Physics Notes - Week of 4.4.16
Physics Notes - Week of 4.4.16 PHYS2001
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This 15 page Class Notes was uploaded by Grace Lillie on Monday April 11, 2016. The Class Notes belongs to PHYS2001 at University of Cincinnati taught by Alexandru Maries in Fall 2016. Since its upload, it has received 13 views. For similar materials see College Physics 1 (Calculus-based) in Physics 2 at University of Cincinnati.
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Date Created: 04/11/16
Chapter 19 – Temperature 19.1 – Temperature and the Zeroth Law of Thermodynamics - You don’t feel actual temperature; you feel the rate of energy transfer by heat - Two objects at different temperatures will reach an intermediate temperature when in contact - thermal contact—energy can be exchanged between them due to temperature difference by heat or electromagnetic radiation - thermal equilibrium—two objects don’t exchange energy by heat or electromagnetic radiation when placed in thermal contact - zeroth law of thermodynamics—If objects A and B are separately in thermal equilibrium with a third object, C, then A and B are in thermal equilibrium with each other. - temperature—the property that determines whether an object is in thermal equilibrium with other objects. Two objects in thermal equilibrium have the same temperature 19.2 – Thermometers and the Celsius Temperature Scale - some physical properties change with temperature: volume of a liquid, dimensions of a solid, pressure of gas at constant volume, volume of a gas at constant pressure, electric resistance of a conductor, color - mercury thermometers use change in volume to measure change in temperature - Celsius temperature scale—based on the ice point and steam point (0° and 100°C) - liquid thermometers depend on the substance used (mercury, alcohol, etc.) 19.3 – The Constant-Volume Gas Thermometer and the Absolute Temperature Scale - constant-volume gas thermometer uses variations in pressure of a gas at a fixed volume - temperature readings are nearly independent of the type of gas used **pressure is zero when temperature is -273.15°C basis of the absolute temperature scale - absolute temperature scale—zero point at -273.15°C, or absolute zero - to convert Celsius to absolute temperature: T K T C 273.15 degree size is the same - ice and steam points vary with atmospheric pressure, so a new absolute temperature scale developed - based on absolute zero and the triple point of water—when liquid, solid, and gaseous water coexist in equilibrium (0.01°C) - called the Kelvin scale, with SI unit of absolute temperature, kelvin 9 - Fahrenheit scale—ice point is 32°F, steam point is 212°F. T F T +3C° F 5 ***ALWAYS CONVERT TEMPERATURES TO KELVINS*** 19.4 – Thermal Expansion of Solids and Liquids - thermal expansion—volume increases as temperature increases - average coefficient of linear expansion—α ∆ L=αL ∆T i Thermal expansion in one dimension (linear) - average coefficient of volume expansion—β ∆ V=βV ∆T i Thermal expansion in three dimensions - water is weird: it expands from 0°C to 4°C and contracts about 4°C (why the surface of ponds freeze) 19.5 – Macroscopic Description of an Ideal Gas - ideal gas—a low-density gas used to simplify equations - ideal gas model—used to make predictions to describe the behavior of gases at low pressures - mole—on mole of a substance is 6.022e23 particles. Number of moles, n=m/M, where M is molar mass - Avagadro’s number—N = 6.0A2*10 23 PV=nRT equation of state for an ideal gas, also known as the ideal gas law - n is the number of moles of a gas - R is the universal gas constant and equals 8.314 J/mol·K - the volume of any gas at atmospheric pressure and 0°C is 22.4L PV=Nk T B the ideal gas law, where N is the total number of molecules - Boltzmann’s constant—k = 1.38*10 -23J/K B - thermodynamic variables—P,V, and T Chapter 20 – The First Law of Thermodynamics 20.1 – Heat and Internal Energy - internal energy—all the energy of a system that is associated with its microscopic components (atoms and molecules) when views from a reference frame at rest with respect to the center of mass of the system - heat—a process of transferring energy across the boundary of a system because of a temperature difference between the system and its surroundings. Also the amount of energy Q transferred by this process * Heat is not energy in a hot substance internal energy * Heat is not radiation electromagnetic radiation * Heat is not warmth of an environment temperature - calorie (cal)—the amount of energy transfer necessary to raise the temperature of 1 g of water from 14.5°C to 15.5°C. - the U.S. customary system unit is the British thermal unit (Btu) - mechanical equivalent of heat—the equivalence between mechanical energy and internal energy: 1 cal = 4.186 J 20.2 – Specific Heat and Calorimetry - heat capacity (C)—the amount of energy need to raise the temperature by 1°C: Q=C ∆T Q - specific heat (c)—the heat capacity per unit mass: c= m ∆T - the greater the specific heat, the more energy needs to be added to change the temperature - Q=mc∆T - calorimetry—a method of measuring specific heat using a calorimeter - heat a sample to a known temperature and put in vessel of water of known mass and temp. - Qcold -Qhot - m w w(−f =−w)c (T xTx) f x 20.3 – Latent Heat - phase change—physical characteristics of a substance change (e.g. melting, boiling) - latent heat—this added or removed energy doesn’t result in temperature change: L= Q ∆m Q=L∆m energy transferred to a substance during a phase change - latent heat of fusion—solid to liquid (L f - latent heat of vaporization—liquid to gas (L ) v - supercooling—like when water drops below 0°C without freezing (perfectly clean, still water) then requires a disturbance to move the molecules and suddenly freeze (look it up on YouTube it’s nifty) - superheating—like if you microwaved clean water and the water doesn’t boil at 100°C because there are no scratches in the cup or impurities in the water. When you take it out of the microwave the disturbance makes the water explosive as bubbles form immediately. 