Compare the magnitude of the amount of energy required to perform various operations in a plant environment. For this problem consider 1 m³ of water. When reporting the answers to this question, report in base or derived SI units using scientific notation. (e.g. report 13 MJ as 1.3 x 107 J) (a) What is the mass of 1 m³ of water [kg], and how many g-moles? (b) Kinetic Energy: It is common to transfer water from one part of a plant to another in a pipeline. A typical design velocity in a water pipeline is 2 m/s. How much energy does it take to accelerate 1 m³ to 2 m/s? (c) Potential energy: A cooling tower is 17 m high. How much energy does it take to raise 1 m³ of water by 17 m? (d) If the pump in part (c) is 75% efficient, how much (electrical) energy was put into the pump? If the inefficiencies all go to raise the temperature of the water, how much did the temperature of the water rise? (e) Work: How much (PV) work is required to raise the pressure of 1 m³ of water by 1000 kPa? (f) Internal Energy from heat: How much (thermal) energy is removed to cool 1 m³ of water by 20°C? (Use the steam tables, or indicate a source for the specific heat of water) (g) How much (thermal) energy is does it take to vapourize 1 m³ of liquid water at P = 1 atm, T= 100°C to saturated steam at P=1 atm (h) Compare the energy required to accomplish steps (b) through (g). Why do we focus on internal energy (and, for flowing systems, enthalpy) when we are doing our energy balances?