告訴你「拉午耳」 「亨利」的壓力有多大 ─自製簡易的 IC 電路板來討論拉?
This research is aimed to make an in-depth exploration into Raoul’s Law and Henry’s Law by using an accurate but simple vapor pressure gauge. The gauge is constructed from non-complicated electronics components- electronics IC PCB, film resistor, digital multi-meter, and battery. In the first step, we measured the vapor pressure of six kinds of liquids and 3 liquid mixtures- water, ethanol, chloroform, acetone, benzene, toluene, mixture of water and ethanol, mixture of chloroform and acetone, mixture benzene and toluene. From the results of this experiments, the vapor pressures of water and ethanol liquid mixture, and chloroform and acetone liquid mixture were slightly lower than their theoretic values-called negative deviation solution, while the vapor pressure of the benzene and toluene liquid mixture was quite close to its theoretic value-near an ideal solution. In the second step, the individual vapor pressures of water, ethanol, and chloroform were measured at various temperatures; the vapor heat(ΔH) were calculated by using the lausius-Clapeyron equation. In the final step, we used the gauge and other non-commercial instruments to measure the B.O.D. values of water from the Kaohsiung Love River, found the P-T correlation using Gay-Lussac’s Law, and calculated the absolute zero temperature value by extrapolation. 本研究是利用一些簡易的電子元件－電路IC板、電阻膜、數位三用電表和電瓶來組裝一 個準確、簡易的氣壓量測器。我們將此量測器用來深入探討「拉午耳定律」及「亨利定律」 。 首先，我們測量了水、乙醇、氯仿、丙酮、苯、甲苯等六種純液體的蒸氣壓，並測量了(水＋乙醇)、(氯仿＋丙酮)、(苯＋甲苯)等兩成份系溶液的混合蒸氣壓。結果發現(水＋乙醇) 、(氯仿＋丙酮)的混合蒸氣壓都比理論值低了一些，此稱為負偏差溶液；(苯＋甲苯)的混合蒸氣壓與理論值差不多，較接近理想溶液。 接下來，我們還測量了不同溫度下水、酒精及丙酮的蒸氣壓，並利用clausius－clapeyron equation求出液體純質的汽化熱( H Δ )。 最後，我們還搭配了自製的儀器裝置，來測定愛河水質的B.O.D.值(生化需氧量)以及探討氣體的給呂薩克定律(P~T關係)，並利用外差法來推求絕對零度。
西爾平斯基船帆與掛毯圖形應用於數位圖形與數位音樂創作
西爾平斯基船帆(Sierpinski Gasket)與西爾平斯基掛毯(Sierpinski Carpet)都屬於碎形(fractals)圖形的一種，可以利用迭代運算系統IFS(Iterated Function Systems)碼來產生，代入迭代運算方程式後，經由多次的運算，可以得到重覆的圖形。本研究中，我將提出一些作法，找出西爾平斯基船帆與掛毯圖形其遞迴關係式，進而討論出其數位圖形之規律性及所涵蓋的內容與性質，著重在推廣西爾平斯基船帆與掛毯圖形的概念，將一段音樂曲取出，把它們看成反覆隨機迭代點，利用程式經由多次的插值運算，計算出各段音符。最後加入基因演算法來解決音符長短的問題，把製造好的音符染色體放置到交配池中，以隨機的方式在交配池中選取其中之一個染色體進行交配的動作，此二音符染色體會交換彼此的基因，產生下一代新的代表音符長短之染色體，應用於數位音樂創作，而衍生的西爾平斯基船帆與掛毯圖形新穎應用與創新的結果，希望能提供數位音樂創作的多樣性，更進而可以找出「好聽的音樂」與數學的直接關聯性。‘Sierpinski Gasket’ and ‘Sierpinski Carpet’ are two graphics that belong to fractals. They can be produced by IFS (Iterated Function Systems). By iterative computation of many times, we can obtain the similar graphics. In my research, there are some methods to generate Sierpinski Gasket, Sierpinski Carpet, and the iterative algorithms. In addition, I would discuss the regularity and the content as well as the properties of those digital patterns. At last, the advanced application of Sierpinski Gasket and Sierpinski Carpet to digital music pieces was presented. The program took a note of several measure of music as the beginning point, and made the IFS calculations for each new note in each measure. But there was no difference in beats if you just make the IFS iteration. So I changed the beats with genetic crossover method. In this research, the expression of the DNA to each beat of note was adopted. The same way, it took a note as a beginning point. And the system obtained the new DNA from the old notes for new ones randomly. That would make a piece of brand new music. What I want to do in this research is improve the multiformity of music and find what the relationship is of ‘good music’ and mathematical algorithms.