20.4 – Work and Heat in Thermodynamic Processes - state variables—pressure, volume, temperature, internal energy - transfer variables—have nonzero value if a process transfers energy across the system’s boundary - quasi-statically—slowly enough that the system remains essentially in internal thermal equilibrium f W=− P∫V Work done on a gas i - PV diagram—used to visualize a process through which a gas is progressing The work done on a gas in a quasi-static process from an initial to final state is the negative of the area under the curve on a PV diagram 20.5 – The First Law of Thermodynamics ∫ ¿=Q+W - first law of thermodynamics: ∆ E ¿ - cyclic process—starts and ends at the same state: change in internal energy is zero so Q = -W 20.6 – Some Applications of the First Law of Thermodynamics ¿=W - adiabatic process—no energy enters or leaves by heat (Q=0): ∫ ∆E ¿ - adiabatic free expansion—both Q and W equal zero - isobaric process—pressure is constant: W=−P(V −Vf) i ∫ ¿=Q - isovolumetric—volume is constant: ∆E ¿ Q=−W - isothermal process—temperature is constant: * Q≠0 energy entering the bas by heat leaves by work so temperature is constant Vf W=− PdV=nRT ln Vi ∫ (V) Vi f 20.7 – Energy Transfer Mechanisms in Thermal Processes - conduction or thermal conduction—energy transfer by heat, represented on an atomic scale as an exchange of kinetic energy between microscopic particles dT P=kA |dx law of thermal conduction - P is the rate of energy transfer by conduction through the object - k is the thermal conductivity of the material - |dT/dx| is the temperature gradient (rate temperature varies with position) - good thermal conductors have higher thermal conductivities A(T −T ) P= h c - for multiple thicknesses and thermal conductivities: ∑ (Li/ki) i A(T hT c) - R-value—the term L/k, so: P= ∑ Ri i - convection—energy transferred by the movement of a warm substance - natural convection results from differences in density, like air around a fire - forced convection is when the heated substance moves because of a fan or pump - thermal radiation—all objects radiate energy as electromagnetic waves caused by thermal vibrations of molecules 4 P=σAeT Stefan’s law - P is the power in watts of electromagnetic waves from the surface of the object -8 2 4 - σ = 5.6696*10 W/m ·K - A is surface area - e varies between 0 and unity depending on the object’s properties o emissivity = absorptivity—fraction of the incoming radiation the surface absorbs o a mirror has very low absorptivity and emissivity; black surface has very high values o ideal absorber—absorbs all the energy incident on it: e=1. also called black body - Dewar flask minimizes energy transfers by conduction, convection, and radiation (like a Thermos) Chapter 21 – The Kinetic Theory of Gases 21.1 – Molecular Model of an Ideal Gas - structural model—theoretical, used to represent a system that cannot be observed directly - kinetic theory—structural model that treats an ideal gas as a collection of molecules with: 1. Physical components: The gas is made of identical molecules inside a cube of side length d. There are a lot of molecules, and the distance between them is large compared to their size So, they occupy negligible volume in the container (the molecules are considered point-like) 2. Behavior of the components: (a) The molecules obey Newton’s laws, but have isotropic motion: each can move in any direction at any speed (b) They interact only by short-range forces during elastic collisions (c) They make elastic collisions with the walls 2 N 1 ´2 P= 3 V ) (2m 0 ) relationship between pressure and molecular kinetic energy - pressure of a gas is proportional to the number of molecules per unit volume and the average translational kinetic energy of the molecules 2 1 2 T= ( m 0 ) relationship between temperature and molecular kinetic energy 3k B 2 1m v = k T 2 0 2 B Average kinetic energy per molecule - theorem of equipartition of energy—Each degree of freedom contributes 3 kBT to the energy of a system, where possible degrees of freedom are 2 associate with translation, rotation, and vibration K =N 1m v = N k T= nRT totaltra(2 0 ) 2 B 2 Total translational kinetic energy of N molecules 3k T 3RT vrmsv√=2 B = root-mean-square (rms) speed of the molecules √ m0 √ M - at a given temperature, lighter molecules move faster than heavier molecules 21.2 – Molar Specific Heat of an Ideal Gas Q=nC ∆V using molar specific heat at constant volume Q=nC ∆T P using molar specific heat at constant pressure. Notes:PC VC 3 3 ∫ ¿=K tot transTB nRT 2 2 Internal energy of an ideal monatomic gas E¿ ∫ ¿=nC VT ∆E ¿ applies to all ideal gases C −C =R C = 3R P V for all ideal gases;V 2 for all monatomic ideal gases C P 5R/2 5 γ= C = 3R/2= 31.67 ratio of molar specific heats for a monatomic ideal gas V 21.3 – The Equipartition of Energy the energies of atoms and molecules are quantized ∫¿= nRT 7 2 ; CV= R=29.1 J /mol∙ K E 2 ¿ energy-level diagram: (Figure 27 from textbook) 21.4 – Adiabatic Processes for an Ideal Gas - adiabatic process—no energy is transferred by heat between a system and surroundings PV =constant relationship between P and V for adiabatic process involving ideal gas - because γ > 1, the PV curve is steeper than for isothermal expansion TV γ−=constant relationship between T and V
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