110年 - 110 國立清華大學碩士班考試入學試題_工程與系統科學系/甲組:材料熱力學#105330

Question 1

(a) The phase diagrams of two alloys (alloy 1 and alloy 2) are illustrated below. In which of the two alloys is there an energetic tendency for the A and B atoms to attract to each other? Briefly explain your answer.

(b) Schematically draw the free energy curves vs concentration for the A-B alloy at temperatures T₁ and T₂ for alloy 1, and Ts for alloy 2, and briefly explain how the phase diagrams are constructed from the free energy curves. Make sure to clearly label all the curves.

(a) Determine the maximum allowed partial pressure of water vapor in wet hydrogen (H₂ + H₂O) at 1 atm in which manganese (Mn) can be heated without oxidation occurring at 1100℃

(b) Is the oxidation of Mn by water vapor exothermic or endothermic? Justify your
answer with data.
There is an Ellingham diagram on the next page for you to check the answer.
Data:

(a) Derive an expression for the change in temperature, AT, between the final equilibrated state after M has been dropped and the initial state before M is dropped. Write your answer in terms of M, h, 8, and the properties of the fluid.

(b) Derive an expression for the change in volume AV with an initial volume V₁.

Question 4

Calculate the heat required to form a liquid solution at 1356 K starting with 1 mole of
Cu and 1 mole of Ag at 298 K. At 1356 K the molar heat of mixing of liquid Cu and
liquid Ag is given by

Data:

Question 5

(a) Derive an expression for

. in terms of the state variables, including I, P, S, V, and the measurable properties of the system, including the heat capacities,

and C,, the isobaric thermal expansivity, a, and the isothermal compressibility, B. A is the Helmholtz free energy defined as U - TS.

(b) Like (a), derive an expression for in terms of the state variables and measurable properties of the system. G is the Gibbs free energy defined as H -TS.

(c) Do the quantities you derived in (a) and (b) depend on the size of the system (i.e. is it intensive or extensive)?

Here are some useful relationships for you to use:

a. A constant volume heating to twice the initial temperature.

b. An adiabatic reversible expansion back to 298 K.

c. An isothermal, reversible compression back to 1 Pa. Calculate the heat (Q), work (W), internal energy change (△U), and entropy change (△S) of the entire cycle. (Gas constant, R = 8.314 J/mol-K)

110年 - 110 國立清華大學碩士班考試入學試題_工程與系統科學系/甲組:材料熱力學#105330

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