110年 - 110 國立臺灣大學_碩士班招生考試_材料科學與工程研究所甲、丙組:材料熱力學#100919

2. (20 points) The adiabatic thermoelastic effect describes the change in temperature with pressure for a brittle solid when it is loaded rapidly. This effect can be used to measure the stress that develop around defects in materials using cyclic loading and thermal imaging. (a) Show that the variation of temperature with respect to pressure at constant entropy (adiabatic condition) is. [10 points] (b) For 1 mole of alumina originally at T = 298 K, please estimate the change in temperature when it is loaded to 500 MPa, given tha [10 points]

3. (20 points) CaO and MgO form a simple eutectic system with limited ranges of solid solubility. Assuming that the solutes in the two solid solutions obey Henry's law with = 6.23 in CaO at the eutectic temperature, calculate the solubility of CaO in MgO and the solubility of MgO in Cao at such temperature.

4. (20 points) Consider the partial decomposition of gaseous Please calculate (a) the temperature at which at a total pressure of I atm [10 points] and (b) the total pressure at whichat 2000 K [10 points], given that△G° = 225,400+7.90TInT -209.47 J for this reaction.

5. (20 points) From electromagnetism it has been shown that the electromagnetic pressure exerted on the walls of a container of volume Vis related to the internal energy U through P=U/3V. With the assumption that: (I) the entropy of the system S(U,V) is a state function and (2) The energy density is related to temperature through UIV=AT² (where A and   λ  are constants), please show that λ=4. (Hint: Start from the law of thermodynamics and express