1. in an oil refinery, a furnace is used to continuously preheat crude oil for a fractionator. the feed to the furnace exhibits larges fluctuations in its flow rate F[kg/min] and temperature Ti [C]. despite, we wish to maintain the temperature of the output crude oil, T[C], at a set point Tsp=390[C] via a feedback control system. a linear, direct-acting temperature sensor/transmitter (TT) measures T and transmits it to the temperature controller (TC) as an electrical signal T~[mA]. the range of the temperature sensor is 200C500C. the temperature controller (TC) is a P-controller. the controller then outputs an electrical signal p~[mA] to a linear, direct-acting current-to-pressure transducer (I/P). finally, this transducer outputs a pneumatic signal p [psig] to a linear, air-to-open control valve that manipulates the flow rate of fuel to the furnace. electric and pneumatic signals obey industrial standard ranges of 4-20 mA and 3-15 psig. (a) (2 points) calculate the internal set point, Tsp[mA]. (b) (2 points) at steady-state conditions, we experimentally observe that T=Tsp when the pneumatic signal to the control valve p=10 psig. calculate the bias p~[mA] of the TC. (c) (4 points) we wish for the control valve to be fully open when T=320C(