To ensure a tight fit, cylindrical metal elements are sometimes made the same size than the holes they will be placed into, and are cooled significantly just before being inserted into them. Suppose that on the UNLV Zebra z-pinch, at 20 degrees Celsius, a cylindrical aluminum alloy cathode of diameter 7 cm needs to be cooled to fit into a hole in a holder. Suppose that the cathode needs to made 68 microns smaller, in order to be inserted. To what temperature (in degrees Celsius) must the aluminum alloy cathode be cooled? The expansion coefficient of the aluminum alloy is 2.4E-5.

Question

anonymous · Answer

There is an equation for thermal expansion$$\Delta l=\alpha  l _{i} \Delta T$$However I am debating how this would change for a diameter. I don't think it would, but I will get back to you if I change my mind lol. Alpha is the coefficient of thermal expansion by the way.

anonymous · Answer

It's been a couple of years since I took mechanics of materials so excuse me for being sort of rusty.