Consider 1 mole of real gas satisfying vdws equation of

Question

Question 1: Using the Dieterici equation of state.

P = (RT/v-b)e^-a/RTv

Show that   

v_C = 2b, T_C = (a/4Rb), P_C = (a/4e²b²),

and find the numerical value of RT_C/P_Cv_C. How does this compare with the tabulated experiment values?

Question 2: (a) Making the use of the cyclical relation, find the expansivity ß of a substance obeying the Dieterici equation of state?

(b) At higher temperatures and large specific volumes (low densities) all gases approximate an ideal gas. Show that for large values of T and v, the expression for ß obtained in (a) goes over to the corresponding equation for an ideal gas.

Question 3: A hypothetical substance has volumetric thermal expansion coefficient ß = bT/v and compressibility Κ = a/(Pv). Find a formula for its equation of state.

Question 4: Rewrite V-d-W's equation as a cubic polynomial with respect to v and show it has only root at v_{c can}. Hint, factor it into an equation of the form P(v-v_c)³

Question 5: Consider 1 mole of real gas satisfying VdW's equation of state. Assume the gas undergoes an isothermal expansion at T_o, From V_i to V_f. What is the configuration work done by the gas?

Question 6: Suppose a photoacoustic system heats by 1mK. Compute the pressure jump induced, assuming stress confinement (isochoric) and soft tissue values for thermal expansion coefficient   ß = 3.6 x 10^-4 1/k and compressibility Κ = 4.4 x 10^-10 1/Pa.