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Study Of Thermodynamics

Thermodynamics is the study of Heat Energy and its Transfer. Note: Though realated to Heat Energy, Temperature and Heat Energy are not the same thing. A more formal way to say this is "Temperature reflects the average kinetic energy of the particles in the matter being observed, while heat is the transfr of thermal energy across a system boundary into the body or from the body to the environment.".

Heat and Temperature:

In the beginning of this study it is often easy to mix up heat and temperature, however they are two distinct concepts. Heat is thermal energy and is measured as a quantity in units such as joules in physics, though often it is still referred to using the term calorie, especially when discussing the energy content of foods. (Note: the heat calories is not the same as a food calorie, though there is a connection between the two.) Temperatre is a measure of the avergae kinetic energy of the particles making up an object (or a substance). Temperatures are expressed in terms of degrees of change and therefore are associated with temperature scales. The amount of change or difference in what the degree represents is based on the person who invented or defined the scale they created in the first place. The most common temperature scales, though not the only ones, are the Fahrenheit, the Celsius, and the Kelvin scales.

Now it is interesitng to think about how you would mesure temperature if you had had no opportunity to have learned about other people's temperature scales, or access to thermometers based on their temperature scales. Take a moment to think about how you or anyone else might go about making a thermometer and coming up with a temperature scale. In some children's science books found in many good library's children sections, it is suggested that you might start out with a drinking straw and a liquid such as water colored with a food dye. In the historical world of science, its seems more likely that early scientists used a glass tube, and probably a liquid more responsive to heat change than collored water. Now give this some serious thought as we explore how these people went about developing a thermometer and inventing a temperature scale.

While other liquids may be used, early scientists used the liquid Mercury (No one reliazed how toxic mercury was before the 20th century). Its a curious element in that it is a liquid metal at room temperature and remains a liquid over a broad range of temperatures. The first discovery in this endeavor was to observe that in a sealed glass tube, a small amount of mercury would expand when the tube was warmed, and it would contract when it was cooled. This gave these individuals the idea that here was a tool that could be used to measure changes in heat of most any object, substance, or environment that the glass tube could survive in. Now they quickly recognized that this tool would not be able to measure the actual heat content of a substance, but it might be used to measure a degree of change within the substances heat content. They soon realized that to identify the change, they needed some reference points so they might have something to to which to compare the level of the liquid in the tube. They also knew that they would need easily accessble and reproducible environments to determine the reference points to be marked on the each thermomenter that they made. Yup! They had to make each of the themometers by hand since there was no mass produced lab equipment supply houses available back in the day. Every scientist had to pretty much make their own lab equipment. So the next thing to consider is "who did what?"

Fahrenheit: Daniel Gabriel Farhenheit proposed his temperature scale in 1724. He decided to use brine (salt water) cooled as low as he could possibly make it for his lowest mark on his newly made glass tube, and human body temperature as his highest mark on the glass tube. These two marks represented his "0 degree" and his "100 degree". Today after many others have doe research on temperature and invented other perhaps more precise temperature scales using the boiling and freezing points of water as references, his scale defines the boiling point of water as 212 degrees Fahrenheit, and the freezing pint of water as 32 degrees Fahrenheit.

Celsius: Anders Celsius (1701 - 1744) created a temperature scale that was based on one of the reference points being the freezing point of water, and indicated as "0 degrees Celsisu", and the the other being based on the boiling point of water, and indicated as "100 degrees Celsius". Of course he, himself, did not name his temperature scle after himself, rather he called it the centigrade temperature scale. He divided the distance between the freezing point and boiling point of water into 100 equal spaces, or degrees, when he defined the freezing point of water as 0 degrees, and the boiling point of water as 100 degrees. It was only later that in honor of his work the name of the temperature scale was chenged from centigrade to Celsius.

Kelvin: William Thomson, who recived the title Lors Kelvin, an engineer and physisist, back in 1848, was looking for a temperature scale that would define zero degrees as the point of infinite cold, as in there is no more heat to be drained out of a system. Through research and using gas laws he established that point as being a -273.16 degrees Celsius. In simple terms he defined that as absolute zero, and using the same size degree of change as the Celsius temperature scale, defined the Kelvin scale as a scale without negative temperatures. This resulted in the freezing point of water being defined on his scale as 273.16 K, and the boiling point of water being defined as 373.16 K. The degree symbol is not used with the Kelvin scale since 1968 when the degree symbol was dropped from the Kelvin temperature measurements.

