Calculate Critical Temperature of Fluid with Helmholtz Energy

Question

Consider a fluid for which the Helmholtz energy is given by A = -RTln (v-b)-a/v + C, where R is the gas constant, T is the absolute temperature, v is the molar volume, a and b are compound-specific constants, and C is an arbitrary constant. For a certain fluid, the constant are a = 3.64L^2bar/mol^2 and b = 0.04267L/mol. The following is a plot of the Helmholtz energy at a temperature of 200K.

A. calculate the critical temperature of this fluid

B. From the plot, estimate the density of the coexisting phases at 200K.

C. At equilibrium, the pressure is equal between phases. How is this guaranteed by a tangent-line construction?

D. Give a general formula for the compressiblity factor from the equation given.

Summary

The question belongs to Chemical Engineering and it is about Helmholtz's energy of a fluid. The critical temperature of the fluid along with the plot estimate of the density have to be calculated at the given temperature. The solution has all the calculations for this problem.

Total Word Count 278