Chapter 1: Temperature and Measurement PDF

Chapter ( I ) Temperature and its measurement  Temperature Introduction :- 1)For a long time, there was a theory that “heat” was an invisible, weightless fluid called “caloric.” 2)“Heat” is a result of the movement of molecules inside the metal, and the greater this movement,...

Chapter ( I ) Temperature and its measurement  Temperature Introduction :- 1)For a long time, there was a theory that “heat” was an invisible, weightless fluid called “caloric.” 2)“Heat” is a result of the movement of molecules inside the metal, and the greater this movement, the greater the amount of heat generated. 3)A fixed amount of work done always results in a fixed amount of heat. Thus, Joule was able to determine the value of what he called the “mechanical equivalent of heat,” which is 4.186 J/calorie. (W=JH ) That is, an amount of work of 4.186 J always produces an amount of heat equal to one kilocalorie 4)Heat is one of the forms of energy found in nature and has become called “thermal energy”. 5) Thermal energy” or “the amount of heat” is defined as “the total kinetic energy of the molecules inside the substance.”  Temperature and its measurement: Using the sense of touch, we can determine whether an object is hot or cold However, determining the level of heat and cold will be a relative matter and vary from one person to another, so we need a number that expresses the degree of heat, which we call “temperature.” Definition of temperature: “It is the average kinetic energy of the particle in the substance, and it determines whether the body is in a state of “thermal equilibrium” with another body when it is in contact with it.”  Temperature Scales The “temperature scale” has two fixed points: The “upper fixed point” is the boiling point of pure water under standard pressure (76 cm.Hg). The “lower fixed point” is the melting temperature of ice under standard pressure. The range between the two points is called the “fundamental interval” and is divided into equal parts, each part of which is called a “degree.” There are three temperature scales: 1)Centigrade Scale:- This scale is based on dividing the “fundamental interval” into one hundred equal parts, each of which is called “degrees Celsius” (0C), so that the boiling point of pure water at standard atmospheric pressure is 100 0C, and the melting point of ice at standard atmospheric pressure is 0 oC. This scale is known as the Celsius scale. (2) Fahrenheit Scale: - The “Fahrenheit scale” is divided into 180 equal parts, each of which is called a “Fahrenheit degree” (F°), starting from the melting point of ice under standard atmospheric pressure, which is 32 °F, to the boiling point of pure water under standard atmospheric pressure, which is 212 °F. (3)The absolute scale: - The Absolute (Kelvin) Scale Zero Celsius on the absolute scale corresponds to what is called absolute zero, which equals -273 °C, where, the absolute zero is defined as :-the temperature at which the energy of molecules is the lowest possible. The relationship between the Celsius scale and the Fahrenheit scale. The relationship between the “Celucis scale and the absolute scale”  The relationship between “the Celsius scale, the Fahrenheit scale, and the absolute scale” We assume that the physical property, (x), changes linearly with temperature (t) by the relationship: Where (a) is constant t ( x )  ax Let the values xL​​ , xu, xt, be the values ​of this property at the “lower fixed point,” the “upper fixed point,” and the unknown temperature (t), respectively. So the change in the characteristic (x) versus the change in temperature (t) gives a constant value expressed by the equation: xu xL x t xL  t u t L t t L  The relationship between “the Celsius scale, the Fahrenheit scale, and the absolute scale” The relations are : x t xL x t xL tc  100C t F ( 180)  32F xu xL xu xL x t xL T( ) 100  273.16K xu xL  The relationship between “the Celsius scale, the Fahrenheit scale, and the absolute scale” The final relation is :- tc t F 32 T  273.16   100 180 100  (Thermomters) If the temperature of an object changes, changes occur in the physical properties of this object. The most important changes that occur are:- 1)Change in body dimensions (stretch phenomenon). 2)The change in pressure of a gas when its volume is kept constant. 3)Change in electrical resistance. 4)The change in electromotive force resulting from the contact of two metals. 5)The change in wavelength of a radiation wave with the temperature changes for a hot object. Measuring these changes is a means of determining the temperature level of hot objects, and measuring devices are called (thermometers ).  Types of thermometers (1)Platinum resistance thermometer. (2) The thermocouple thermometer. (3) Thermopile. (4) Optical pyrometer.  (1) Platinum resistance thermometer Its use:- It is used to measure the temperature of liquids and solutions. The idea of ​its work:- It depends on the phenomenon of changing resistance with changing temperature. If (Rt) and (Ro) are the resistances of the conductor at two degrees (t) and (0) , then the resistance of the conductor changes with its temperature according to the equation: - Rt = Ro(1 + α t) Where (α) : the coefficient of increase in resistance with temperature.  Rt = Ro ) 1 + α t ) Rt = Ro + Ro α t T = Rt - Ro / Ro α R₁oo = Ro + Ro α * 100 Ro α = R1oo - Ro / 100 T = ( Rt - Ro ) * 100 / R1oo - Ro ##  Construction of platinum resistance thermometer The thermometer consists of a platinum wire wrapped around a thin sheet of insulating mica, and the ends of the wire a and b (the suspension wires of the thermometer) are connected to a sensitive device for measuring resistance, usually installed in a Whitestone Bridge. The platinum wire is placed as one of its arms, then there is an equilibrium position, that is, no deviation in the galvanometer, and from it the value of the resistance of the wire can be calculated. To equalize the change in resistance of the conducting wires ab of the platinum thermometer - as a result of their presence inside the hot medium whose temperature is to be measured - equalizing wires a`b` are placed in the arm of the bridge opposite the thermometer, similar to the conducting wires of the platinum wire, and they are placed in the same hot medium until their resistance changes by the same amount as the wires. Connecting the thermometer wire, so the change in resistance recorded by the Whitestone Bridge results only from the change in the resistance of the platinum wire alone with the temperature of the medium in which the thermometer is placed. How to use a platinum resistance thermometer to measure an unknown temperature The first method :-( Find Ro , R1oo , Rt ) 1) We attach the thermometer as an arm in a Whitestone Bridge using suspension wires a,b, and connect equalizing wires a', b’ to the opposite side of the thermometer. The thermometer is placed in ice, then we change the resistances until we reach a state of equilibrium at which there is no deflection of the galvanometer, and by applying the law of equilibrium to the bridge. The value of (Ro) can be found. 2) 2) We place the thermometer and the equivalent wires in boiling water, then change the resistors until we reach a state of equilibrium at which there is no galvanometer deviation. We find a value of (R1oo). 3) We repeat the above by placing the thermometer in the liquid whose temperature is to be measured, and let the resistance value of the thermometer be (Rt). 4) 4) By substituting into the equation, T = ( Rt - Ro ) * 100 / R1oo - Ro the temperature of the liquid can be found. The second method:- (Calibration method) for measuring a temperature between zero and 100 degrees Celsius using a metric bridge: - The metric bridge is another form of the Whitestone bridge, in which two resistors are replaced with a meter-long metric bridge wire with a unit cross-sectional area, and this wire represents a resistance , where (L α R). 1)Place the platinum resistance thermometer and the equivalent wires on the opposite side in an ice. Then we move the slider and determine the equilibrium position on the meter wire AB, so this position represents the temperature of zero degrees Celsius. 2) The platinum resistance thermometer and the equivalent wires are placed on the opposite side at a liquid temperature of 100 degrees Celsius. Likewise , this position represents the temperature of 100 degrees Celsius. 3) We divide the distance between the two (zero & 100) position into 100 equal sections, each section representing one degree Celsius. Thus, we have calibrated the metric bridge wire to measure the temperature directly. 4) We place the thermometer in the medium whose temperature is to be measured, then we determine the equilibrium position using the slider, and this position directly gives the temperature of the medium to be measured.  (2) The thermocouple thermometer Sebek found that when two different metals - such as copper and iron, for example - are connected to form a thermocouple, an electromotive force is generated that depends on: (i) The type of wires and (ii) The difference between the temperatures of the two connections. When the temperature of one of the two junctions rises relative to the other, a current arises, and the intensity of the resulting current depends on the temperature difference between the two junctions. This phenomenon is known as :- the thermoelectric property.  How to use a thermocouple thermometer to measure an unknown temperature The first method: - (to compare the temperatures of two liquids) 1)We put the cold contact point at zero degrees. 2) We place the hotspot at the first unknown temperature. 3) The deviation of the galvanometer is (α) to the temperature of the first medium. 