Temperature Conversions: As it turns out when comparing these three afore mentioned temperature scales that the Kelvi and the Celsius degree sizes are the same. So converion between these two temperaure scales is relatively simple. However, because the degree size on the Farhenheit scale is only 5/9 as large as the degree size on the Celsius scale, the equation to convert between them requires more than one step.

Farhenhenheit -> Celsius: ______Deg C = (_____Deg F - 32) * (5/9)

Celsius -> Fahrenheit: ______Deg F = (9/5) * _____Deg C + 32

Celsius -> Kelvin: _____K = _____Deg C + 273.16

Kelvin -> Celsius: _____Deg C = _____K - 273.16

Equilibrium and Thermometry:

To measure temperature a thermometer has to be in contact with the object, substance, or environment. As the thermometer is brough in contact with the thing it is to measure the temperature of, it achieves a thermal equilibrium with the thing it is to be measuring. The heat energy of the an object, substance, or environment, is described in terms of the kinetic energy of the particles making up the object, substance, or environment. So as a thermometer is iontroduced into the system, it will be in one of three states. 1. the particles of the liquid inside of the thermometer will have the same kinetic energy as the object's particles that the thermometer has made contact with, and so the level of the liquid will remain the same. 2. the particles of the liquid inside the thermometer have less kineteic energy than the particles of the object with which it is in contact, resulting in some of this energy to be transferred to the particles of the liquid in the themometer... this increase in kinetic energy results in the liquid in the thermometer expanding unitl it reaches an equilibrium state with the particles of the object with whch the thermometer has made contact. 3. the particles of the liquid inside the thermometer have more kineteic energy than the particles of the object with which it is in contact, resulting in some of this energy to be removed from the particles of the liquid in the themometer... this decrease in kinetic energy results in the liquid in the thermometer comtracting unitl it reaches an equilibrium state with the particles of the object with whch the thermometer has made contact. These three statement descibe what happens to a thermometer when it is used to measure the temperature of an object, substance, or environment. As compared to the freezing / boiling point definition of the particular scale you can read the degree of difference of the thing whose temperature is being measured. Now of what use is that to you other than having a degree of difference between the object being measured and one or two reference points. Well, for starters you can compare one of more things' temperatures as a weatherperson is always doing on the news. You can also relate temperature changes to heat energy changes as we shall see as we continue with these notes.

At this point there is an interesting question that could be raised. It is "How is heat energy moved or transferred?". Well as most science teachers and sceintists will tell you, there are three common ways the heat energy can be transferred. Each is descibed below.

Conduction: Heat can be trtnsferred through direct contact. This is why you have to either have special handles on pots and pans when you cook or use some sort of hot pads to protect your hands when handing such hot object when you are cooking.

Convection: Using another reference from the kitchen, if you look carefully at a pot of water as it is heating, you'll notice that the water at the bottom of the pot is heated by conduction, but then that heated water rises towards the top, while the cooler waer sinks to the bottom. This movement of heated particle through cooler particles is what we mean by convection. Steam heat distributed through radiators uses this same principle. The hot radiator heats the air in contact with it. The heated air rises and moves across the ceiling of the room, while the cool air in the room deecends and cisulates towards the radiators. This cylce continues over and over again keeping the room relatively warm.

Radiation: The easiest example of this form of heat transfer, is the sun itself. It sends out enormous amounts of heat energy everyday in the form of radiation. If you are sitting behind a glass window on a day when its cool outside, you can feel the heat radiation coming through the window glass in the form of infrared wave energy.

Specific Heat: This is a useful concept when ascertaining energy changes in an object when it is heated or it is cooled. It falls within the category of measurements referred to as Heat Capacity, which is the measurable physical quantity of heat energy required to change the temperature of an object by a givem amount. Specific Heat is defined as the heat capacity per unit mass of a material. In physics the units to express specific heat values are "J / Kg K", where J is joules, Kg is kilograms, and K is kelvins. In the equation below, which allows you to calculate the total heat transferred. Q is the amount of heat energy transferred into or out of a material when heat is added or removed from of the material, m is the mass of the material, and /\T is the change in temperature due to the addition or the removal of heat energy to or from the material.

