4.5 A system obeys the fundamental thermodynamic relation U = U(S,V,n) = Kn5/3 (V — nb)−2/32S/3n R - n²a V where K is a constant. Find expressions for P, T, and μ. Show that the system obeys the van der Waals equation of state.
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- 5) Starting from the expression Cp – G, = T (P/ər), (V/ar). ' use the appropriate relations between partial derivatives to show that T(V/ar), Cp – Cy =(3A) Calculate the Gibbs free energy of mixing for 50.0 g water and 50.0 g ethanol at constant 298 K and1.00 bar. What is it about your answer that tells vou that this mixing is spontaneous?AmixG = NRT (x1 In x1 + x2 In x2)Derive the following thermodynamic equation of state. ne = -P + T av Apply the equation to the following. (a) an ideal gas (b) a van der Waals gas Comment on your results. Step 1 of 7 Derive the following thermodynamic equation of state. (), au = -P + T IT av aT V Differentiate the equation dU = –PdV + TdS with respect to V while keeping T constant to obtain an () as expression for Use the following as necessary: P, S, T, V, and ASV¡ to represent av IT av au nRT av V -P+T·ASVT Step 2 of 7 (), and (), (ux Identify the relationship between Use the following as necessary: P, S, T, V, and APTV to represent as
- ) Use the Maxwell relations to express the derivatives (35) and (35) in terms T as P of measurable quantities Cp, a, K, among others.2. Give handwritten answer4. (1) Write the mathematics expression of Gibbs rules. (2) Using the Gibbs rule to discuss of the freedom F of one component system. (3) Draw and discuss the P-T phase diagram of water system.
- Derive the following thermodynamic equation of state. au = -P + T av Apply the equation to the following. (a) an ideal gas (b) a van der Waals gas Comment on your results. Step 1 of 7 Derive the following thermodynamic equation of state. au = -P + T du Differentiate the equation dU = –PdV + TdS with respect to V while keeping T constant to obtain an expression for Use the following as necessary: P, S, T, V, and av as ASVī to represent nRT = V -P+T·ASVT Step 2 of 7 as Identify the relationship between and Use the following as necessary: P, S, T, V, and APTy to represent as1. Calculate the value of Cp at 298 K and 1 atm pressure predicted for CH4(g) and C2H4(g) by the classical equipartition theorem. Compare the predicted results with the experimental results and calculate the percent of the measured value that arises from vibrational motions. Repeat the calculations at 800 K and 1 atm using the relation below: J T T? T³ Cp, m molk =A(1)+A(2),+A(3)+A(4) K³ 3 mol.K K K?22-8. Determine C, - C, for a gas that obeys the equation of state P(V – b) = RT.
- The differential for the Gibbs function, G, at constant composition is: ?G = −S?T + Vdp Using the criterion for exact differentials, write the Maxwell relation that is derived from this equation.Physical Chemistry, image provided of full question:Derivation Derive the following thermodynamic equation of state. au = -P + T avT Apply the equation to the following. (a) an ideal gas (b) a van der Waals gas Comment on your results. Step 1 of 7 Derive the following thermodynamic equation of state. du = -P + av () as Differentiate the equation dU = -PdV + TdS with respect to V while keeping T constant to obtain an expression for av Use the following as necessary: P, S, T, V, and ASV7 to represent nRT (), - du av V -P+T·ASVT Step 2 of 7 dP Use the following as necessary: P, S, T, V, and APTV to represent ) Identify the relationship between and av. as -S+ΤΔΡΤV