Problem 1: A 100 ft long pipe transporting steam through the PSU campus is made of AISI 316 stainless steel. The pipe is an 8"Schedule 40 pipe (note that 8" is the nominal dimension but you need to look up the actual dimensions of an 8" Schedule 40pipe!). The pipe transports steam through an open space of air at T,=20°C and a heat transfer coefficient of 10 W/m²K. The steady-state inside wall temperature of the steam pipe is at 140°C. Note that you can look up thermal conductivity and other thermophysical properties in Appendix A of the course textbook,or through other reputable sources. (a) Determine the rate of heat loss from the steam pipe if it DOES NOT have insulation. Ans: 25 kW (b) If we want to reduce the heat loss to 10% of its value from part (a), what thickness of calcium silicate pipe insulation should be added to the outside of the pipe? You can assume that the inside surface temperature of the steam pipe remains at 140°C, as well as the outside air conditions. You may need to use an iterative solver (such as Exceľ's Goal Seek, in Data->What If Analysis->Goal Seek; or perhaps Matlab,or even a guess-and-check method).