Question No. 1 A liquid Ni-Al alloy sphere is levitated with an induction coil in an excellent vacuum chamber at 500 C. Stirring of the droplet is intense so that the melt composition is uniform at any time. If the sphere has a radius of one cm and an initial Al mole fraction of 1%. Derive an expression which should describe the Al content of the droplet at any time. Identify any properties or parameters required State your assumptions If the vacuum were poor, a smoke(or fog) would be observed around the droplet. Explain the mechanism of smoke(or fog) formation Is the rate of Al loss higher in the excellent vacuum or upon the formation of smoke? Why Question No. 2 Discuss the use of statistical mechanics for the calculation of thermodynamic properties such as entropy, internal energy, and free energy. Illustrate your answer by reference to a simple diatomic cule Question No. 3 (a)(i) Demonstrate that the variation of the chemical potential of a component in a mixture with applied pressure at constant temperature is given by the partial molar volume of the component in the mixture le (ii) Convert the preceding expression to find an expression for aIn ai aP Where ar is the activity of component I with respect to pure 1 (b)For a particular binary system (many alloy systems exhibit this behavior) "retrograde solubility"is established as shown in the accompanying sketch. Note that the solubility of in a is a minimum at Tr, the "retrograde temperature". Sketch Gibbs energy-composition curves for the binary system at Tr and slightly below Tr. Can you draw any conclusions about the relative stability of 8 at lower temperaturesQuestion No. 1 A liquid Ni-Al alloy sphere is levitated with an induction coil in an excellent vacuum chamber at 1500 C. Stirring of the droplet is intense so that the melt composition is uniform at any time. If the sphere has a radius of one cm and an initial Al mole fraction of 1%. Derive an expression which should describe the Al content of the droplet at any time. Identify any properties or parameters required. State your assumptions. If the vacuum were poor, a smoke (or fog) would be observed around the droplet. Explain the mechanism of smoke (or fog) formation. Is the rate of Al loss higher in the excellent vacuum or upon the formation of smoke? Why? Question No. 2 Discuss the use of statistical mechanics for the calculation of thermodynamic properties such as entropy, internal energy, and free energy. Illustrate your answer by reference to a simple diatomic molecule. Question No. 3 (a) (i) Demonstrate that the variation of the chemical potential of a component in a mixture with applied pressure at constant temperature is given by the partial molar volume of the component in the mixture.1.e. 1 1 VT P u ⎟ = ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ (ii) Convert the preceding expression to find an expression for: T P a ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ ln 1 Where a1 is the activity of component 1 with respect to pure 1. (b) For a particular binary system (many alloy systems exhibit this behavior) “retrograde solubility” is established as shown in the accompanying sketch. Note that the solubility ofε in α is a minimum at Tr, the “retrograde temperature”. Sketch Gibbs energy-composition curves for the binary system at Tr and slightly below Tr. Can you draw any conclusions about the relative stability of ε at lower temperatures?