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*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.

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Right. If you have a loose fit at room temperature you can afford differential expansion without getting stuck at higher temperatures. You are on the right track.

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Provided that the gap is fairly small, it could be filled with a lubricant such as oil, which is gradually squeezed out as the temperature increases and the gap decreases.

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