Physics 101 Lecture 1 (Heat) 2005 PDF

Faculty of Women Physics Department Physics 101 (heat) Lecture 1 Prepared By: Dr. Doaa Abdallah Reference: Peter J. Nolan - Fundamentals of College Physics, Vol. 1, 5th Updated Edition (2005, Pearson Custom Publishing) Temperature and Heat Temperature : Temperature is a measure of the hotness or coldness of a body. That is, if a body is hot it has a high temperature, if it is cold it has a low temperature. This is not a very good definition. it is one that most people have a "feel" for, because we all know what hot and cold is. Or do we? Let us reconsider the "thought experiment". We place three beakers on the table, as shown in figure (1). Several ice cubes are placed into the first beaker of water, whereas boiling water is poured into the third beaker. We place equal amounts of the ice water from beaker one and the boiling water from beaker three into the second beaker to form a mixture Figure (1) A “thought experiment’’ on temperature. First, put your right hand and plunge it into beaker one, you will conclude that it is cold. Then, dry off your right hand, and place it into the middle mixture. After coming from the ice water, the mixture in the second beaker feels hot by comparison. So you will conclude that the mixture is hot. After that, take your left hand and plunge it into the boiling water of beaker three. You will conclude that the water in beaker three is certainly hot. Finally, Dry off your hand again and then place it into beaker two. After the boiling water, the mixture feels cold by comparison, so you will conclude that the mixture is cold. Conclusion: After this relatively scientific experiment, your conclusion will be contradictory. That is, you found the middle mixture to be either hot or cold depending on the sequence of the measurement. Thus, the hotness or coldness of a body is not a good concept to use to define the temperature of a body. Although we may have an intuitive feel for hotness or coldness, we can not use our intuition for any precise scientific work. In order to make a measurement of the temperature of a body, a new technique, other than estimating hotness or coldness, must be found. Let us look for some characteristic of matter that changes as it is heated. The simplest such characteristic is that most materials expand when they are heated. Using this characteristic of matter we take a glass tube and fill it with a liquid, as shown in figure (2). When the liquid is heated it expands and rises up the tube. The height of the liquid in the tube can be used to measure the hotness or coldness of a body. The device will become a thermometer. In order to quantify the process, we need to place numerical values on the glass tube, thus assigning a number that can be associated with the hotness or coldness of a body. This is the process of calibrating the thermometer. The Thermometer In order to make a measurement of the temperature of a body, a new technique, other than estimating hotness or coldness, must be found. Let us look for some characteristic of matter that changes as it is heated. The simplest such characteristic is that most materials expand when they are heated. Using this characteristic of matter we take a glass tube and fill it with a liquid, as shown in figure (2). When the liquid is heated it expands and rises up the tube. The height of the liquid in the tube can be used to measure the hotness or coldness of a body. The device will become a thermometer. In order to quantify the process, we need to place numerical values on the glass tube, thus assigning a number that can be associated with the hotness or coldness of a body. This is the process of calibrating the thermometer. Figure (2) A thermometer First, we place the thermometer into the mixture of ice and water of beaker 1 in figure (1 ). The liquid lowers to a certain height in the glass tube. We scratch a mark on the glass at that height, and arbitrarily call it 00 degrees. Since it is the point where ice is melting in the water, we call 0 the melting point of ice. (Or similarly, the freezing point of water) Then we place the glass tube into beaker three, which contains the boiling water. (We assume that heat is continuously applied to beaker three to keep the water boiling.) The liquid in the glass tube is thus heated and expands to a new height. We mark this new height on the glass tube and arbitrarily call it 1000. Since the water is boiling at this point, we call it the boiling point of water. Because the liquid in the tube expands linearly, to a first approximation, the distance between 00 and 1000 can be divided into 100 equal parts. Any one of these divisions can be further divided into fractions of a degree. Thus, we obtain a complete scale of temperatures ranging from 0 to 100 degrees. Then we place this thermometer into the mixture of beaker two. The liquid in the glass rises to some number, and that number, whatever it may be, is the temperature of the mixture. That number is a