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.

Amass of 1.5 kg of air at 120 kpa and 24°c is contained in a gas-tight, frictionless piston-cylinder device. the air is now compressed to a final pressure of 720 kpa. during the process, heat is transferred from the air such that the temperature inside the cylinder remains constant. calculate the boundary work input during this process.

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20°c. air approaches the tube bank in the normal direction at 0°c and 1 atm with a mean velocity of 4 m/s. the tubes are arranged in-line with longitudinal and transverse pitches of sl- st 1.5 cm. there are 30 rows in the flow direction with 15 tubes in each row. determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. evaluate the air properties at an assumed mean temperature of -5°c and 1 atm. is this a good assumption?

Plan an experiment to measure the surface tension of a liquid similar to water. if necessary, review the ncfmf video surface tension for ideas. which method would be most suitable for use in an undergraduate laboratory? what experimental precision could be expected?