Physics 111 Lecture 35 (Walker: 16.1-3) Thermal Physics I: Temperature Thermal Expansion April 29, 2009 Lecture 35 1/26 Temperature (T) Temperature (T) is a measure of how hot or cold something is Temperature is a measure of the random kinetic energy of each particle in an object. The greater the motion/vibration the greater the T The smaller the motion/vibration the lower the T SI Unit: kelvin (K) E.g., room temperature is about 295K Kelvin is the natural temperature scale 0 K is lowest possible temperature No negative temperatures Random internal KE is zero at T = 0 K Lecture 35 2/26
Random kinetic energies of atoms at different temperatures. Low T liquid. High T liquid. Lecture 35 3/26 The Three Basic Phases of Matter Solid Liquid Gas Sequence of increasing molecule motion (and energy) Lecture 35 4/26
Other Temperature Scales The Celsius scale: Water freezes at 0 Celsius. Water boils at 100 Celsius. The Fahrenheit scale: Water freezes at 32 Fahrenheit. Water boils at 212 Fahrenheit. Lecture 35 5/26 Kelvin Temperature Scale The Kelvin scale has the same step size (size of one degree) as the Celsius scale, but the Kelvin scale has its zero at absolute zero. Conversion between a Celsius temperature and a Kelvin temperature: Lecture 35 6/26
Temperature Scales Compared Lecture 35 7/26 Thermometers Thermometers are instruments designed to measure temperature. In order to do this, they take advantage of some property of matter that changes with temperature. Length of a solid or liquid column Volume of a solid, liquid, or gas Electromagnetic waves (infrared light) given off by hot objects Lecture 35 8/26
Common thermometers used today include the liquid-in-glass type and the bimetallic strip. Lecture 35 9/26 Thermoscan Ear Thermometer - Reads infrared light emission from body. Lecture 35 10/26
Thermal Expansion Most substances expand when heated; the change in length or volume is typically proportional to the change in temperature. Linear expansion occurs when an object is heated. The increased atomic motion at higher temperatures keeps the atoms further apart. Here, α is the coefficient of linear expansion. Lecture 35 11/26 L = L 0 + L Example: Steel bridge is exactly 1000m long when T=10 C. How long is it at 40 C? L = αl 0 T = (12x10-6 / C)(1000m)(30 C) = 0.36m L = L 0 + L = 1000.36m Lecture 35 12/26
Coefficients of Linear Expansion Lecture 35 13/26 Thermal Expansion Differences A bimetallic strip consists of two metals of different coefficients of thermal expansion, A and B in the figure. It will bend when heated or cooled. Lecture 35 14/26
Thermal Expansion of Areas The expansion of an area of a flat substance is derived from the linear expansion in both directions: Holes expand as well: Lecture 35 15/26 You have a (glass) jar and you can t get the metal lid off. What should you do: a) ask your friend b) run the jar & lid under cold water c) run the jar & lid under hot water Lecture 35 16/26
You have a (glass) jar and you can t get the metal lid off. What should you do: a) ask your friend b) run the jar & lid under cold water c) run the jar & lid under hot water Because the metal has a substantially higher coefficient of thermal expansion than the glass, heating them will make both of them bigger, but the metal will be more bigger. Lecture 35 17/26 Volume Thermal Expansion The change in volume of a solid is also derived from the linear expansion: V = βv T 3αV T Liquids and gases have relatively large volume expansion. V = V 0 + V Lecture 35 18/26
Air 3.7 x 10-3 Lecture 35 19/26 Example Balloon containing 0.1m 3 of air at 10 C heated to 50 C. What is new volume? V = βv T = (3.7x10-3 / C)(0.1m 3 )(40 C) = 0.015 m 3 V = V 0 + V = 0.115 m 3 Lecture 35 20/26
Thermal Expansion of Water 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 has left a bottle in the freezer to cool and then forgets about it can testify. Lecture 35 21/26 Water Density vs. Temperature This explains why lakes freeze from the top. Lecture 35 22/26
Definition of heat: Heat (Q) Heat is the energy transferred between objects because of a temperature difference. Can think of heat as disordered work. Random KE in one object transfers to random KE in another by collisions and other methods. Objects are in thermal contact if heat can flow between them. When the transfer of heat between objects in thermal contact ceases, they are in thermal equilibrium. (The objects will then be at the same temperature.) Lecture 35 23/26 Units for Heat Since heat is just a flow of energy, the SI unit is the energy unit, the joule (J). Other heat units calorie (cal): Heat needed to raise temperature of 1 gram of water by 1 C (or 1 K) Calorie (Cal or kcal): Heat needed to raise temperature of 1 kg of water by 1 C (or 1 K) Calorie also used to measure energy content of food Conversions: 1 cal = 4.186 J 1 kcal = 1 Cal = 4.186 kj These factors called mechanical equivalent of heat Lecture 35 24/26
End of Lecture 35 For Friday, May 1, read Walker 16.4-5. Homework Assignment 16a is due at 11:00 PM on Friday, May 1. Lecture 35 25/26