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Thermodynamics I

Thermodynamics I Temperature Thermal Equilibrium and Temperature. Temperature scales Absolute Temperature Scale. The Ideal-Gas Law The Kinetic Theory of Gases. Pressure and Temperature

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Thermodynamics I

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  1. Thermodynamics I • Temperature • Thermal Equilibrium and Temperature. Temperature scales • Absolute Temperature Scale. The Ideal-Gas Law • The Kinetic Theory of Gases. Pressure and Temperature • Heat • Heat. Heat capacity and Specific Heat • Change of Phase and Latent Heat • Thermal expansion and Phase Diagrams • Heat Transfer • Transport Laws References: Tipler; wikipedia, Britannica

  2. Thermodynamics II • The First Law of Thermodynamics • Heat and Work. First Law of Thermodynamics • Heat and Work on Quasi-Static Processes for a Gas. • The Second Law of Thermodynamics • Heat Engines and the Second Law of Thermodynamics • Refrigerators and the Second Law of Thermodynamics • The Carnot Engine • Heat Pumps • Irreversibility and disorder. Entropy References: Tipler; wikipedia,…

  3. Temperature Thermal Equilibrium and Temperature. Temperature scales Our sense of touch can usually tell us if an object is hot or cold. Usually we need get in touch –physical contact- to appreciate if a body is hot or cold. But our perception is very subjective. Temperature: measure of hotness and coldness in terms of any arbitrary scales and indicating the direction which energy spontaneously flows (from a hotter body to a colder one) A thermometer is any of class of instrument that measures the temperature. Temperature is the physical magnitude that is measured by thermometers. A physical property that changes with the temperature is called a thermometric property - most solids an liquids expand when they are heated - electrical resistance change when is heated - in a gas pressure and volume change when it is heated - radiation from the surface of a body depends on the surface temperature -…… References: Tipler; Britannica

  4. Temperature • Thermal Equilibrium and Temperature. Temperature scales Thermal contact: Heat energy is transferred between the bodies in thermal contact Thermal equilibrium: When the thermometric properties of the bodies in thermal contact do not change If two objects are in thermal equilibrium with a third, then they are in thermal equilibrium each other (Zeroth Law of thermodynamics) Two objects are defined to have the same temperature if they are in thermal equilibrium with each other. Temperature may be defined as the property of a system that determines whether it is in thermal equilibrium with other system. Temperature is one of the seven basic physical quantities in term of which all other physical quantities are defined. It is an “intensive” property, as pressure or density. Length, mass are “extensive”

  5. Thermodynamics. Temperature • Temperature scales Calibration of a thermometer: Reproducibility and Reliability. When the thermometric property changes lineally with the temperature, two fixed points can be used to calibrate the thermometer. Ice point temperature (normal freezing point of water) Steam-point temperature : normal boiling point of water Centigrade Temperature Scale (Celsius scale) Fahrenheit Temperature ScaleAbsolute Temperature Scale Derive and check the above expressions to convert Fahrenheit degrees temperature to centigrade degrees temperature and the inverse relationship. The same to convert Kelvin scale to centigrade. Apply to obtain the Fahrenheit normal human temperature if it is 36.5 Celsius degrees

  6. Thermodynamics. Absolute Temperature Scale. Kelvin Scale. A constant-volume gas thermometer It is possible to define a temperature scale in a independent way of the used thermometric substance Temperature of the boiling point of sulfur measured with constant-volume gas thermometers . P100 is the pressure of the gas at 100ºC The ideal-gas temperature scale is defined so that the temperature of the triple point state is 273.16 kelvins, K. The triple point of water is the unique temperature and pressure at which water, water vapor and ice coexist in equilibrium. [0.01 ºC and 4.58 mmHg] Plot of pressure versus temperature for a gas, as measured by a constant-volume gas thermometer. When extrapolated to zero pressure, the plot intersects the temperature axis at the showed value of - 273.25 ºC T

  7. Thermodynamics. Ideal Gas Law The properties of gas samples that have low densities led to the definition of the ideal-gas temperature scales. The behavior of gases at this low densities was described (1) by Boyle´s Law (1661) PV = constant (for a constant temperature) (2) by Charles and Gay-Lussac Law (about 1800) P = C1 T (for a constant volume) V = C2 T (for a constant pressure) T absolute temperatures; C1 and C2 constants Ideal Gas-Law Equation of state of ideal gas n = amount of gas expressed in moles R :Universal gas constant R = 8.314 J/(mol •K) = = 0.082 atm • L/(mol • K) The temperature of 0º (273.15 K) and the pressure of 1 atm are often referred as standard condition. A mole (mol) of any substance is the amount of substance that contains the Avogadro number, NA, of atoms or molecules, defined as the number of carbon atoms in 12 g of 12C.

