A $200-$ft$-$long section of a steam pipe whose outer diameter is $4$ in$.$ passes through an open space at $50$F$.$ The average temperature of the outer surface of the pipe is measured to be $280$F$,$ and the average heat transfer coefficient on that surface is determined to be $6$Btu$/$h$$ft$2$F$.$ a$)$ Determine the rate of heat loss from the steam pipe. b$)$ Determine the annual cost of this energy loss if steam is generated in a natural gas furnace having an efficiency of $86\%$ and the price of natural gas is $$1/$therm $(1$therm$=100,000$Btu$).$