numerical measure of the hotness or coldness of the body. We call this device a thermometer, and in particular this scale of temperature that has 00 for the melting point of ice and 1000 for the boiling point of water is called the Celsius temperature scale and is shown in figure (3a). This scale is named after the Swedish astronomer, Anders Celsius, who proposed it in 1742. Another, perhaps more familiar, temperature scale is the Fahrenheit temperature scale shown in figure (3b). The melting point of ice on this scale is 32 0F and the boiling point of water is 212 0F. Gabriel Fahrenheit, the German physicist proposed his scale in 1714. Figure (3) The temperature scales. In addition to the Celsius and Fahrenheit scales there are other temperature scales, the most important of which is the Kelvin or absolute scale, as shown in figure (3c). The melting point of ice on this scale is 273 K and the boiling point of water is 373 K. The Kelvin temperature scale does not use the degree symbol for a temperature. The Kelvin scale is extremely important in dealing with the behaviour of gases. In fact, it was in the study of gases that Lord Kelvin first proposed the absolute scale in 1848. For the present, however, the implications of the Kelvin scale can still be appreciated by looking at the molecular structure of a solid. The simplest picture of a solid, if it could be magnified trillions of times, is a large array of atoms or molecules in what is called a lattice structure, as shown in figure (4). Figure (4) Simple lattice structure. Each dot in the figure represents an atom or molecule, depending on the nature of the substance. Each molecule is in equilibrium with all the molecules around it. The molecule above exerts a force upward on the molecule, whereas the molecule below exerts a force downward. Similarly, there are balanced forces from right and left and in and out. The molecule is therefore in equilibrium. In fact every molecule of the solid is in equilibrium. When heat is applied to a solid body, the added energy causes a molecule to vibrate around its equilibrium position. As any one molecule vibrates, it interacts with its nearest neighbours causing them to vibrate, which in turn causes its nearest neighbours to vibrate, and so on. Hence, the heat energy applied to the solid shows up as vibrational energy of the molecules of the solid. The higher the temperature of the solid, the larger is the vibrational motion of its molecules. The lower the temperature, the smaller is the vibrational motion of its molecules. Thus, the temperature of a body is really a measure of the mean or average kinetic energy of the vibrating molecules of the body. It is therefore conceivable that if you could lower and lower the temperature of the body, the motion of the molecules would become less and less until at some very low temperature, the vibrational motion of the molecules would cease altogether. They would be frozen in one position. This point is called absolute zero, and is 0 on the Kelvin temperature scale. From work in quantum mechanics, however, it is found that even at absolute zero, the molecules contain a certain amount of energy called the zero-point energy. Temperature Conversions: For the present, however, it is still necessary to convert from one temperature scale to another. That is, if a temperature is given in degrees Fahrenheit, how can it be expressed in degrees Celsius, and vice versa? It is easy to see how this conversion can be made. The principle of the thermometer is based on the linear expansion of the liquid in the tube. For two identical glass tubes containing the same liquid, the expansion of the liquid is the same in both tubes. Therefore, the height of the liquid columns is the same for each thermometer, as shown in figure (5). The ratio of these heights in each thermometer is also equal. Therefore, Figure (5) Converting one temperature scale to another These ratios, found from figure (5), are Solving for the temperature in degrees Celsius Simplifying ………. (1) Equation (1) allows us to convert a temperature in degrees Fahrenheit to degrees Celsius. Example (1) If room temperature is 68 0F, what is this temperature in Celsius degrees? Solution The temperature in Celsius degrees, found from equation (1), is To convert a temperature in degrees Celsius to one in Fahrenheit, we solve equation (1) for t 0F to obtain ……………….. (2) Example (2) A temperature of −5.00 0C is equivalent to what Fahrenheit temperature? Solution The temperature in degrees Fahrenheit, found from equation (2), is We can also find a conversion of absolute temperature to Celsius temperatures from figure (5), as Therefore, the conversion of Kelvin temperature to Celsius temperatures is given by ………………. (3) And the reverse conversion by …………….... (4) Example (3) Normal room temperature is considered to be 20.0 0C, find the value of this temperature on the Kelvin scale. Solution The absolute temperature, found from equation (4), is ❖ What is required to