1- find the minimum (x ∗ ∗ ) ) of: ) = −x 3 + 3 4 x 4 a) using the golden search method. a. (20 points) assume = 0.5 and start from ) to bracket the minimum. b. (20 points) after the minimum is bracketed, manually perform 3 steps of the golden section search and report the values of ,), ), ), at each step.

Carbon dioxide gas expands isotherm a turbine from 1 mpa, 500 k at 200 kpa. assuming the ideal gas model and neglecting the kinetic and potential energies, determine the change in entropy, heat transfer and work for each kilogram of co2.

Air inially occupying a volume of 1 m2 at 100 kpa, 27 c undergoes three internally reversible processes in series. process 1-2 compression to 500 kpa during which pv constant process 2-3 adiabatic expanslon to 100 kpa process 3-1: constant-pressure expansion to 100 kpa (a) calculate the change of entropy for each of the three processes. (b) calculate the heat and work involved in each process. (c) is this cycle a power cycle or refrigeration cycle?

The sum of the normal stresses does not change as the stress state rotates through an angle. a)-trune b)- false