4) We put the hot contact point at the second unknown temperature. 5) The deviation of the galvanometer is (α) to the temperature of the second medium. So: - By comparing the extent of the galvanometer’s deflection for the two media, it is possible to compare the temperatures of the two media. The second method:- (Calibration method) for measuring a temperature between zero and 100 degrees Celsius:- 1)The equilibrium galvanometer connected to the thermocouple circuit is divided into equal sections starting from zero. 2) We place the cold contact point at zero degrees Celsius, and the hot contact point at 100 degrees Celsius, so the galvanometer pointer deviates until it stabilizes at a value, so this value is equivalent to 100 degrees Celsius. 3) We divide the galvanometer scale into 100 equal parts. 4) We place the cold contact point at zero degrees Celsius, and place the hot contact point in the hot environment whose temperature is to be measured. 5) The pointer of the galvanometer will deviate, and the fixed position of the pointer directly gives the temperature of the medium whose temperature is to be measured.  (3) Thermopyl It consists of a large group of thermocouples connected in series to increase the sensitivity of the device. It is used as a recording tool for the infrared spectrum. It is used to compare between the thermal radiations. When the front connections are exposed to thermal radiation, their temperature rises relative to the temperature of the back connections, as they are kept inside the device away from radiation. The difference in temperature between the front and back connections causes an electric current, which results in the galvanometer deflecting by an amount proportional to the intensity of the incident radiation. To compare two thermal radiations: 1)We place the first radiation in front of the front links and observe the deflection of the galvanometer. 2) We place the second radiation in front of the front links and observe the deflection of the galvanometer. Radiation that has a greater deflection indicates that its intensity is greater, and so on.  (4) Optical Pyrometer Idea of its work:- When a body is heated to a high temperature, reaching a certain degree, its color begins to redden. Then, as the temperature increases, the body reaches the point of glowing, and thermal radiation with a wavelength is emitted from the body, which indicates that the temperature controls the length of the light wave radiated from the body, and the lengths of these waves decrease as the temperature rises. Thermal radiation is directly proportional to the temperature of the radiating body and inversely proportional to the wavelength Its uses :- An optical pyrometer or a disappearing filament pyrometer is used to measure extremely high temperatures, such as in factory stoves and blast furnaces.  (4) Optical Pyrometer Composition:- An optical pyrometer consists of a telescope with a red light filter inside its stem, and a small electric bulb connected to an electrical circuit consisting of a battery, an ammeter, and a rheostat. It is used in two ways:- The first method: (the disappearing wick method) 1)The electrical circuit is open: - The hot body is placed in front of the objective lens of the telescope. The field of view of the eyepiece appears as a bright red circle due to the presence of the red filter in the path of the rays emanating from the body. At the same time, the filament of the electric lamp is seen as a dark line in the field of vision. 2)The electrical circuit is closed: - By passing the electric current through the lamp filament, and we gradually raise its intensity using variable resistance, the filament begins to glow and then we reach a point where it is completely impossible to see the lamp filament (the disappearing filament) when: - Lamp filament temperature = radiation temperature from the hot body By knowing the current intensity in the lamp filament, the temperature of the filament can be calculated, which is equal to the temperature of the hot body. The second method:- (calibration method) :- In this method, we use several thermal radiations whose temperatures are known, and through them, the ammeter is calibrated to give a direct reading of the temperatures. 1)We place the first radiation in front of the objective lens, close the circuit, and increase the current through the circuit via the rheostat until we obtain the position of the filament hidden through the objective lens, and we note the position of the ammeter indicator, which indicates the temperature of the first radiation. 2) We repeat the first step for several rays whose temperatures are known, and each time we determine the position of the ammeter indicator that indicates the temperatures of the different rays. 3) The ammeter scale is divided into equal sections, so that each section gives the temperature directly. 