Engineering Homework Help

Problem 1 (6 points total): An ingot of Al-5 wt.% Cu is directionally solidified. Assume that there is no diffusion in the solid and that there is perfect mixing in the liquid. Pure aluminum melts at 660 °C. At the eutectic temperature of 548 °C, the liquid composition is 33.2 wt.% Cu and the solid composition is 5.35 wt.% Cu. Assume that the liquidus and solidus are straight lines. Please do the following.

1. Calculate the composition of the liquid when the solidification is 40% complete.

2. What is the average composition of the solid, Csav., at this point when the solidification is 40% complete.

3. What is the solid-liquid interface temperature at this point when the solidification is 40% complete?

4. How much eutectic will be formed when the solidification is complete?

——

Problem 2 (3 points total): The solubility of carbon in y-Fe is given as C -1.165 exp(-/RT), where the value of Q is 121,168 J/mol, C is the atomic fraction of carbon, and R is gas constant. Please use this equation to predict the solubility limit of carbon at 800°C. Please express your answer as wt%.

Problem 3 (3 points total): During the solidification of nickel, please calculate the critical radius r* of nucleus if the nucleation of solid phase is homogeneous for the undercooling of 0.1K and 10K respectively. The value for the latent heat of fusion is 293 kJ/kg and yLS = 0.255 J/m?. The melting temperature of nickel is 1455°C.

Problem 4 (3 points total): You are given an alloy of copper containing 10% Zn, 2% Al, and 3% Sn. Please calculate the electron-to-atom ratio.