Use the Maxwell relations to express the following derivatives in terms of the expansion coefficient a,...
Section IV 1 (av vap 1 and isothermal compressibility KT use the 1. Knowing expansion coefficient a T Maxwell relations to justify the following equations: (a) The Joule coefficient is Ay Justify t,Cy p-aT/Kr. T (b) Justify the thermodynamic equation of state tr -p. av ан Justify Hr=-T T +V (c) The isothermal Joule-Thomson coefficient is ur
Calculate the isothermal compressibility and the expansion coefficient of a perfect gas and a van der Waals ga:s (ii) Show, using Euler's chain relation, that KTR α(Vin-b) (iii) Make use of the definitions of the coefficient of thermal expansion, α, and 1. (i) (15) the isothermal compressibility, KT, and start from the expression for the total differential dV in terms of T and P to show that: OT
Let S = V-1 (V/T)S be the isoentropic coefficient of thermal expansion. Use a Maxwell relation and the expansion, chain and inversion relationships to show that S = - CV/VT
Problem I (40 pts): Simplify and evaluate the following thermodynamic quantities for an ideal gas (assuming n-1.0 mole, T-300 K, and P-0.1 MPa). a) (10 pts) The Joule-Thompson coefficient (1) ar ОР V(Tap-1) H b) (10 pts) The isobaric thermal expansion coefficient (AP) c) (10 pts) The isothermal compressibility (KT) d) (10 pts) The heat capacity at constant pressure (C)
(Thermodynamics, Maxwell relations. Mathematics) 3 Consider the microcanonical formula for the equilibrium energy E(S, V,N) of some general system.58 One knows that the second deriva- tives of E are symmetric; at fixed N, we get the same answer whichever order we take partial derivatives with respect to S and V (a) Use this to show the Marwell relation (3.70) OS S,N (This should take two lines of calculus or less.) Generate two other similar formulae by taking other second partial...
The adiabatic thermal expansion coefficient is defined by the relation αs=Cv/T(dV/dT)s. (a) Evaluate αs in terms of α(expansivity), β(compressibility), Cv, T, and V. (b) Show that αs=-Cv/nRT for an ideal gas.
The correct answer does not depend on K or V.
- Part A - The dependence of U on V Given the relationship (%), =T(E), -P, use the cyclic rule to write (@uſav), in terms of the measurable quantities P, B, T, and K. Recall that B and k are the isobaric volumetric thermal expansion coefficient and the isothermal compressibility, respectively, defined by B= + () and k=-* (*) Express your answer in terms of P,B, T, and K. ►...
Express the following in terms of a series expansion. sin(x) cos(x) tan(x); use only (i) and (ii) to evaluate tan(x). (2+x)1/2 for 0 < x <0.01 exp(2*x) log(x) for 0<x<0.01
Find the following derivatives. Express your answer in terms of the independent variables. 2x-2z ws and w, where wy+2z , X= s + t, y = st, and z s -t (Type an expression using s and t as the variables.)
Part A Explain why chemists conducting quantitative work using liquid solutions prefer to express concentration in terms of molality rather than molarity. Match the items in the left column to the appropriate blanks in the sentences on the right. Reset Help less is independent of The molality of a solution is the preferred unit because it P and T. is a conserved quantity, independent of temperature and pressure. , however, changes as T or P are varied because the thermal...