Question
need #1
A certain gas obeys the van der Waals equation of state. Show that for just one critical state specified by a critical temperature T_c and critical volume V_c that both (partial differential P/partial differential V)_r = 0 and (partial differential^2 P/partial differential V^2)_T = 0 Write the equation of state giving p = P/P_c in terms of t = T/T_c and v = V/V_c. Make plots of p as a function of v for t = 1/2, t = 1, and t = 2. Derive an expression for the isothermal compressibility, of an van der Waals gas in the reduced units. Make plots of p as a function of v for t = 1/2, t = 1, and t = 2. Derive an expression for the isothermal compressibility, k_p of a van der Waals gas in the reduced units. Make plots of k_T vs. v at t = 1/2, t = 1, and t = 2.
Explanation / Answer
the critical isotherm on a p-V diagram has a point of inflection where dP/dV= 0 as well as d2P/dV2= 0 ( this is shown in the diagram)
