You are to design a small, directional control rocket to operate in space by providing as many as 100 bursts of 5 seconds each with a mass flow rate of 0.5 lbm/s at a velocity of 400 ft/s. Storage tanks that will contain up to 3000 psia are available, and the tanks will be located in an environment whose temperature is $40^\circ F.$ Your design criterion is to minimize the volume of the storage tank. Should you use a compressed-air or an R-134a system?

Find out how the specific heats of gases, liquids, and solids are determined in national laboratories. Describe the experimental apparatus and the procedures used.

In an article on tire maintenance, it is stated that tires lose air over time, and pressure losses as high as 90 kPa (13 psi) per year are measured. The article recommends checking tire pressure at least once a month to avoid low tire pressure that hurts fuel efficiency and causes uneven thread wear on tires. Taking the beginning tire pressure to be 220 kPa (gage) and the atmospheric pressure to be 100 kPa, determine the fraction of air that can be lost from a tire per year.

An electrical-generation utility sometimes pumps liquid water into an elevated reservoir during periods of low electrical consumption. This water is used to generate electricity during periods when the demand for electricity exceeds the utility’s ability to produce electricity. Discuss this energy-storage scheme from a conversion efficiency perspective as compared to storing a compressed phase- changing substance.

A solid normally absorbs heat as it melts, but there is a known exception at temperatures close to absolute zero. Find out which solid it is, and give a physical explanation for it.

Let S be the standard basis for R3, and let B = {v1, v2, v3) be the basis in which v1 = (1, 2, 1), v2 = (2, 5, 0) , and v3 = (3, 3, 8). (a) Find the transition matrix PB→s by inspection. (b) Find the transition matrix PS→B. (c) Confirm that PB→S and PS→B are inverses of one another. (d) Let w = (5, -3, 1). Find [w]B and then compute [w]S. (e) Let w = (3, -5, 0). Find [w]s and compute [w]B.