磁場中的離子轉速-探討離子遷移速度變因
帶電的離子受到垂直的磁場與電場作用，會因為受到洛倫茲力而產生有趣的轉動現象。我們利用上述原理設計簡易的裝置設備，探討電解質溶液不同濃度、不同離子電荷數，受到不同離子間靜電力，產生不同的離子移動速度。經由所測量的時間與圓周運動的距離，可計算電解質的絕對遷移速度。由實驗結果推論在固定電場下，當電解質濃度降低，正、負離子間的相互作用力降低，離子遷移速度(migration velocity)加快，莫耳電導率 Λ（mole conductance)也隨之增加。同濃度時，電解質2-1 價型硝酸銅與2-2 型硫酸銅離子強度(ionic strength)不同，2-2型硫酸銅離子強度較大，遷移速度較小，莫耳電導率Λ 也較小。Because of the effect of Lorentz force, charged ion will have interesting rotation under the vertical magnetic and electric field. We use the above principle to design a simple instrument or tool, in order to evaluate and study the formation of different ionic mirgration velocities. The velocity of the charged ion in the instrument is affected by differences in the electrolyte, the charge differences of the ion tested and the differences in electrostatic forces between ions. From the experiment we can deduct that at a fixed constant electric field, when the concentration of the electrolyte is reduced, the interaction of forces between positive and negative ions will be reduced. When the migration velocity of ions increase, the mole conductivity Λ (mole conductance ) will also increase. At the same concentration, the ionic strength between copper nitrate ( 2-1valency type ) and copper sulfate ( 2-2 valency type ) are not identical. Copper sulfate, a 2-2 valency type has higher ionic strength, the velocity is slower and the mole conductivity Λ is also smaller.
滿足
之M點是否為重心之探索
滿足之M 點，我們稱之為Pi(i=1…n)的均值點。當n=3，M 恰為△P1P2P3 的重心 (G); n=4 時，M 亦為三角錐P1P2P3P4 的重心！因此不免引人遐思：滿足之M 點是否皆為其重心？
我們藉由電腦幾何作圖軟體GSP 協助觀察，掌握了圖形變化間之不變性，再配合向量解析及推理，得以發現均值點、多邊形的重心、以至多面體的重心、及平行多邊形的一般性作法。附帶又發現：任意相鄰三頂點即可決定一平行n 邊形。並進而證實：平行四邊形為四邊形M＝G 的充要條件。但當n≧5 時，平行n 邊形只是n 邊形M＝G 的充分非必要條件！一般而言，具有對稱中心O 的n 個點所構成的圖形必可使M 與G 重合於O 點上。
The point M satisfying is called “the mean point of Pi(i=1…n)”. As n=3, M is the center of gravity (G) of the △P1P2P3. If n=4, then M is also the center of gravity of the triangular pyramid P1P2P3P4. Therefore, I began to wonder if the following assumption stands: The point M that satisfies is always a center of gravity.
By using the computer software GSP (The Geometer’s Sketchpad) to observe figures. It is found that when a figure is changing there is still constancy. Furthermore, supported by the analysis based on vectors, general constructions can be established concerning the mean point, the center of gravity of polygon, the center of gravity of polyhedron, and the parallel polygon. Also, I find that any three neighboring vertexes decide a parallel polygon. And thus it is verified that the parallelogram is the sufficient and necessary condition for quadrilateral M=G. As n≧5, the parallel n-sides shape is the sufficient, not necessary condition, for n-sides shape M=G. In general, a central figure of n points having the center of symmetry O can make M and G meet on O.
