Physics Principles of Physics
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1 Physics Principles of Physics Lecture 33 Chapter 17 November 19, 2008 Announcements Lecture notes SI Session (Mitchell Lowery) Thu. 4:30 6:00 Holden Hall 226 Sung-Won Lee Sungwon.Lee@ttu.edu Chapter 17 Temperature, Thermal Expansion, and the Ideal Gas Law Contents!Atomic Theory of Matter!Temperature and Thermometers!Thermal Equilibrium & the 0-th Law of Thermodynamics!Thermal Expansion & Thermal Stress!The Gas Laws and Absolute Temperature!The Ideal Gas Law!Ideal Gas Law in Terms of Molecules!Ideal Gas Temperature Scale
2 17-1 Atomic Theory of Matter Atomic and molecular masses are measured in unified atomic mass units (u). This unit is defined so that the carbon-12 atom has a mass of exactly u. Expressed in kilograms: 1 u = x kg Brownian motion is the jittery motion of tiny flecks in water; these are the result of collisions with individual water molecules Atomic Theory of Matter Atomic arrangements in (a) a crystalline solid, (b) a liquid, and (c) a gas. On a microscopic scale, the arrangements of molecules in solids (a), liquids (b), and gases (c) are quite different. Path of a tiny particle (pollen grain, for example) suspended in water. The straight lines connect observed positions of the particle at equal time intervals Atomic Theory of Matter Example 17-1: Distance between atoms. The density of copper is 8.9 x 10 3 kg/m 3, and each copper atom has a mass of 63 u. Estimate the average distance between the centers of neighboring copper atoms. Temperature is a measure of how hot or cold something is. Most materials expand when heated. Expansion joint on a bridge
3 Thermometers are instruments designed to measure temperature. In order to do this, they take advantage of some property of matter that changes with temperature. Early thermometers: Thermometers built by the Accademia del Cimento ( ) in Florence, Italy!! A thermometer is a device that is used to measure the temperature of a system!! Thermometers are based on the principle that some physical property changes as the system s temperature changes!!!! These properties include:!! The volume of a liquid!! The dimensions of a solid!! The pressure of a gas at a constant volume!! The volume of a gas at a constant pressure!! The electric resistance of a conductor, etc!! A temperature scale can be established on the basis of any of these physical properties Common thermometers used today include the liquid-in-glass type and the bimetallic strip. (left) Mercury- or alcohol-inglass thermometer (right) Bimetalic strip a thermometer using a coiled bimetallic strip.!! A common type of thermometer is a liquid-inglass!! The liquid is usually mercury or alcohol!! As a result of thermal expansion, the level of the mercury in the thermometer rises as the mercury is heated by water in the test tube. Liquid in Glass
4 Temperature is generally measured using either the Fahrenheit or the Celsius scale. The freezing point of water is 0 C, or 32 F; the boiling point of water is 100 C, or 212 F. T( 0 C) = 5/9[T( 0 F) -32] T( 0 F) = 9/5T( 0 C) +32 Celsius and Fahrenheit scales compared. Example 17-2: Taking your temperature. Normal body temperature is 98.6 F. What is this on the Celsius scale? T( 0 C) = 5/9[T( 0 F) -32] so, 37 0 C Reminder; Temperature!! We associate the concept of temperature with how hot or cold an objects feels!! Our senses provide us with a qualitative indication of temperature. Our senses are unreliable for this purpose!! So, we need a technical definition of temperature Thermal Contact!! Two objects are in thermal contact with each other if energy can be exchanged between them!! The exchanges will be in the form of heat!! Again, the energy is exchanged due to a temperature difference Calibrating a Thermometer!! A thermometer can be calibrated by placing it in contact with some natural systems that remain at constant temperature!! Common systems involve water!! A mixture of ice and water at atmospheric pressure!! Called the ice point of water!! A mixture of water and steam in equilibrium!! Called the steam point of water Celsius Scale!! The ice point of water is defined to be 0 o C!! The steam point of water is defined to be 100 o C!! The length of the column between these two points is divided into 100 increments, called degrees
5 17-3 Thermal Equilibrium 17-3 Zeroth Law of Thermodynamics!! Thermal equilibrium is a situation in which two objects would not exchange energy by heat if they were placed in thermal contact Zero-th Law of Thermodynamics!! If objects A and B are separately in thermal equilibrium with a third object C, then A & B are in thermal equilibrium with each other!! Let object C be the thermometer ( see next slide)!! Note: Since they are in thermal equilibrium with each other, there is no energy exchanged among them!! C (thermometer) is placed in contact with A until they achieve thermal equilibrium!! C is then placed in contact with B until they achieve thermal equilibrium!! If the two readings are the same, A and B are also in thermal equilibrium 17-4 Thermal Expansion 17-4 Thermal Expansion Linear expansion occurs when an object is heated. A thin rod of length l 0 at temperature T 0 is heated to a new uniform temperature T and acquires length l, where l = l 0 +!l. Here,! is the coefficient of linear expansion.
6 17-4 Thermal Expansion Example 17-3: Bridge expansion. The steel bed of a suspension bridge is 200 m long at 20 C. If the extremes of temperature to which it might be exposed are -30 C to +40 C, how much will it contract and expand? 17-4 Thermal Expansion Conceptual Example 17-6: Opening a tight jar lid. When the lid of a glass jar is tight, holding the lid under hot water for a short time will often make it easier to open. Why? The lid may be struck by the hot water more directly than the glass and so expand sooner. Also, metals generally expand more than glass for the same temperature difference.! (coefficient of linear expansion) is greater Thermal Expansion 17-4 Thermal Expansion Volume expansion is similar, except that it is relevant for liquids and gases as well as solids: Example 17-7: Gas tank in the Sun. The 70-liter (L) steel gas tank of a car is filled to the top with gasoline at 20 C. The car sits in the Sun and the tank reaches a temperature of 40 C (104 F). How much gasoline do you expect to overflow from the tank? Here, " is the coefficient of volume expansion. For uniform solids, " " 3!.
7 17-4 Thermal Expansion Water behaves differently from most other solids its minimum volume occurs when its temperature is 4 C. As it cools further, it expands, as anyone who leaves a bottle in the freezer to cool and then forgets about it can testify Thermal Stresses A material may be fixed at its ends and therefore be unable to expand when the temperature changes. It will then experience large compressive or tensile stress thermal stress when its temperature changes. The force required to keep the material from expanding is found from: where E is the Young s modulus of the material. Therefore, the stress is: Behavior of water as a function of temperature near 4 C. (a) Volume of 1 g of water, as a function of temperature. (b) Density vs. temperature. Summary so far..!all matter is made of atoms.!atomic and molecular masses are measured in atomic mass units, u.!temperature is a measure of how hot or cold something is, and is measured by thermometers.!there are three temperature scales in use: Celsius, Fahrenheit, and Kelvin.!When heated, a solid will get longer by a fraction given by the coefficient of linear expansion.
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