measure temperature? Any physical property of body which varies a uniformly with temperature will serve to measure temperature. Some of these properties are: (a) the variation in volume of a fixed mass of liquid (b) the variation in resistance of a metal, for example a length of platinum wire (c) the variation in the electromotive force of a thermocouple when the two junctions are at different temperatures (d) the pressure of a fixed mass of gas at constant volume. ❖ Liquid-in-glass thermometers The thermometer in Figure is probably the most familiar type. liquid is contained in a thin- walled bulb at the end of a long thick-walled capillary tube. Glass is a bad conductor of heat energy so the walls of the bulb are thin to enable the heat energy to pass through quickly, and the liquid to attain the temperature of its surroundings. Since the bulb is small, the bore of the capillary tube must be very fine so that a small change in temperature produces a reasonable movement of the liquid column. If you look end-on at a broken thermometer stem, you will need a magnifying glass to see the bore of the tube. It is easy to see the liquid thread in the thermometer, because the thick-walled tube acts as a cylindrical magnifying glass. Liquid-in-glass thermometers are not particularly accurate. They have a limited range and are easily broken. They can be read more accurately if the size of the interval between the graduations is increased. This is done either by increasing the size of the bulb or by using a finer bore capillary tube or by a combination of both. If the bulb is larger the increase in volume of the liquid will be greater for the same rise in temperature, and the mercury will move a longer distance along the stem. Decreasing the bore produces a greater length of liquid for the same increase in volume and the same rise in temperature. ❖ How long does it take for a thermometer to reach the temperature of its surroundings? This depends upon the quantity of liquid in the bulb. The larger the quantity of liquid the longer it takes. Some clinical thermometers are known as 'half-minute thermometers and some as 'one-minute thermo- meters' for obvious reasons! The temperature reading is necessary to have a fixed scale of temperature. A scale must be defined by two fixed reference points which are easily obtainable and easily reproducible. Lower fixed point (X0) this is the temperature of pure melting ice, at a pressure of one standard atmosphere. Upper fixed point(X100) this is the temperature of dry steam from water boiling at a pressure of one standard atmosphere. Fundamental interval This is the distance between the fixed points. It is divided into a number of equal divisions. Each division is one degree. General equation Earlier it was stated that any physical property of a body which varied uniformly could be used to measure temperature. The general equation for the Celsius temperature θ is 𝑿𝛉 −𝑿𝟎 𝛉= × 𝟏𝟎𝟎 ………………… (5) 𝑿𝟏𝟎𝟎 −𝑿𝟎 where X is the property which varies 'uniformly' with temperature. For example, X could be the resistance of a platinum wire or the electromotive force of a thermocouple. ❖ Example)4( In an unmarked mercury thermometer, the length 𝑙0 was 4 cm, and 𝑙100 24 cm. What are the temperatures when 𝑙θ is (a) 16 cm, (b) 28 cm and (c) 2 cm? (a) 𝑙0 = 4cm, 𝑙100 = 24 cm, 𝑙θ =16 cm 𝑙 θ − 𝑙0 θ= × 100 𝑙100 − 𝑙0 (16 − 4)𝑐𝑚 12 θ= × 100 = × 100 = 60𝑜 𝐶 (24 − 4)𝑐𝑚 20 (b) 𝑙0 = 4cm, 𝑙100 = 24 cm, 𝑙θ =28 cm θ =? 𝑙 θ − 𝑙0 θ= × 100 𝑙100 − 𝑙0 (28 − 4)𝑐𝑚 24 θ= × 100 = × 100 = 120𝑜 𝐶 (24 − 4)𝑐𝑚 20 (c ) 𝑙0= 4cm, 𝑙100 = 24 cm, 𝑙θ =2 cm θ =? 𝑙θ − 𝑙0 θ= × 100 𝑙100 − 𝑙0 (2 − 4)𝑐𝑚 −2 θ= × 100 = × 100 = −10𝑜 𝐶 (24 − 4)𝑐𝑚 20 ❖ Thermometric liquid The two liquids normally used in thermometers are mercury and alcohol. Both have advantages and disadvantages. ❖ Mercury The advantages of using mercury in a thermometer are: (a) it does not wet (cling to the sides of) the tube (b) it is a good conductor and the whole liquid quickly acquires the temperature of the surroundings (c) it expands uniformly (d) it has a high boiling point (357 °C) (e) it has a low specific heat capacity. The disadvantages of using mercury are: (a) it has a high freezing point (-39 °C) (b) its expansivity is fairly low. The high freezing point means that it cannot be used in winter in countries here the temperature gets very low. ❖ Alcohol The advantages of using alcohol in a thermometer are: (a) it expands uniformly (b) it has a large expansivity (c) it has a low freezing point. (-115 °C). The disadvantages of using alcohol are: (a) it wets the tube (b) it has a low boiling point (78°C) (c) it has a high specific heat capacity. Note: It is sometimes stated that being colourless is a disadvantage, but this is not really a problem as it is quite easy to add a little colouring matter. Alcohol is used in cold countries in winter, because of its low freezing point. ❖ Why Water cannot be used as a thermometer liquid ? Water cannot used as a thermometer liquid because of its usual