Acylinder with a piston contains 0.200 mol of oxygen at 2.00×105 pa and 360 k . the oxygen may be treated as an ideal gas. the gas first expands isobarically to twice its original volume. it is then compressed isothermally back to its original volume, and finally it is cooled isochorically to its original pressure. part afind the work done by the gas during the initial expansion. w initial = jpart bfind the heat added to the gas during the initial expansion. q initial = jpart cfind internal-energy change of the gas during the initial expansion.δu initial = jpart dfind the work done during the final cooling; w final = j

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)