6. Derive the Clapeyron equation for liquid-vapor boundary:
[Hint: Starting with the concept that the chemical potentials must be equal when two phases are in equilibrium] (10%)

3. On a pressure-volume plot, why the curves are steeper for an adiabatic process compared to isothermal process. [Hint: You should provide equations and explain the physics behind the equations you present] (10%)

4. Draw a two-component, temperature-composition, solid-liquid diagram for a system where compound of formula AB2 forms that melts incongruently, and there is a negligible solid-solid solubility. Label the regions of the diagrams, stating what materials are present and whether they are solid or liquid. (15 %)

(a) Derive the phase rule. (10%)

(b) Draw a one-component phase diagram (pressure-temperature) and use phase rule to rationalize your diagram. [Hint: Why "point", "line" or "area" in the diagram] (10%)

7. For polymers, the glass transition and melting are either "first-order" or "second- order" phase transition? Please explain your answer. (10%)

8. Molecular bromine is 24 % dissociated at 1600 K and 1.00 bar in the equilibriumCalculate equilibrium constant K at (1) 1600 K, (iil) 2000 K given that the standard reaction enthalpy over the temperature range. (15%)

一、文言作文  《史記．游俠列傳》： 「及若季次、原憲，閭巷人也，讀書懷獨行君子之德，義不茍合當世，當世亦笑之。故季次、原憲終身空室蓬戶，褐衣疏食不厭。死而已四百餘 年，而弟子志之不倦。」季次、原憲生前窮困潦倒，世人笑之，然沒而弟子永志不忘。現今世局動盪，社會變遷紛擾，世人熙熙攘攘，汲汲營營。請以「知識份子應 如何處世」為題，說明個人之體認及自許。

二、白話作文題目：請在閱讀過李維菁的文章後，以「物質」、「精神」和「情感」為軸，自訂題目，寫一篇六百至一千字的短文。      物質是很重要的。在物質上慷慨的人，在情感上未必大方。但物質上吝嗇的人，在情感上必然吝嗇。      心意光用嘴巴說，卻沒禮物，這種人絕對不可信。那感覺就像是懷念祖先，用心就好，何必掃墓祭祖。很重朋友，何必寫信電話或見面。總在夜裡懷念舊人，所以根本不需照片。      現實是不去掃墓你三年都不會想起列祖列宗。不連絡見面，卻說是好友，這種話是做直銷的愛講。不翻照片，你不追悔曾辜負過誰。人沒有那樣高尚。形式很重要。      所有藝術史的演進就是物質與形式的一再革命與突破。以詩為例，因為既有的語言表達方式再也不能表達內心激切的感情了，因此打破了現有的形式，打碎了慣例，創造新的語言型態，滿足那份亟欲溝通的渴望。視覺藝術的進程也出自物質形式的一再變革，因為對這世界的看法新穎充沛，必須創造新的物質組合，形式到位，精神的進步相隨，前衛因此誕生。      愛情也是，必然飽含某種創造性的欲望。將心意轉化成某種印記，對過往賦予重要性與象徵性。物質是虛幻情意的穩固支點，物質與精神從來不站在對立面，而是彼此的救贖。      這不是拜金戀物，我真正明白物質的美好。      我身邊就有這樣的人，每天說思念，跟你談傅柯，卻連一杯美式咖啡的錢都不願替你付。還有長髮瀟灑男，你從家裡帶出兩顆大水梨，他吃完他手上的，還指著要你手上的那顆。你聽到他說，你家反正比較有錢，你常吃。      一個習慣掠奪或支配不屬於自己物質的人，必然貪婪無義。當我摩搓喀什米爾披肩，感受到頸項之間的細緻柔滑，我總覺得，情人不死也會跑，物質與回憶會天長地久。物質不滅定律，可情感無常。                                                   ----摘錄自李維菁《老派約會之必要》（台北：印科，2012）

1. (20 points) (a) Consider I mole of ideal gas undergoes a reversible isothermal expansion from V = 1 liter to 2 liters. The temperature is kept at 300 K. Please calculate the change of ertropy of the gas system. (10 points] (b) Now consider the same I mole of ideal gas undergoes an irreversible free expansion process such that the volume is changed from V= 1 liters to 2 liters. What is the change of entropy of the gas? [10 points]

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]