expansion. It has other disadvantage namely a low boiling point and high freezing point. Its colourless is not really a problem as there is no difficulty in adding a little colouring matter so that it can be seen easily. ************************************************************************** ❖ Maximum and minimum thermometers A maximum thermometer records the highest temperature it has reached during a given period, while a minimum thermometer records the lowest temperature it has reached. ❖ Clinical thermometer A very important maximum thermometer is the clinical thermometer, which is used to take the temperature of the human body. Mercury is the liquid used in this thermometer, which is shown in Fig. (6). The glass wall of the bulb is very thin so that the mercury quickly acquires the temperature of the body. Figure (6) Clinical thermometer The bore of the capillary tube is very fine to give a large change in length for a small change in temperature. The feature that transforms it into a maximum thermometer is the constriction in the capillary just above the bulb. When the temperature rises the expansion of the relatively large volume of mercury in the bulb produces a force which pushes the mercury through the constriction and up the tube. When the thermometer is taken out of the patient's mouth or armpit, the mercury cools and contracts. The cohesive forces between the mercury molecules are not strong enough to pull the mercury back, through the constriction, and the thread breaks at the constriction. Thus, the mercury in the capillary tube cannot get back into the bulb, and the maximum temperature (the patient's temperature) can be read off. The thermometer stem is usually triangular in shape to increase the magnification, and enable the thermometer to be read more easily. The thermometer is given a sharp shake to get the mercury back into the bulb. Note :The scale is restricted to a small range 35-42 °C. Normal body temperature is 36.9 (37 °C to the nearest degree). The short range enable the stem to be reasonably short. Under no circumstances should the thermometer be washed in very hot water after being taken out of the patient's mouth or the thermometer is likely to burst. It should be sterilised using a sterilising solution. ❖ Maximum thermometer Figure(7) Maximum thermometer Figure (7) shows another maximum thermometer in which a steel index is inserted in the capillary tube above the mercury column. As the temperature rises the index is pushed up by the mercury column because steel floats on mercury. When the temperature falls the index remains in position helped by the small spring. The bottom of the index gives the maximum reading. A magnet is used to reset the thermometer by bringing the index back to the top of the mercury column. ❖ Minimum thermometer Alcohol is used in the minimum thermometer in Fig (8) and the index is inside the liquid. When the temperature falls the alcohol contracts and the index is pulled back by the force of surface tension in the meniscus. Figure (8) Minimum thermometer meniscus. When the temperature rises the alcohol flows past the index which remains in position. The index does not fit as tightly as that in the maximum thermometer, and the thermometer is used in a horizontal position (e.g. to measure the minimum temperature of the ground at night). If the thermometer is tilted gently the index slides down the tube and comes to rest at the meniscus. This resets the thermometer. ❖ Six's combined Maximum and Minimum Thermometer This thermometer Fig. (9) is used in meteorological stations to measure the maximum and minimum air temperature over twenty- four hours. Alcohol is the thermometric liquid and is contained in the bulb A. Bulb B also contains alcohol and in the space above the alcohol is a mixture of alcohol vapour and air. A thread of mercury separates the two columns of alcohol. This thread of mercury pushes up the indexes, which are made of steel and have a spring so that they remain in position when no force Figure (9) Combined maximum and acts upon them. minimum thermometer When the temperature increases the alcohol in A expands, flowing past the minimum index and pushing the mercury thread round the tube. This in turn pushes up the maximum index and the air in B is compressed. When the temperature falls the alcohol in A contract. The air in B is now under less pressure and expands to push the alcohol and mercury thread round the tube. The maximum index remains in position as the alcohol flows past and the mercury pushes the minimum index towards A. Thus, the bottom of the index in the right-hand column gives the maximum reading, and the bottom of the index in the left-hand column gives the minimum reading. A magnet is used to reset the indexes by drawing them down to their respective mercury levels. ❖ Bimetallic thermometer A bimetallic strip wound into a coil, may be used to make a thermometer Fig. (10a). When the temperature increases the curvature of the coil increases