Problem 8 The smooth rigid-body cavity is filled with liquid 6061-T6 aluminum. When cooled it is 0.3 mm from the top of the cavity. If the top of the cavity is (a) covered (b) not covered and the temperature is increased by 110\deg C, determine the stress components \sigma _(x),\sigma _(y), and \sigma _(z) in the aluminum. Hint: Use the generalized Hooke's law with an additional strain term of \alpha \Delta T.