Chapter 16, Problem 16.18Q

3. Differentiate f(x) = x² sin(x). 4. Evaluate the limit: lim x 0 sin(2x) X

Differentiate between an ideal and a regular solution consisting of a mixture of A andB atoms. Which of these solutions, is likely to contain a random mixture of atomsat all temperatures? For the binary A-B ideal-solution, differentiate the equationfor the configurational entropy of mixing with respect to concentration. Hence showthat the slope of the free energy of mixing versus concentration curve is towards±infinity when the mole fraction is 0 or 1. Does this make it easy or hard to purifymaterials?

Question During the solidification of a binary alloy, with a positive temperature gradient in the melt, a planar solid-liquid interface is moving at the steady state, Fig. Q1(i). The variation of the solute concentration, C, in the melt ahead of the interface is given by, b) If m is the liquidus gradient, or the slope of liquidus, Fig.Q1 (iv), how does the equilibrium temperature, T, vary with the melt composition C? T₁ = C=C1+ exp R.x D (equation 1.1) T L Solid Melt (iv) T₁ S S+L where Co is the nominal solute concentration in the alloy, Ko is the equilibrium distribution coefficient, R is the solid-liquid interface moving rate, D is the solute diffusivity in the melt and x is distance into the liquid phase, Fig. Q1(ii). Answer the questions in the steps below, to show that the level of constitutional supercooling is governed by both the actual temperature, T, and the composition, C, in the solidification front. a) Consider a point in the melt at a distance x away from the solid/melt…

Practise question of phase transformations topic that I need help on thank you.

Practise question:

Barium titanate can exist in both the cubic and tetragonal crystal structures. Explain why the tetragonal form exhibits piezoelectricity whereas its cubic form does not. The transformation from cubic to tetragonal BaTiO3 occurs when the former is cooled below the Curie temperature of 120 ◦C. Describe how the change can be verified experimentally based on measurements made at ambient temperature.

Calleb Sandl Soda ash 5% crushing Recycling melting furnace C float bath 600 annealing Mixing Sec Packing cutting Lime Salt Care Dolomite Powder Coal Glass plant has the follownig manufacturing process in figure is the glass where the produced glass contain the following composition: SiO2 72.5%, CaO 12.3% Na20 14.0%, Fe203 0.8%, MgO 0.4% and the production capacity of the plant is 32000 ton /year and the melting furnace consist the following reaction equations: Na CO,+ aSiO, NagO aSiO + CO₂ (1) CaCOy + b$iO, → CaO - bsiO, + CO, (2) Na,SO, + cSiO2 + C-Nago cSiO, + SO₂ + CO (3) The last reaction may take place as in equations (4) or (5), and (6): Na₂SO, C Na₂SO3 + CO 2Na2SO4 + C Na,SO+cSiO, 2Na₂SO3 + CO2 - Na₂O eSiO2 + SO2 (5) (6) The ratios Na₂O/SiO, and CaO/SiO, are not molar ratios. The ratio may be of the type Na O/1.8SiO,, for example. In an ordinary window glass the molar ratios are approximately 1.5 mol Nago, I mol CaO, and 5 mol SiO,. Other glasses vary widely (Table 11.2).…

1-A counterflow, concentric tube heat exchanger is used to cool the lubricating oil for a large industrial gas turbine engine. The flow rate of cooling water through the inner tube (Di = 25 mm) is 0.2 kg/s, while the flow rate of oil through the outer annulus (Do = 45 mm) is 0.1 kg/s. The oil and water enter at temperatures of 100 and 30 C, respectively. The exit temperature of hot fluid and cold fluid is 60 and 40 C. calculate the LMTD. Calculate the surface area of the heat exchanger. How long must the tube? Properties: unused engine oil: cp = 2131 J/kg K, μ=3.25 ×10^-2 N.s/m^2, k = 0.138 W/m.K, 4178 J/kg .K, u= 725×10^-6 N.s/m2, k = 0.625 W/m.K, Pr = 4.85 water: cp neer in which steam is condens

please... please. , how can I use the boundary conditions for this question (two fixed pates and the distance between plates is h).