Specific Heat Equation: Q = m * c * /\T ... where "c" is the symbol for the heat capacity as defined by the term specific heat.

Some Common Substances' Specific Heats: All values have the following unit... J / Kg K

Aluminum - 897... Brass - 376... Carbon - 710... Copper - 385... Glass - 840... Ice - 2060... Iron - 450... Lead - 130... Methanol - 2450... Silver - 235... Steam - 2020... Water - 4180... Zinc - 388

Change of State: The word state is used similar to the word phase as in "what state or phase is a material found to be in?". The states or phases that materials are found in are solid, liquid, gas, and plasma (This is not blood plasma, but rather is a highly energized gas where electrons have been stripped off of the atoms and only charged particles are moveing around.). At room tempearature (~22 deg C -> 25 deg C, depending on who is doing the reporting) materials are usually found to be in one of three states, solid, liquid, or gas. Plasma requires a different kind of environment, so under ordinary circumstances we would not expect to find a substacne in a plasma state at room temperature.

Phase changes or changes in state of substances, occur at specificly defined temperatures. For example Melting (solid -> liquid) occurs at a melting point temperature, and boiling (liquid -> gas) occurs at a boiling point temperature. FYI, a substance's freezing point temperature is the same as it melting point. Its just a matter of whether heat is being added causing melting, or heat is being removed causing freezing. likewise the condensation point is the same as the boiling point, and it too is just a mater of whether heat is being added or removed in terms of what you call the temperature. Each material / substance has it own unique phase change temperatures.

Heat of Fusion: This can be described as the change in heat energy required to change the state of a defined amount of a material going from solid to liquid or from liquid to solid. (Remember states of matter refer to solid, liquid, and gas (also included is plasmas).

Heat of Fusion Equation: Q = m * Hf ... where Hf is the symbol for the heat of fusion of a material.

Some Common Substances' Heats of Fusion: All values have the units J / Kg ... there is no /\T value, becasue during phase changes the temperature remains fixed at the Melting / Freezing point temperature.

Copper - 2.05 x 10^5 ... Mercury - 1.15 * 10^4 ... Gold - 6.30 * 10^4 ... Methanol - 1.09 * 10^5 ... Iron - 2.66 * 10^5 ... Silver - 1.04 * 10^5 ... Lead - 2.04 *10^4 ... Water (ice) - 3.34 * 10^5

Heat of Vaporization: This can be defined as the chnage in heat energy required to change the state of a defined amount of material going from liquid to gas or from gas to liquid. (Remember states of matter refer to solid, liquid, and gas (also included is plasmas).

Heat of Vaporization Equation: Q = m * Hv ... where Hv is the symbol for the heat of vaporization.

Some Common Substances' Heats of Vaporization: All values have the units J / Kg ... there is no /\T value, becasue during phase changes the temperature remains fixed at the Boiling / Condensation point temperature.

Copper - 5.07 x 10^6 ... Mercury - 2.72 * 10^5 ... Gold - 1.64 * 10^6 ... Methanol - 8.78 * 10^5 ... Iron - 6.29 * 10^6 ... Silver - 2.36 * 10^6 ... Lead - 8.64 *10^5 ... Water (ice) - 2.26 * 10^6

Calorimetry: Though in physics and more and more in the other sciences energy is now expressed in the unit defined as the joule, the calorie is still used as a unit of energy in some instances and the process of determining values such as specific heat as well as other values involving heat transfer still uses terms derived from the word calorie. The term calorimetry is often described in terms of words and phrases as described here ... "Calorimetry is the process of determining changes in the values of chemical reactions, physical changes and phase changes, for the purpose of deriving the heat or heat transfer associated with those changes.". The device most often used to determine such values is a calorimeter, which usually consists of an outer cup separated from an inner cup with a layer ofsome sort of insulation and sealed with a non-heat conducting lid. A thermometer of some sort is inserted through a tiny hole in the lid so any temperature change occuring within the inner cup can be monitored as a process takes place within the inner cup. The purpose of the insulation is to prevent any heat energy from being passed between the process occuring in the inner most cup and the outside environment. A calorimeter provides an isolated, closed system in which to measure energy transfer.

