Solid mechanics thermal stress of infinite cylinder

[Taexzyn]

Homework Statement

My problem is to calculate the Thermal stress of a Cylindric shell with inner radius a and outer radius b the inner surface is experiencing Temperature T1 and the outer surface is experiencing T2 with T1>T2 assuming that the linear thermal expansion coefficient is a, the Young modulus E and that the heat gradient within the shell is linear how to obtain the thermal stress (S) induced by these conditions?

Homework Equations

Thermal stress as given by most sources I could find, no equation given in the problem
S=Ea (T1-T2)

The Attempt at a Solution

I attempted to solve the problem with the equation above however I am hesitant to if it is right or not

 

[nvn]

Taexzyn: The final answer is listed in some textbooks, usually without showing the derivation. Most people just copy the final answer out of a textbook, without knowing how it was derived. I would say, almost no one knows how to derive it. Do you just need to copy the final answer out of a textbook? Or do you need to also copy a derivation out of a textbook? Or instead, do you need to be able to derive it yourself, from only fundamental principles already in your own mind?

I briefly tried to derive it myself, and currently got stuck.