A 200.0-liter water tank can withstand pressures up to 20.0 bar absolute before rupturing. At a particular time the tank contains 165.0 kg of liquid water, the fill and exit valves are closed, and the absolute pressure in the vapor head space above the liquid (which may be assumed to contain only water vapor) is 3.0 bar. A plant technician turns on the tank heater, intending to raise the water temperature to 155°C, but is called away and forgets to return and shut off the heater. Let t₁ be the instant the heater is turned on and t₂ the moment before the tank ruptures. Use the steam tables for the following calculations. 

(a) Determine the water temperature, the liquid and head-space volumes (L), and the mass of water vapor in the head space (kg) at time t₁. 

(b) Determine the water temperature, the liquid and head-space volumes (L), and the mass of water vapor (g) that evaporates between t₁ and t₂. (Make use of the fact that the total mass of water in the tank and the total tank volume both remain constant between t₁ and t₂.) 

(c) Calculate the amount of heat (kJ) transferred to the tank contents between t₁ and t₂. Give two reasons why the actual heat input to the tank must have been greater than the calculated value. 

(d) List three different factors responsible for the increase in pressure resulting from the transfer of heat to the tank. (One has to do with the effect of temperature on the density of liquid water.) 

(e) List ways in which this accident could have been avoided. 

(f) One of the suggestions you may have made in Part (e) is to put a relief valve on the top of the tank. Suppose that one had been installed and that it was designed to open when the tank pressure reached 10 bar. The design calls for the opened valve to allow steam to escape into a pipe that vents it to the atmosphere. At what temperature would the valve open? At what rate would the relief valve need to release steam (kg/kJ of added heat) in order to keep the tank pressure from rising above 10 bar?