A Common Form of a Calorimetry Equation: Q(hot) = Q(cold) where the Q's may be those of specific heats, heats of fusion, or heats of vaporization. The whole concept is that when two different materials at different temperature meet in the cup, heat will flow from the hot object (the one with more heat energy) to the cold object (the one with less energy). Eventually a state of thermal equilibrium will be achieved when the temperature within the container stops changing. The result is the two objects intially having different temperature when intially introduced into the calorimeter together, have reached a point where they now have the same temperature, what is called an equilibrium temperature. From such a process things like an unknown soecific heat value can be calsulated assuming all other parameters are known.e

Example of an Expanded Calorimetry Equation: m(hot material) * c(hot material) * /\T(hot material) = m(cold material) * c(cold material) * /\T(cold material) ... if the inner calorimeter cup is made of a heat conducting material, another m*c*/\T has to be added to the cold side of the equation to allow for the inner cups participation in the heat exchange process. Remember "m" is mass, "c" is specific heat (a form of heat capacity), and /\T refers to a temperature change in a material (as in T(final) minus T(initial) or simply /\T = Tf - Ti).

Thermal Expansion: It is known through qualitative observations as well as quantitative observations (measurements) that in general materials tend to expand when heated and to contract when cooled. To quantify the amount of thermal expansion, and contraction in solids and liquids researchers developed a term called "Coeffcient of Thermal Expansion". Each substance either a solid or liquid will most often ahve its coeffcient of thermal expansion predetermined and it can be looked up in a table somewhere such as in a CRC Handbook, or online on a website addressing such concepts. (CRC originally stood for Chemical Rubber Company, but now refers to a very large comprehensive handbook of sceince information called the CRC Handbook of Chemistry and Physics)

Expansion of Solids: We begin the study of thermal expansion by examining the concept of linear expansion. When solid substances are heated they tend to expand and observing lengh expansion is not that difficult, especailly since it affects a number of things in our live, such as roads, railroad tracks, and structures like bridges. Most things that humans build on a large scale require expansion joints, whcih are designed spaces in the structure being built where certain parts of the structure have a space in which to expand so the enitire structure does not experience stress forces that cause the entire sturcture to buckle and/or collapse. Examples of failure to account for thermal expansion in terms of construction of railroad track, bridges, and buildings in general, can be found with a little effort. In terms of thermal expansion we tend to most often find a correlation between the amount of expansion and the change in temperature. This relationship can be expressed in terms of the measurements we call Coeffcients of Thermal Expansion. The symbol for the coeffcients of solid linear expansion is the greek letter alpha.

Coefficient of Linear (L) Solid Expansion Equation: L(new) = Lo + alpha * Lo * /\T) or /\L = alpha * Lo * /\T... where alpha is the coeffcient of linear exapansion of solids, L(new) is the new length, Lo is the original length, and /\T is the change in temperature. Also alpha = /\L / (Lo * /\T).

Some Coefficient of Solid Linear Exapansion: The unit for the coeffcient is what ever the unit of length happens to be (usually a meter) divided by the unit Celsius degree ... i.e. m/C deg.

Aluminum ... Glass (soft) - 25 * 10^-6 (or 2.5 * 10^-5)... Glass (ovenproof) - 9 * 10^-6... Concrete - 3 * 10^-6... Copper 16 * 10^-6 (or 1.6 * 10^-5... Note for the sake of easy comparison, some values are not written in correct scientific notation.

Coefficent of Solid Surface Area Exapansion Equation: A(new) = Ao + 2 * alpha * Ao * /\T

Coefficent of Solid Volume Expansion Equation: V(new) = Vo + 3 * alpha * /\T

Coffcient of Liquid Volume Exapansion Equation: Liquids do not have a length, a width, or a height / thickness, and so they do not have an alpha value. Their coefficents of thermal expansion are determined independently of any alpha value and have their own designated value called a beta value.

Some Coefficents of Liquid Volume Exapansion: the unit is that ever the volume unit measure is divided by degree Celsius ... i.e. liter / C deg,

Methanol - 1200 * 10^-6 (or 1.200 * 10^-3)... Gasoline - 950 * 10^-6 (or 9.50 * 10^-4... Water - 210 * 10^-6 (or 2.10 * 10^-4)

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