ChE 211, Adv. Chem. Eng. Thermodynamics 09/21/2015

BCME, San Jose State University Lilian Chang, Fall 2015

Homework 4 Due Date: Monday, 09/28/2015 1. Derivation of Raoults Law: a. Determine the relationship between the vapor pressure of a solvent on the concentration of a (not very volatile) dissolved substance. Consider the vapor and the solution to be ideal. Start from the equilibrium condition: i. ! , = !" ,,!" (Hint: This is Exercise 3.3 in your textbook. Go through the derivations as we did in class for other derivations.) b. Why is Raoults law not a good approximation? c. Determine the resulting change in temperature (increase in the boiling point). 2. An experimentalist determines that the heat capacity of a substance obey the empirical relation Cv (T, V) = T2v2, where is a constant. The experimentalist also discovers that the entropy and energy are zero at absolute zero, for all volumes. Compute the per-particle thermodynamic potentials: U(S, V), H(S, p), A(T, V), and G(T, p). Hint: Start with the definition of heat capacity. 3. Instead of using Legendre transformation on U = U (S, V, N) to A (T, V, N), start with S (U, V, N) and use analogous derivation to derive: a. The Legendre transform of S with respect to U, S[U] (T, V, n). b. Its differential dS[U]

Note: Legendre transforms of the entropy are important in statistical mechanics and are called Massieu functions / potentials.