26-12-09

Happy boxing day! 用了TeXnicCenter打pdf, 真係好令~ 目前rewrite緊我篇Basic Algebraic Skills 目前框架為 1)Polynomial -factorizing, identity *skill of substitution (Intro) 2)Fucntion -degree, domain *sequences (Intro) 3)Equation -linear -quadratic analysis ->sum and product -complex numbers -eliminating terms -beyond quadratic 4)Sequences -Recursive -characteristic equation -chain function 5)Function revisited -rational function -root function -logarithm -Absolute function 6)Inequality -solving -The sum and product sign -AM-GM Ineq. -Triangular Ineq. 7)Algebraic Trigon -Co-goem system -Definition and extention of trigon function -Complex number ion Trigon mean -Application 8)Common Technique in Olympiad Mathematics -assumption of extreme value

Merry Christmas!

HKCEC。 今天的電玩展終於完結。Cos players身上的布料依舊的少，龍友相機的閃光依舊的猛。同時舉辦四個大型展覽的會展，從裡面往外一看：港灣道一排街燈照耀著下方數不清、滿載而歸的人(也許節目還沒完呢)；再往外看是天星小輪，在燈飾的襯托下成為海面的主角。對岸的燈飾有如百花齊放，教人目不暇給，用錢堆出來的璀璨竟也可能給人溫暖的感覺。 龍友發動了總攻勢，拉(拐？)著十個Cosers少女走了，其他同行自然不甘寂寞，紛紛尋歡渡佳節。會展頓時變靜了。 「我走了。」少女吐出一句話。 「嗯。」我低著頭應道。 天星小輪彷彿被六十八年的子彈打中了，在不大的風浪中搖得特別的厲害。不，那時是「黑色聖誕」，今天是個溫暖的聖誕，我－－ 十二下鍾聲隱約傳來，把我從思緒中拉回來。眼前的她早已不見縱影。 眼前的夜景是那麼的華麗。腦海中的她是那麼的悅目。 不知道明年、後年、大後年，還有這個機會一起麼？ fin. 大家聖誕快樂。虛構故事，如有雷同，實屬巧合。聖誕小品，小試牛刀，文筆生疏，敬請原諒 =] 凌晨十二時 楓 筆於會展

一萬字 Ch. 14.3

翌日。 我望了一下窗外的情形，原來已經刮起了強風，遠處的吐露港已經掀起了白頭浪；風把樹葉吹得沙沙作響，而縣掛信號的柱子上原本的圓柱和盤子上下倒調了，在水平的角度看就是個倒T字。 三號風球。 同時，電腦發出了聲響。我走近一看，原來是內聯網的IRC(In Room Chat，聊天室)發了訊息過來。 「早安，睡醒了沒有？」 說話的是頌明。 「托你的福，我現在很清醒……」 頌明：「你要習慣早上被電腦叫醒哦。反正很多比賽都是紫欣安排和編出來的。」 我：「……編出來？」 雪婷：「用來嚇我們特訓的手段，我都見慣了。」 頌明：「所以今天就來跟你說一聲，其實晚上的比試不是真的。」 我：「真的嗎？」 雪婷：「不信的話，你可以……」 正午十二點，風勢稍為平靜了一點，雖然大家也明知這是「暴風雨前的寧靜」，可是紫欣還是叫了我再去特訓一下。 無論是那一種的運動，訓練都一定是枯燥沉悶的。打乒乓球的要反複把發球機的發球打回，打羽手球的也要不停練習扣殺的技巧；單車也是一樣，每天走過的，也是同一條路罷了。 一個月去一、兩次或許可能讓自己放鬆，但每天都踩的話就未免太悶了。但運動就是這樣，沒有刻苦的訓練就沒有健碩的成果。 今天可能是個例外，我沒試過在三號風球之下踩單車。 「你遲到了哦。」 「啊哈哈哈──這麼大風怎會走得快嘛。」 「說得也是，你大概以前沒試過打風踩單車吧？」說罷，她騎上單車順著風向駛去。她的速度在風力的推動下又加快了一層，瞬間就把她帶到遠處。在遠處她又駛回來，奇怪的是，她似乎沒有受到逆風的影響，以平時的連度回飆過來！ 面對著目瞪口呆的我，她笑問：「你知不知道為甚麼不受逆風影響？」

Transfer process

Conduction: It is the process that heat is transferred through a body from a region of higher temperature to region of lower temperature.