4) For any radiation whose temperature we want to know, we place it in front of the objective lens, close the circuit, and change the intensity of the passing current until we obtain the position of the hidden filament and read the position of the ammeter indicator, which directly gives the temperature of the radiation.  Definitions of some basic quantities 1)Amount of heat: If we have a mass (m) of water and then raise its temperature from T₁ to T₂, the amount of heat used for this is: The unit of heat is known as the Calorie. Where (specific heat of water = 1) 2)Calorie: It is the amount of heat needed to raise the temperature of one gram of water by one degree Celsius. 3)Heat capacity: It is the amount of heat needed to raise the body temperature by one degree Celsius. (The heat capacity of a body depends on its nature. A gram of copper has a different heat capacity than a gram of iron.) 4)Specific Heat: It is the heat capacity of one gram of a substance. 5) Water equivalent for the body: - It is the amount of water whose temperature rises by one degree Celsius, if the same amount of heat is given as that given to the body.  Determine the specific heat of a body or liquid by mixing When two bodies with different temperatures touch, heat is transferred from the hot body to the cold body until they are equal in temperature. The condition is then called thermal equilibrium. If the mass of the first body is m₁, its temperature is t₁, and its specific heat is c₁, then the amount of heat stored inside it is m₁c₁t₁. If we thermally mix this body with another body whose mass is m₂, whose temperature is t₂, and whose specific heat is c₂, until the state of thermal equilibrium, and by applying the law of conservation of energy, it is: the heat gained from the body Cold = heat lost from a hot body That is: Where (t )is the final temperature of the mixture at thermal equilibrium. We neglected the heat lost through radiation, for example, and considered the group to be a thermally insulated system. This equation is used to find the specific heat of a body , In order for the degree of accuracy to be reasonable, the heat capacities of each of the two mixed bodies must be close.  Determination of the specific heat of a gas under constant volume: cv (Jolly steam calorimeter) Construction of the device:- It consists of two identical balls, (A) and (B), that are emptied and suspended on the palms of a sensitive balance. They hang in a water vapor chamber at temperature (t). Below each ball there is a cone to collect the droplets of vapor condensing on each ball. Around the suspension wires are placed heating coils through which an electric current passes to raise their temperature to prevent condensation. Water vapor around. Steps:- 1)We compress the gas whose specific heat is to be determined under a fixed volume inside the sphere (A), then using a sensitive balance we find the mass of the gas and let it be (m₁). 2) The steam is passed into the chamber and the steam condenses on the two balls, but it is in a larger quantity on ball (A) than on ball (B). This is because the gas absorbs an amount of heat, raising its temperature to 100 degrees Celsius. Thus, the balance of the sensitive scale changes. 3) We rebalance the sensitive balance and thus find the weight of the condensed vapor, (m). 4) So: the steam lost heat, the gas gained heat That is, a heat exchange occurred and it continues until we reach thermal equilibrium The amount of heat absorbed by the gas = the amount of heat lost from the steam. Where (L) : the latent heat of steam, and the value of (cv) can be determined Precautions to be taken into account:- 1)Place a cone under each ball to collect the droplets of steam condensing on each ball. 2) Heating coils are placed around the suspension wires through which an electric current is passed to raise the temperature of the suspension wires to prevent water vapor from condensing around them. _________________ Determination of specific heat by Cooling method - Newton's law of Cooling If a hot body is left in air, it will cool at a rate that depends on: 1)The nature of the hot surface. 2) The surface area of ​the body radiating heat. 3) The difference between the body temperature and the surrounding environment. Definition of the cooling rate of a hot body: 1)It is the amount of heat lost from the body per second 2)It is equal to the body's water equivalent multiplied by the rate of decrease in temperature. Cooling curve: It is the curve that shows the change in body temperature with time. Newton's Law of Cooling: The rate of cooling of a hot body cooled in air is directly proportional to the difference between the temperatures of the body and the surrounding environment, provided that this difference is not large. Proving the validity of Newton's law of cooling practically: We will first assume the validity of the law, then