A stream of propane at an average temperature T = 566°R and absolute pressure P = 6.8 atm flows from a hydrocarbon processing plant to a nearby customer’s production facility. A technician at the processing plant periodically measures the volumetric flow rate of the stream, V̂(ft3 /h), and reports the value to the billing office. The customer is charged for the propane at a rate 

where S($/lb_m) is the unit cost of propane. 

(a) Derive the given formula, assuming ideal-gas behavior. 

(b) One day a recent chemical engineering graduate working at the processing plant comes across the formula used to calculate the charge for the propane stream. She figures out the basis of the formula and uses the generalized compressibility chart to derive an improved formula. What is her result? Calculate the percentage by which the plant was overcharging or undercharging the customer (state which) when it used the old formula.

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SPV C($/h) = 60.4 T