# Temperature and Heat

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1 Temperature and Heat Foundation Physics Lecture Jan 10 Temperature, Internal Energy and Heat What is temperature? What is heat? What is internal energy?

2 Temperature Does a glass of water sitting on a table have any energy? Internal Energy No apparent energy of the glass of water on a macroscopic scale. Microscopic kinetic energy is part of internal energy. Molecular attractive forces are associated with potential energy.

3 Atoms, molecules, Phases of Matter Matter (solid, liquid or gas) is made up of atoms and molecules or particles which are in continual motion. Total kinetic energy of the particles in a given body is directly proportional to the absolute temperature of the body. Kinetic energy of the gas molecules would become zero at absolute zero, and molecular motion would cease. Potential energy of the particles is due to electrostatic interactions of the electrons and the nuclei which exert forces on each other. Total internal energy of a body is the sum of potential energy and kinetic energy of the molecules in the body. Phases (solid) Solid Solid: In a solid material, the attractive forces are strong enough that the molecules are packed closely in an orderly way. At the same time, there are also repulsive forces so that the molecules cannot penetrate into one another. Thus the molecules are held in more or less fixed positions. The molecules in a solid vibrate about their nearly fixed positions, usually in an array known as crystal lattice.

4 Phases (Liquid) Liquid: In a liquid, the molecules are moving more rapidly, or the forces between them are weaker, so that they are sufficiently free to roll over one another. Liquid Phases (Gas) Gas Gas: In a gas, the forces are so weak, or the speeds so high, that the molecules do not even stay close together. They move rapidly every which way, filling any container and occasionally colliding with one another. For an ideal gas, the intermolecular forces are assumed to be negligible and thus, potential energy is zero.

5 Microscopic Explanation We look at the interaction potential of to neighbouring atoms E p r 0 r 1 r 0 : Distance between two atoms at T 0 = 0K (minimal thermal motion of the atoms) E r 1 : Average position of the atom at T 1 >T 0 r 1 >r 0 : due to the asymmetry of the potential Thermometers and Temperature Scales Objectives are to: define what a thermometer is describe the physical principles on which the use of a thermometer is based state the Zeroth Law of Thermodynamics, and discuss its physical implications with respect to thermometers explain how a temperature scale is constructed convert temperatures from one scale to another obtain a feel for the range of temperature values in everyday life and throughout the Universe

6 Temperature and Heat Temperature is the physical property which determines the direction of net flow of heat. Heat is the net energy that is transferred from one object to another due to temperature difference between the two objects in thermal contact. Thermal equilibrium exists for two bodies which are in thermal contact with no net flow of heat between them. Zeroth Law of Thermodynamics states that if bodies A and B are separately in thermal equilibrium with a third body C, then A and B are in thermal equilibrium with each other. Scales of temperature The Thermodynamic Scale of Temperature (also known as Kelvin Scale) is totally independent of the properties of any particular substance and is therefore an absolute scale of temperature. The fixed points are the triple point of water ( K or 0.01 C) and absolute zero (0 K or C). The kelvin is the SI unit of temperature in the thermodynamic scale. One kelvin is thus defined to be 1/ of the thermodynamic temperature of the triple point of water. The Celsius Scale is related to the Thermodynamic Scale by the equation t/ o C = T/K

7 Zeroth Law of Thermodynamics If bodies A and B are separately in thermal equilibrium with a third body, C, then A and B will be in thermal equilibrium with each other if placed in thermal contact. Temperature Scales

8 Conversion of temperature sclaes [ ] [ ] ) ( ) ( 32 ) ( 5 9 ) ( 32 ) ( 9 5 ) ( + = + = = C T K T C T F T F T C T Problem: Frozen alcohol makes as good a candle as wax, with one disadvantage: Alcohol melts at -114 o C. What Fahrenheit temperature is this? Temperature Ranges

9 Temperature Ranges Thermal expansion The Golden Gate Bridge has an over all length of ~2800m (mainly steel). If the bridge experiences temperature extremes from -20 o C to +40 o C, what will its change in length be?