旋光性介質對電磁波影響的分析與討論
This experiment mainly aims at three kinds of solution - Dextrose, Saccharose, and Fructose. By changing its temperature, density, length of tube, as well as different wave length factor of polarized light, we observe the influence of the direction of polarization by those factors. The experimental result showed as follow. The Dextrose and the Saccharose can cause the polarized light with the rotary direction of clockwise, so both are ‘dextrorotatory’. The Fructose can cause the polarized light with the direction of counterclockwise, so it is the ‘laevorotatory’. For the Dextrose, when the\r temperature is lower than 20℃, the direction of polarization has changed observably, but doesn’t have any rule. When the temperature is higher than 20℃, the direction of polarization increase slowly. For those three kinds of solution, when\r density increased, the polarization increased observably. When the polarized light passed through the solution with longer path, the direction of polarization has more change. When the wave length of the polarized light changed, the direction of polarization has been changed observably. When the wave length of the polarized light is shorter, the direction of polarization change increased.本實驗主要針對葡萄糖、蔗糖、及果糖等三種旋光性溶液，改變其溫度、濃度、容器管長、以及不同波長的偏振光等因子，觀察這些因素對偏振方向所造成的影響。實驗結果顯示：葡萄糖與蔗糖會使得偏振光的偏振方向以順時針旋轉，屬右旋性之光學異構物；果糖會使得偏振光的偏振方向以逆時針旋轉，屬左旋性之光學異構物。若溶液為葡萄糖，當溫度低於20℃時，偏振光的偏振方向會有明顯的改變，但無規則可尋；當溫度大於20℃時，偏振方向旋轉角位移則以非常緩慢的方式增加。當此三種溶液之濃度增加時，偏振光的偏振方向有明顯遞增的現象。此外，當容器長度越長（即偏振光在介質中的行程越長）時，偏振方向的改變亦越明顯。當偏振光的波長改變時，偏振光的偏振方向有明顯的變化，且當偏振光的波長越短，偏振方向的改變越大，似乎與波長呈反比，但此結果與理論值（即旋光度與波長平方成反比）仍有一些差距。
溫差電池的熱力學研究與應用
溫差電池中若僅進行的反應，則其電池電壓與溫差成正比，且純粹是利用化學反應將熱能轉換成電能，我們稱之為「典型溫差電池」，由熱力學公式可推導出典型溫差電池的電動勢(ΔS = S(s)—S(aq)，S為絕對熵， n為得失電子數，1F = 96487 C )，且得到下列三項推論來說明溫差電池的特殊現象。 (1) 同一溫差電池，其電動勢與溫差成正比 (ε∝ ΔT)。(2) 不同的溫差電池，當溫差一定時，電壓ε 與ΔS 成正比，與得失電子數n 成反比。典型溫差電池中，電解液濃度越小，金屬離子濃度也愈小，會使得ΔS = (S(s)—S(aq))的絕對值變大，因此溫差電池的電壓也就愈大。(3) ΔS 值的正負決定電壓ε 的正負。Cu(NO3)2 及ZnSO4 溫差電池的ΔS 為正值，所以高溫杯為正極；AgNO3 溫差電池的ΔS 為負值，所以高溫杯為負極。因水溶液中陰、陽離子不能單獨存在，所以單一離子水溶液的絕對熵無法求得，但科學家把氫離子水溶液的標準絕對熵定為零，藉以求出其它離子的絕對熵，然而我們測得在一定溫差時典型溫差電池的電動勢ε，再查得金屬的標準絕對熵 S(s)，代入S(aq) = S(s) — nFε/ΔT，便可得到離子水溶液的絕對熵。Cu(NO3)2 溫差電池的電解液中若含有1M 或0.5M 的KNO3，電池電壓仍然與溫差成正比， 但卻可獲得較大的電流，我們稱此類溫差電池為「改良型溫差電池」。我們利用改良型溫差電池的原理，自製環保、節約能源、可重複使用的實用溫差電池，以PVC 水管當容器，上、下兩端開口用銅片封住當電極，管內裝海棉及0.125M Cu(NO3)與 1M KNO3 溶液，熱源加熱上層銅片形成溫差，當溫差維持在70℃，電壓約為70 mV，若串聯30 個實用溫差電池，電壓可達2 V 以上，就可以對鉛蓄電池充電。實用溫差電池的熱源可由回收冷氣機、工廠的廢熱，或直接利用太陽能來當熱源。
If the temperature difference cell only goes through the following reaction Then the potential created by the cell is proportional to the temperature difference, and such a reaction purely changes the thermal energy into electrical energy through chemical reaction, which we often name it “typical temperature difference cells”. We can come to the following formula for the typical temperature difference cells through a series of thermodynamic formula: ε= ΔT ． ΔS/ nF (ΔS = S(s)—S(aq), where S is the standard 3 entropy, and n is the number of electrons gained or lost, and 1F = 96487 C). We also provide the following three inferences to demonstrate the special phenomenon for the temperature difference cells: 1. Within the same temperature cell, the electromotive force (EMF) is proportional to the temperature difference. 2. When the temperature difference keeps constant, the electromotive force is proportional to the ΔS in different temperature cells, and is inversely proportional to the number of electrons gained or lost. Within the typical temperature difference cells, when the concentration of the electrolyte becomes more diluted, the concentration of the metal ions also proportionally become lower, which will make the absolute value of the following equation bigger, as a result, will make the electric potential of the temperature difference cells bigger: ΔS = (S(s)—S(aq)) 3. The value of ΔS decides the value of the electromotive force. The ΔS of the following temperature difference cells is positive value: Cu(NO3)2 and ZnSO4 . As a result, within the copper and zinc temperature difference cells, the higher temperature glass is the anode. On the other hand, the ΔS of the AgNO3 temperature difference cell is negative, which means that within the silver temperature difference cell, the higher temperature glass is the cathode. Meanwhile, because the cations and anions can not exist alone, therefore, it is not possible to find the standard entropy of the single ion solution. However, scientists define the standard entropy of the solution containing hydrogen ion to be zero, as a result, we only have to determine the electromotive force for a typical temperature difference cell, while keeping the temperature difference constant, followed by finding the standard entropy for the said metal S(s). Inserting it into the following equation to find the standard entropy for the ion solution. S(aq) = S(s) — nFε/ΔT If the electrolytes for the Cu(NO3)2 temperature difference cell contains 1M or 0.5M KNO3 , the electromotive force is still proportional to the temperature difference, and we can obtain bigger electric current. We call this kind of temperature difference cells “improved version of the typical temperature difference cells”. We try to make more environmental, energy saving, and recyclable temperature difference cell by applying the theory of the improved version of the typical temperature difference cells. We use PVC water pipe as the containers, both edges of the pipe sealed with copper metals, also work as the electrodes. Within the pipe filled with sponge and 0.125M Cu(NO3) and 1M KNO3 solution. The heat source keeps heating the upper copper metal to keep constant temperature difference. When the temperature difference is kept around 70℃, the electric potential is 70 mV. If we can connect 30 practical temperature difference cells in a series, the electric potential will reach 2V, which can then charge the lead rechargeable battery. The heat sources of the practical temperature difference cells can be supplied by the recycled air conditioners, heat waste from a factory, or directly comes from the solar power.
