Problem #1: The first steam-driven 'heat engines' were single-cycle steam pipes used to lift water from the bottom of mine shafts. To operate the device, a long pipe closed at one end was filled with saturated steam at atmospheric pressure. Then the open end of the pipe was submerged in the liquid water at the bottom of the mine shaft. The steam inside the pipe would cool, reducing the pressure and drawing liquid water into the pipe. When thermal equilibrium was reached between the steam and surroundings, the liquid water raised in the pipe was removed. Closed End D Final State 2 TI Initial State! Sat. Vapor L Liquid Water Surface Open End Assume that the atmospheric conditions in the mine are Tg = 50 °F and 14.696 pisa. The steam lift pipe has dimensions of length L = 40 ft and diameter D=2 ft. The pipe is initially filled with saturated steam at atmospheric pressure. The steam cools, lifting the liquid water to height 'h' at which point the steam reaches thermal equilibrium with the surroundings. For this process determine:a) the final pressure of the condensed steam (psia),b) the rise 'h' of liquid water in the lift pipe (ft),c) the amount of heat transferred from the condensed steam in the cooling process (Btu),d) the entropy generation that occurs in the cooling process (Btu/R). If liquid water from the mine is boiled to produce the steam that initially fills the lift pipe, e) how much heat is required (Btu)? If there is a difference between the values for parts c) and e), explain the reason for the difference.