10 Bimetalic strip Nanomechanical Transducer Peltier test for sensor mechanical check IBM laboratories, Rüschlikon, Switzerland 500µm long 100µm wide 0.5µm thick def. nm heating test 30s, 0.75 C µm min Functionalized A Functionalized B Functionalized C Fucntionalized D Functionalized E Functionalized F

11 Thermal Expansion Formulae Sample Expansion Problem Find the coefficient of expansion for a mysterious metal bar and use the table 5.1. to identify the metal. A bar with length 300 cm expands by 8.7mm when heated by 100 o C Δl = α l ΔT Δl is the change in length α is the coefficient of expansion ΔT is the temperature change in o C Coefficients of Linear Expansion at 2O o C Solids α (1/ o C) Aluminum 25 x 10-6 Brass 19 x 10-6 Gold 14 x 10-6 Iron or steel 12 x 10-6 Lead 29 x 10-6 Silver 18 x 10-6 Glass (ordinary) 9 x 10-6 Glass (Pyrex) 3 x 10-6 Quartz 0.4 x 10-6 Concrete, brick 12 x 10-6 Marble (average) 2.5 x 10-6 Liquids Ether 550 x 10-6 Ethyl alcohol 370 x 10-6 Gasoline 320 x 10-6 Glycerin 170 x 10-6 Mercury 60 x 10-6 Water 70 x 10-6 Gases Air and most others 1100 x 10-6 at atmospheric pressure

12 Problem: linear expansion copper? In the bimetallic strip shown the upper material is copper. Which of the following materials could be used for the lower metal? a) steel; b) brass; c) aluminum Problem: linear expansion The aluminum cone has been exactly fitted at 20 o C to the copper block. Then it is taken out of the hole and at 180 o C again placed inside. How much does the aluminum cone then stick out of the copper? (α Cu = K -1, α Al = K -1 h2 2 o Al 4 cm Cu h1 3 cm

13 Density In physics, density is mass (m) per unit volume (V) the ratio of the amount of matter in an object compared to its volume. A small, heavy object, such as a rock or a lump of lead, is denser than a larger object of the same mass, such as a piece of cork or foam ρ = m V where, in SI Units: ρ (rho) is the density of the substance, measured in kg m 3 m is the mass of the substance, measured in kg V isthevolumeof the substance, measured in m 3 cgs units grams per cubic centimeter -> 1g/cm 3 =10 3 kg/m 3 Densities of various Substances (unless otherwise specified at 0 o C and 1 atm) Solids Aluminum 2.70 Brass 8.44 Copper' (average) 8.8 Gold 19.3 Iron or steel 7.8 Lead 11.3 Silver 10.1 Uranium 18.7 Concrete 2.3 Cork 0.24 Glass 2.6 Granite 2.7 Wood Ice (0 o C) Bone 1.7 Liquids Water (4 o C) Blood, plasma 1.03 Blood, whole 1.05 Seawater Mercury 13.6 Ethyl alcohol 0.79 Gasoline 0.68 Glycerin 1.26 Olive oil 0.92 Gases (unless otherwise spec. at 0 o C and 1 atm) Air 1.29 x l0-3 Carbon dioxide 1.98 x 10-3 Carbon monoxide 1.25 x 10-3 Hydrogen x l0-3 Helium 0.18 x 10-3 Methane 0.72 x 10 -g Nitrogen 1.25 x 10-3 Nitrous oxide 1.98 x 10-3 Oxygen 1.43 x l0-3 Water (100 o C steam) 60 x l0-3

14 Heat capacity and latent Heat Heat is defined as energy that flows as a result of temperature difference. Heat capacity, C p, of a body is defined as the quantity of heat absorbed or liberated, Q, by the body per unit temperature change,. The S.I. unit for heat capacity is J. K-1. Q= s m ΔT s=specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the temperature of a unit quantity of a substance by a certain temperature interval. Latent heat is defined as the quantity of heat absorbed or liberated by a substance in order to change a substance from one phase to another phase without a temperature change. The SI unit for latent heat is J. Specific latent heat of fusion of a substance,, is defined as the quantity of heat required per unit mass to change the substance from the solid phase to the liquid phase without a change in temperature. Specific latent heat of vaporization of a substance,, is defined as the quantity of heat required per unit mass to change a substance from the liquid phase to the vapour phase without a change in temperature. Specific Heats of various substances at 20 C Substance s (cal/g.º C, kcal/kg.º C) Substance s (cal/g.º C, kcal/kg.º C) Aluminum Brass Copper Gold Iron or steel 0.11 Lead Silver Glass 0.20 Ice (-5 C) 0.50 Porcelain 0.26 Wood 0.4 Human Body (average) 0.83 Protein 0.4 Ethyl Alcohol 0.58 Glycerin 0.60 Mercury Water (15 C) Gases at Constant Pressure Air 0.25 Carbon Dioxide Helium 1.24 Nitrogen Oxygen Water (100 C steam) 0.482

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