A steam trap is a device to purge steam condensate from a system without venting uncondensed steam. In one of the crudest trap types, the condensate collects and raises a float attached to a drain plug. When the float reaches a certain level, it "pulls the plug," opening the drain valve and allowing the liquid to discharge. The float then drops down to its original position and the valve closes, preventing uncondensed steam from escaping. a) Suppose saturated steam at 25 bar is used to heat 100 kg/min of an oil from 135C to 185C. Heat must be transferred to the oil at a rate of 1.00 \times 10^(4} \mathrm{kJ} / Imathrm{min} to accomplish this task. The steam condenses on the exterior of a bundle of tubes through which the oil is flowing. Condensate collects in the bottom of the exchanger and exits through a steam trap set to discharge when 1200 g of liquid is collected. How often does the trap discharge? b) Especially when periodic maintenance checks are not performed, steam traps often fail to close completely and so leak steam continuously. Suppose a process plant contains 1000 leaking traps (not an unrealistic supposition for some plants) operating at the condition of Part (a), and that on the average 10% additional steam must be fed to the condensers to compensate for the uncondensed steam venting through the leaks. Further suppose that the cost of generating the additional steam is $7.50 per million Btu, where the denominator refers to the enthalpy of the leaking steam relative to liquid water at 20C. Estimate the yearly cost of the leaks based on 24 h/day, 360 day/yr operation.