Relative conductivity of heat of different materials:

Metal (Ag>Cu>Al>Fe)>glass>plastic (rubber)>wood>cotton>polystyreneUsually liquid and gas is poor conductor of heat (good insulator of heat).

Molecular motion about conduction:

We know that molecules with higher K.E. vibrate more vigorously. Intermolecular force bonds the molecules together. Therefore when one end of the substance is hotter than another side, molecules with higher K.E. set their neighbouring molecules to vibrate more vigorously. Then the energy is transferred to those neighbouring molecules.

Within metallic bond, free (mobile) electrons and ions exist. Those electrons move freely within that piece of metal. When they receive energy, their K.E. increase and quickly transfer to other electrons or ions, then energy is transferred quickly. Therefore metals are good conductors of heat, and non-metals are usually poor conductors of heat.

Factors affecting rate of conduction

There’re four factor: conductivity of heat of the material; temperature difference between two ends; length between two ends and cross-section of the body.

Experiment about conduct heat of different materials

Soak a piece of filter with Cobalt(II) chloride solution, place four rods (copper, brass, aluminium and glass) with the same length and cross-sectional area on the paper. Heat one end of the rods by Bunsen flame. Compare the relative conductivity of heat by looking the colour of the filter paper.

Applications on conduction

Good conductors of heat for heating: Cookware (Cu exterior) and metal skewer.

Good conductors of heat for cooling: heat sink (Cu, Al) in CPU and radiator in a car.

Good insulators of heat for keeping warm: fur on animals, jackets, polystyrene food containers, plastic handles for cookware and refrigerator.

Conduction: It take place in a fluid (liquid/gas). It’s a process which heat is transferred by the movement of the fluid from one to each other.

When a fluid is heated, the molecules inside it moves (vibrate) faster. As a result fluid expands and become less dense.

Then it has a lower density than other surrounding fluid so that it’ll rises. Cooler fluid flows down because it has a higher density. As a result, convection current is formed: Hotter fluid rises and cooler fluid sinks.

The convection current taught us that air conditioners should be set in a higher place of a room so that cooler air sinks. Also radiators should be set in a lower place such that warm air flows up.

In the environment sea breezes and land breezes also shows the convection current.

Sea breezes in fine and warm weathers: Air in the land is heated faster and it rises, as a result, air in the sea is heated in a slow way (water has a high specific heat cap.) so that it sinks. Then gas pressure in the land decreases and sea breezes come from the sea.

Land breezes in the night: air in the sea cool down slowly so that it is comparatively hotter, it rises while air in the land sinks, As a result, land breezes go to the sea.

Radiation is a process in which heat is transferred from one place to another by means of electromagnetic waves (mainly IR, for hotter object it emits visible lights as well.)

It can take place in a vacuum since electromagnetic waves (light) can pass through vacuum. Object with temperature above absolute zero emits radiation and hotter objects emit stronger radiation.

Objects were heated when they receive (absorb) radiation and objects were cooled through emitting radiation. (It’ll emit in all temperature higher than absolute zero, despite the surrounding temperature.)

Dull black surface are good absorbers (since they don’t reflect most of the light) and good emitter of radiation while shiny silver surface is a poor absorbers (they reflect most of the light) and poor emitters of light.

Applications on radiation:

Silvery surface: oil tanks, car sunshields, white-painted house, kettle, aluminium foil.

Black surface: Radiator and solar power panel.

