# How to calculate the minimum diameter of a steel cylinder for allowing it operate with brass pistons?

*As a new mechanical engineer for Engines Inc., you have been assigned to design brass pistons to slide inside steel cylinders. The engines in which these pistons will be used will operate between $$20.0ºC$$ and $$150.0ºC$$. Assume that the coefﬁcients of expansion are constant over this temperature range. (a) If the piston just ﬁts inside the chamber at $$20.0ºC$$, will the engines be able to run at higher temperatures? Explain.

(b) If the cylindrical pistons are $$25.0 \text{cm}$$ in diameter at $$20.0ºC$$, what should be the minimum diameter of the cylinders at that temperature so the pistons will operate at $$150.0ºC$$?*

For the first part I have answered: Pistons will get stuck because they are made of brass, and this material has a greater thermal expansion coefficient:

$$\alpha_{\text{brass}}= 2.0 \cdot 10^{-5} ºC^{-1}> \alpha_{\text{steel}}=1.2\cdot 10^{-5}ºC^{-1}$$

BUT, the second part -b)-, I have not been able to understand it.

If I know that that they have different thermal expansion coefficients, and the brass pistons will expand greater than the steel cylinders, how it can be possible that they can operate at higher temperatures -like $$150º\text{C}$$?

Initially, I think that the cylinders diameter should be slightly greater than the pistons diameter.