyway.

deltaT * 41 * 10^-6 /K = 1 or

deltaT = 1/(41 * 10^-6/K) = 24390 K