Problem
a) In the design of a chemical process, the specifications are such that the density and temperature are known for a fluid going through a throttling (expansion) valve. Determine an expression in terms of (T, P, V, Cp, Cv, α, KT) to calculate the density of the fluid after the expansion given that the temperature is known.
b) Estimate the density change for this fluid upon expansion. This fluid has a density of 7220 mol/m3 and is at 410 K. The temperature of the fluid after the expansion is 290 K. For this fluid, the average value of a between 290 and 410 K is 4.31 x 10-3 K-1. The value of KT is 3.49 x 104 bar-1 at 290 K and 3.71x10-2 bar-1 at 410 K. The value of Cv is 79 J/mol.K at 290 K and 109 J/mol.K at 410 K.