Question

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.