Change of state; latent heat

Three state of matter: solid, liquid and gas. (Ionized gas or plasma is the fourth state.) Heating process: Heat until solid reaches melting point (MP). It absorbs latent heat of fusion and melt (fusion). Heat that liquid until it reaches the boiling point (BP). It absorbs latent heat of vaporization and vaporizes. Cooling process: Cool down some gas until it reaches boiling point. It releases latent heat of vaporization and condenses. Cool down that liquid until it reaches the melting (freezing) point. It releases latent heat of fusion and freeze(solidification). Cooling curve: when we cool down some liquid/gas, the behavior of temperature is: cool down in a concave curve, stays constantly in the BP/MP, after it is totally condensed/frozen, it cools down in a curve again. *In the experiment about cooling down octadecan-1-ol, we can data-logger to record the cooling curve. Latent heat is the energy released or absorbed when a substance changes its state without changing it’s temperature. The unit of latent heat is Joule(J). Latent heat of vaporization is energy released or absorbed when a substance changes its state from liquid to gas (or gas to liquid) without changing it’s temperature.*(1) Latent heat of fusion is energy released or absorbed when a substance changes its state from liquid to solid (or solid to liquid) without changing it’s temperature.*(2) Specific latent heat is the energy required to change the state of 1kg of substance without changing its temperature. The uinit is Jkg^-1 Specific latent heat of vaporization the energy required to change the state of 1kg of substance between gas and liquid without changing its temperature. *(3) Specific latent heat of fusion the energy required to change the state of 1kg of substance between solid and liquid without changing its temperature.*(4)We use the symbol (1) L_v, (2)L_f , (3)l_v , (4)l_F to represent those physical quantities. (Note: L_v means that the "v" is written in the right-bottom corner of L, etc.) We have l=Q/m=L/m=Pt/m. This formula is the way to calculate the specific latent heat through a graph. Important specific latent heat: vaporization 2.26*10^6 Jkg^-1 fusion: 3.34*10^5 Jkg^-1 *experiment of measuring specific latent heat of fusion Experimental set-up: electrical supply -> Joulemeter->immersion heater fully inserted into the crushed melting ice(to ensure that it’s 0˚C) , in a filter funnel. Under the filter funnel there’s a beaker measuring amount of water being melted. Control set-up: immersion heater without electrical supply, ceteris paribus. By l_f=Q/m , Specific latent heat of fusion = energy transferred/mass of ice melted. Note that “mass of water melted” is equal to “water melted in the experimental set-up minus water melted in the control set-up” to ensure that the “mass of water melted in the formula” is about “ice melted by the energy from the heater”. Energy transferred can be obtained from the difference between initial and final reading of Joulemeter. Assumption: 1) No energy was absorbed by the ice from the surrounding air. 2) All energy from the heater is absorbed by the ice. *experiment about measuring specific latent heat of vaporization Electrical supply->kilowatt-hour meter->immersion heater fully immersed into a beaker of water on a triple beam balance. By l_v, Specific latent heat of vaporization = energy transferred/amount of water vapourized. Assumption: 1) All energy from the heater is transferred to the water. 2) No energy lost from heater/water to the surroundings. 3) No water is split out before vaporized and condensed back to the beaker. Evaporation is the process that changes liquid below BP (boiling only occurs at BP) to gas on the surface of the liquid (Boiling occurs through out the liquid). Evaporation in terms of molecular motion: In the liquid molecules moving in wide range of speeds and hence containing a wide range of kinetic energy. When they collide each other, some gain energy and some lose energy. When some of them obtain enough KE, they escape from the liquid and become vapour. As those escaped molecules contain more kinetic energy than the liquid, the average kinetic energy of the remaining liquid decreases and therefore evaporation gives a cooling effect. Condensation: warm air can hold more water (vapour) than cold air. When warm air is cooled suddenly, some of the vapour condenses. Since they releases latent heat of vaporization during condensation, it rises the temperature on the object which it condenses. Missing table: factors affecting vaporization notes available. Sorry for putting so much thing into 2 pages. I'll try to put them in a better way after try to add some extra concepts.

Heat and internal energy

Definition: Heat is the energy transferred from one body to another as a result of temperature difference between two bodies. The unit is Joule (J).

Note that “heat” is not energy, it’s just a transferring process of energy.

Internal energy : energy stored in the object, equal to the sum of kinetic energy due to random motion and potential energy of all its molecules. (Σ(K.E)+Total P.E.)

The unit of internal energy (energy) is Joule.

Higher temperature means higher average kinetic energy, then the formula of internal energy tells us the internal energy will be higher with the temperature as well.

Power : the rate of transfer (energy). The unit is Watt (W). We have:

Power = energy/time P=E/t (E=Pt or t=E/P)

Definition:

1W=1J/1s=Js^-1

1W power means transferring 1 Joule of energy in 1 second.

Another unit of energy if kilowatt-hour. It’s the amount of energy transferred by 1000W (kilowatt) in 1 hour. Its unit is kWh. 1kWh= 3,600,000J = 3.6*10⁶J = 3.6 MJ.

