Question

Suppose we have a metal bar of length L0 metres at temperature T0 in degrees Celsius.When the bar is heated or cooled, the length of the bar changes. The amount that the length changes is proportional to the product of the temperature change and the original length of the bar L0. Let á be the proportionality constant of this change where the units for á is measured in m/m◦C (metres per metres degree Celsius). Find an expression for the length L of the metal bar as a function of the temperature T.Draw a sketch of the graph of this function, labelling the point where T = 0."

I am having trouble coming up with the equation. How can I turn the proportionality equation described above to one with L as a function of T?

Answer 1

dL = a Lo dT
L = a Lo T + constant
when T = 0, L = Lo
so
L = (a Lo) T + Lo

To is y (or in this case L)axis intercept
(a Lo) is slope

Answer 2

Thanks for your help. I see the question much clearly now.