Maintaining pipe wall temperature. Maintaining a constant pipe wall temperature in some hot-process applications is critical. A technique that utilizes bolt-on trace elements to maintain temperature was presented in the Journal of Heat Transfer (November 2000). Without bolt-on trace elements, the pipe wall temperature of a switch condenser used to produce plastic has a uniform distribution ranging from 260° to 290°F. When several bolt-on trace elements are attached to the piping, the wall temperature is uniform from 278° to 285°F.

a. Ideally, the pipe wall temperature should range between 280° and 284°F. What is the probability that the temperature will fall in this ideal range when no bolt-on trace elements are used? When bolt-on trace elements are attached to the pipe?

b. When the temperature is 268°F or lower, the hot liquid plastic hardens (or plates), causing a buildup in the piping. What is the probability of plastic plating when no bolt-on trace elements are used? When bolt-on trace elements are attached to the pipe?