Heat capacity

Definition: Heat capacity of an object is the energy required to transfer by heating to the object to raise the temperature of the object through 1˚C. It’s symbol is C.

C=Q/ΔT where Q (energy transfer) and ΔT (change in temperature) have unit of J and ˚C respectively, therefore the unit of C is J˚C^-1

Specific heat capacity

Definition: Specific heat capacity of a substance is the energy transferred by heating required to raise the temperature of a unit mass (kg) of the substance through 1˚C. It’s symbol is c.

c=Q/mΔT=C/m (or mc=C), where m is the mass.

*experiment about finding specific heat capacity of water*

Put m kg of water into a polystyrene cup, then insert an immersion heater, stirrer and thermometer into the cup. The power supply of immersion heater passes through a Joulemeter.Assume the initial readings of temperature and energy is E and T and the final readings is E’ and T’ respectively.

c=Q/mΔT=(E'-E)/m(T'-T)

Note that immersion heater should be fully immersed into the water to ensure that all energy from the heater is transferred to the water.

Assumption:

1) No energy lost from the water to the surrounding air/cup.

2) No energy lost from the heater to the surrounding air.

3) The temperature within water is unique such that the readings of thermometer is accurate (we use stirrer to make this more accurate)

4) All energy from the heater is transferred to the water (we record the highest temperature reading after the heater is off)

Another experiment about specific heat capacity of aluminium has similar procedure. But stirrer is not needed. Instead, a polystyrene tile is under the aluminium block and cotton wool surrounding the block. Also we put some oil into the immersing holds to keep a well thermal contact between the block, heater and thermometer.

Law of conservation of energy states that the total amount of energy in a system must remain constant. Then energy lost of an object = energy gain of another object.

(mass of a)(spec. heat cap. of a)(temp. diff. of a)=(mass ofb)(spec. heat cap. of b)(temp. diff. of b)

Or

(heat cap. of a)(temp. diff. of a)=(heat cap. of b)(temp. diff. of b)

If the object contains the same substance, then

(mass of a)(temp. diff. of a)=(mass of b)(temp. diff. of b)

Importance of high specific heat capacity of water (4200Jkg^-1˚C^-1)

1) As a coolants for motors, CPUs…

2) Reduce daily temperature range for coastal area. (Coastal area have more water stored with the area. In day, water absorb energy in a more effective way than soil. In night they release energy.)

3) Monitoring body temperature: we release energy through sweating. Moreover 70% of our body is water. We can gain or loss a large amount of energy without a big change in body temperature.

Physics unit 1 - Temperature

Definition: It’s a physical quantity that measures the degree of hotness or coldness of an object. The unit is degree Celsius. (˚C)

Temperature scale can be defined by an upper fixed point, lower fixed point and dividing scale.

The pair of fixed point should be easily obtained and reproducible, therefore we define the lower fixed point as the temperature of pure melting ice at 1 apm (standard atmospheric pressure) and the upper fixed point as the temperature of pure boiling water at 1 apm.

Calibration of thermometer (to mark the thermometer) :

Put it into pure melting ice (lower fixed point) followed by the pure boiling water. Liquid level is recorded in each case and the separation between the two markings is divided into 100 equal divisions. Each division represent 1˚C.

Thermometric properties: of a matter is a measureable physical quantity of the matter which changes along with the temperature. For example, density.

Thermometer: a device with measurable property which changes with temperature.

Liquid-in-glass thermometer consist of a narrow glass tube, one end consists a bulb that contains liquid (alcohol or mercury). When temperature rises, liquid expands and rises in the tube. Oppositely they contract and fall in cooler temperature.

If the length of liquid in the tube changes more in a given quantity of temperature change, then we say it has a higher sensitivity.

Clinical thermometer has an extra constriction between the bulb and the tube to prevent the mercury flowing back to the bulb.

Temperature in terms of molecular motion

It is the measure of the average kinetic energy due to the random motion of the molecules of the object.

Equal temperature means equal average kinetic energy.

1-12-09

十二月好。 來說一說今年會打的筆記吧! Physics: Heat and gases: -thermometer -heat cap.; states; latent heat Mechanics: -Position and motion -acceleration and deceleration Chemistry: -Atmosphere; ocean; rock and minerals -Chemical bonds -Metals and its reactivity Economics: -economic basics -firms and production Maths: 未定，可能有 另，<<車神>>等idea中...