test the validity of its results. If the results are correct, the hypothesis is valid. Proof steps:- 1)We draw the cooling curve for a hot body between θ and t 2) We draw a horizontal line at room temperature θo 3)We take two points, such as A₂ and A₁, on the curve and draw two tangents to the curve. They intersect the axis that shows the room temperature at the two points B₁ and B₂. We project on this axis two perpendiculars from the points A₁ and A₂, to form A₂C₂ and A₁C₁. 4) The difference between the temperature of the body and the environment = A₁C₁ = (θ₁ - θo) 5) The cooling rate of the body at A₁ is proportional to (the slope of the tangent at A₁) = A₁C₁/C₁B₁ 6) If we assume that Newton's law of cooling is correct. The ratio between the cooling rate and the difference between the temperature of the body and the medium must be a constant amount. That is: That is, if the law is correct, the location of the tangent C₁B₁ must be on the room degree axis θo, and it must be a fixed quantity that does not depend on the temperature of point A₁. If we take another point, such as A₂, on the cooling curve and find the location of the tangent at this point on the θo axis, then:- Experimentally, this result was found to be correct, which proves the validity of Newton's law of cooling. Finding the specific heat of a liquid using the cooling method We have two calorimeters that are identical in shape and from the same material. We put a certain volume of water in the first calorimeter and the same volume of liquid in the second calorimeter. If we raise their temperature and then leave them to cool in the air, the cooling rate for each of them will be equal at the same temperature, despite the difference in the thermal nature of each. To conduct the experiment, both water and liquid are heated, then the cooling curve is drawn for each of them, as in the figure. The temperature of a water calorimeter decreases at a lower rate than a liquid calorimeter, because the heat capacity of a gram of water is greater than that of any other liquid. If we assume that m₁ and m'₁ are the empty masses of the two calorimeters and that the specific heat of the substance of each of them is S₁ M₂ and m’₂ are the masses of equal volumes of water and liquid, respectively. The temperature of both calorimeters decreases from θ₂ to θ₁ at times t₁ and t₂, respectively, and can be determined directly from the cooling curves. The cooling rates of water and liquid are equal in the region between θ₂ and θ₁. The cooling rate = an equivalent body of water (multiplies) X rate of temperature loss (dθ/dt). That is:- Where C₂ is the specific heat of the liquid and can be determined from the equation:  Problems 1)A platinum resistance thermometer has a resistance of 7.395 ohms at zero degrees and at 100◦C its resistance is 8.965 ohms. If its resistance in the medium is 8000 ohms, find the temperature of the medium. 2) A body weighing 50 grams was dropped into an oven, then it was thrown into cold water with a mass of 200 grams, so its temperature rose by 5 degrees. Find the temperature of the oven, knowing that the specific heat of the body’s substance is 0.1 cal/g/1ᴼC. 3)A body cools in the air from 45ᴼC to 40ᴼC in 10 minutes, so if the room temperature is 15ᴼC. What is the body temperature after another ten minutes? 4)Two identical copper calorimeters (specific heat 0.1 cal/g/1ᴼC) each weighing 150g, the first containing 100 cm3 of water and the second containing 100 cm3 of liquid. He heated the two calorimeters and then left them to cool in the air. It was found that the temperature dropped from 60ᴼC. To 40°C in a time of 10 minutes for water and a time of 6 minutes for liquid. Find the specific heat of the liquid, given that its density is 0.8 g/cm3. 5)Drop 100 g of ice at -10°C into water at 0°C and find that 10 g of water has frozen and all of them are at 0°C. Find the specific heat of the ice (the latent heat of fusion of ice is 80 calories/g). 6)Find the amount of heat needed to convert 10 g of ice at 0°C into steam at 100°C. 7) Three liquids whose initial temperatures are 27, 19, and 15 °C, respectively. When the first and second were mixed, the temperature of the mixture became 16 °C, and when the second and third were mixed, the temperature of the mixture became 24°C.What is the temperature of the mixture of the first and third? 8)A container with a water equivalent of 50 g contains 450 g of water at 25°C. Heat it with a constant temperature source, so its temperature rises to 30°C in one minute. Find the time it takes for 50 g of water to evaporate when it begins to boil if you know that (the latent heat of sublimation is 540 calories/g). 9)A body cools in the air from 95°C to 90°C in half a minute and from 66°C to 50°C in two and a half minutes. Find the room temperature. Then find the time required for the body temperature to drop from 95°C to 50°C.