causing the pulley to which the movable end is attached to rotate and thus move the pointer over the scale. This type of thermometer can be robust and very compact (about as big as a pocket watch) and is used to record the temperature in freezers, ovens etc. The coil can also be made into a helix Fig. (10b) and a pen attached to the end of the pointer. If the pen is positioned to touch a rotating drum it will give a continuous recording of the temperature. This instrument is called a thermograph. Figure 10 (a) Bimetallic thermometer, (b) thermograph ❖ Platinum resistance thermometer Figure (11) Platinum resistance thermometer This thermometer uses the variation with temperature of the resistance of a coil of platinum wire as its standard. It is made from a double coil of platinum wire wound on a strip of notched mica and placed inside a porcelain tube. The coil is doubly wound to counteract the effects of electromagnetic induction. A pair of compensating leads are added to nullify the change in resistance of the leads to the platinum coil. The thermometer is placed where the temperature is required and the resistance of the coil is measured on a Wheatstone Bridge. Usually, a scale will be calibrated to read the temperature directly, but if the actual resistance R0 is measured the temperature can be calculated from 𝑹𝛉 −𝑹𝟎 𝛉= × 𝟏𝟎𝟎 …………………………(6) 𝑹𝟏𝟎𝟎 −𝑹𝟎 where R0 and R100 are the resistances at 0°C and 100 °C respectively. This temperature will obviously be in °C. The advantages of a resistance thermometer over a liquid-in-glass thermometer are: (a) it is far more accurate (b) it has a very large range (c) it can be read at a distance if it has long leads. The observer does not need to be close to where the temperature is being measured, e.g. in a furnace. ❖ Example (5) The resistance of a platinum resistance thermometer at 0o C is 6.00Ω at 100°C, 8.4 Ω and at θ°C 14.4 Ω. Find the value of θ. The thermometer is then placed in a thermos, flask containing liquid nitrogen at -200 °C. What will be the value of its resistance? R0 = 6.0 Ω R100 = 8.4 Ω Rθ = 14.4 Ω θ =? 𝑅θ −𝑅0 θ= × 100 𝑅100 −𝑅0 (𝑅θ −6.0)Ω −200 = × 100 8.4 − 6.0 Ω 𝑅θ − 6.0Ω −2 = 2.4Ω −4.8Ω = 𝑅θ − 6.0Ω 𝑅θ = 6.0Ω − 4.8Ω = 1.2Ω ❖ Thermo-electric thermometers Different metals contain different numbers of free electrons per unit volume. Suppose metal A contains n₁ m-3 and metal B has n2 m-3. When A and B are brought into contact so that the electrons can move freely from one to the other Fig. (12), they will redistribute themselves until the number on each side is the same, say n. Thus, if A loses electrons, it will have a net positive charge, and if B gains electrons, it will be negatively charged, and thus an electromotive force is set up across the junction. This electromotive force produces a current depends upon what happens to the other ends of A and B. Obviously these ends have to be joined, either directly or by other wires, and charge will only flow if these ends are at a different temperature from the junction of the metals. Figure (12) Electromotive force when different metals are in contact ❖ Thermocouple Figure (13) Thermocouple The value of the net electromotive force produced, and hence the current, depends upon this temperature difference. The copper connecting wires have no effect on the electromotive force. Basically, the thermometer is made by joining one pair of ends and placing these where the temperature is to be determined see Fig. (13). The other pair of ends are well away from the heat and are connected to a sensitive galvanometer. The galvanometer deflection is proportional to the electromotive force 𝐸θ −𝐸0 θ=𝐸 × 100 ………….(7) 100 −𝐸0 The advantages of a thermo-electric thermometer are: (a) it has a low thermal capacity and can be used to measure fluctuating temperatures (b) it has a very large range, from -200 °C to 1500 °C depending upon the metals used for the Thermocouple (c) it can measure the temperature at a point. ❖ Thermopile By using a lot of thermocouples in series a sensitive heat-detecting device called a thermopile can be made. This is the instrument used to detect the radiation. Strips of two metals are joined alternately Fig. (14a) and then wound round a non-conducting frame so that half the junctions are on one side and half on the other Fig. (14b). One side, with junctions, is painted black to absorb radiation and so become hot more easily. The rest of the junctions remain cool. The frame is then placed at the end of a cone Fig. (14c) so that radiation is concentrated onto the black surface. The free ends of the thermocouples are connected to a sensitive galvanometer. Figure (14) Thermopile Since the thermocouples are in series, the electromotive forces add up and a measurable deflection is obtained on the galvanometer. This instrument is sensitive enough to detect the heat from a lighted match some distance away.

Physics 101 Lecture 1 (Heat) 2005 PDF

Document Details

Tags

Related

Summary

Full Transcript

Upgrade to continue