蝴蝶眼斑的探討
在眾多的蝴蝶中有不少是具有眼斑。傳統上認為眼斑的功能是驚嚇天敵或欺騙天敵。有關眼斑本身結構的瞭解很少。我們利用臺灣及馬祖產的蝴蝶，分別記錄圖鑑上峽蝶、眼蝶及灰蝶合計 60 種以上，以及鳳蝶幼蟲七種的眼斑特性。記錄的眼斑特性包括數目、組成的色彩結構，以及記錄眼斑在翅的腹面或背面明顯。進一步測暈孔雀峽蝶、台灣波眼蝶、蘇鐵小灰蝶等三種蝴蝶的眼斑和翅面積。眼斑在腹面及背面都有，但以腹面明顯者佔多數，而眼斑數 l 一 7 個都有，在後翅者佔多數。眼斑慕本是由數個同心圓組成，分別為輪廓、眼白、虹彩及障孔。在峽蝶及眼蝶的結構都相當完整，輪廓為褐或深褐，眼白為黃色為主，虹彩都為黑色或深褐色，障孔為白色或淡藍色。在灰蝶的眼斑較不完整，大都輪廓不清晰，眼白的黃色或橙色部份比例高，但都缺少障孔。幼蟲有眼斑成蟲不一定有。鳳蝶的幼蟲（ 8 種）都為綠色，其眼斑輪廓黑色，眼白為白色及紅色但明顯比上述成蟲的眼斑之眼白部位要小，而黑色的虹彩都很大。幼蟲的障孔為白色的細線形，我們認為這和立體形狀的幼蟲及成蟲平面翅的差異所造成，在文中也討論到水棲蝶魚的眼斑和蝴蝶眼斑的差異。眼斑和翅面積的相關分析結果變異很大，在統計上正相關及負相關都有。眼斑數目的不定及和翅面積並沒有一定關係，我們討論到蝴蝶的眼斑在不同種類有些可能有求偶生殖上的功能。這方面值得科學家大量投入研究。Quite a few species of butterflies have colorful eyespots on their wings. The main functions of these eyespots were considered to startle or deceive predators by most scientific researchers. In fact, only limited literatures dealt with the basic structure and color patterns of butterfly eyespots. The purpose of this study is to study the basic structure and color patterns of these eyespots. We measured the surface area of eyespots v.s. wings from specimens. From the color plates of Taiwan and Matsu butterfly field guide, we recorded the eyespots either on ventral or dorsal side of wings, and the color patterns for more than 60 species. \r The number of eyespots on wings varies from I to 7 among individuals we checked. Majority of eyespots were found on ventral side of wings. The basic structure of eyespots were formed by I to 3 concentric circles, i.e., outboundary, cornea, iris and pupil . Pupil was not found in certain species. The color in cornea section is yellow and in iris is black or dark brown. The contrast in these two areas is quite prominent just as the contrast showed in warning coloration of after animals. The pupil is either white of light blue. Caterpillars with eyespots were found in Papilionidae, their adult stage were without this character. We checked 8 species of caterpillars, their basic structure of eyespots were similar to other butterflies, with cornea, iris and pupil. The cornea is either red or white color, and the iris is black in colors. The ratio(iris/cornea) is much higher in caterpillar than in butterfly. The pupil is a thin thread shape instead of a tiny spot like the one in butterfly wings. We discussed the difference of pupil between juveniles and adults from the aspect of dimension structure of a subject. In the paper we also discussed the difference of eyespots between butterfly and butterfly fish in the coral reef. Base on the no significant relationship between the surface area of eyespots and wings. We suspect that butterfly eyespots may have another function, such as intersexual selection between males and females beside startling and deceiving predators.\r