  8. Thermodynamics. Dealing with theIdeal Gas Law Ideal Gas-Law Equation of state of ideal gas n = m/ M [mass of the substance in g/molecular mass] molR = 8.314 J/(mol •K) = 0.082 atm • L/(mol • K) The mass per mole of a substance is called its molar mass. (The terms molecular mass or molecular weight are sometimes used A gas has a volume of 2 L, a temperature of 30ºC, and a pressure of 1 atm. When the gas is heated to 60ºC and compressed to a volume of 1.5 L, what is the new pressure What is the density of dry air at standard conditions of pressure and temperature?. The same at 20ºC; The same at 20ºC and 933 mb. Molecular mass of dry air: 28.97 g. An automobile tire is filled to a gauge pressure of 200 kPa when its temperature is 20ºC. After the car has been driven at high speeds, the tire temperature increases to 50ºC. (a) Assuming that the tire volume does not change, find the gauge pressure in the tire (b) Calculate the gauge pressure if the volume of the tire expands by 10%.

  9. Thermodynamics. The Kinetic Theory of Gases. Molecular Interpretation of Pressure and Temperature Goal : To relate macroscopic point of view aboutt pressure and temperature with the microscopic motion. For a solid, these microscopic motions are principally the vibrations of its atoms about their sites in the solid. For an ideal monatomic gas, the microscopic motions are the translational motions of the constituent gas particles. For a multiatomic gas, vibrational and rotational motion should be included too. The kinetic theory of gases is able us to establish quantitatively the relationship between pressure and temperature with molecular motion for gases The pressure that a gas exerts on its container is due to collisions between gas molecules and the container walls. This pressure is a force per unit of area and, by Newton´s second law, this force is the rate of change of momentum of the gas molecules colliding with the walls. References http://en.wikipedia.org/wiki/Image:Translational_motion.gif The absolute temperature is a measure of the average kinetic energy of the molecules. Crystalline Solids

  10. Thermodynamics I • Temperature • Thermal Equilibrium and Temperature. Temperature scales • Absolute Temperature Scale. The Ideal-Gas Law • The Kinetic Theory of Gases. Pressure and Temperature • Heat • Heat. Heat capacity and Specific Heat • Change of Phase and Latent Heat • Thermal expansion and Phase Diagrams • Heat Transfer • Transport Laws References: Tipler; wikipedia, Britannica

  11. Thermodynamics. Heat. Heat capacity and Specific Heat Heat is the energy that is being transferred from one system to another as a result of difference in temperature. If two bodies at different temperature are brought together, energy is transferred –i.e. heat flows- from the hotter body to the colder. The effect of this transfer of energy usually, but non always*, is an increase in the temperature of the colder body and an decrease of the hotter body; the amount of heat that leaves one equals the amount that enters the other. Heat Capacity and Specific Heat The amount of heat energy Q needed to raise the temperature of a substance is proportional to the temperature change and to the mass of substance. cwater: 1 cal/(g•ºC)= 1kcal/(kg•ºC)= 4.184 kJ/(kg•ºC) = 4.184 kJ/(kg•K) Units of heat: Calorie [cal] : the amount of energy to be transferred to raise the temperature of one gram of water one centigrade degree. 1cal = 4.184 J The heat capacity per mole is called the molar specific heat The specific heat of a substance depends of the way as the heat is transferred. The most commonly determined specific heats are the specific heat at constant pressure and the specific heat at constant volume * The exceptions occurs during a change of phase

  12. Thermodynamics. Heat. Heat capacity and Specific Heat Heat capacity: The amount of heat energy Q necessary to raise the temperature of a substance by one degree. The Heat capacity per unit mass is called specific heat The Heat capacity per amount of substance (mol) is called the molar specific heat Air cP = 29.19 J/(mol•K); cV = 20.85 J/(mol•K). M=28.84 g cP= 1.012 kJ/(kg•K); cV = 0.723 kJ/(kg•K);

  13. Thermodynamics. Heat. Heat capacity and Specific Heat Heat Capacity and Specific Heat The amount of heat energy Q needed to raise the temperature of a substance is proportional to the temperature change and to the mass of substance. cwater: 1 cal/(g•ºC)= 1kcal/(kg•ºC)= 4.184 kJ/(kg•ºC) = 4.184 kJ/(kg•K) How much heat is required to change 1.5 kg of ice at -20ºC and 1 atm into steam. Typical volumetric heat capacity of a soil is 2.1 MJ/(m3 K). Estimate the absorbed heat energy by a layer of 1 m of depth when its temperature is increased by10ºC. Calculate the specific heat of the soil if the bulk density of the solid is 1.7 Mg/m3. A great part of the soil are pores that can be filled by water. Then the volumetric heat capacity of a soil will vary with its content of water. Explain the behavior when the content of water increase.

  14. Thermodynamics. Change of Phase and Latent Heat Common types of phase change include fusion (liquid to solid), melting (solid to liquid), vaporization(liquid to vapor or gas); condensation (gas or vapor to liquid), and sublimation (solid directly to vapor). When a phase change appears there is no temperature change when the thermal energy is being transferred to the body in which the phase change is occurring. In the case of a phase change the specific heat (or capacity) is infinitum. Latent Heat Latent heat of fusion [or melting], Lf. At a pressure of 1 atm, the latent heat of fusion for water is Lf =333.5 KJ/kg Latent heat of vaporization, LV . For water at a pressure of 1 atm, the latent heat of vaporization is Lf = 2.25 MJ/kg (at boiling point). Latent heat of vaporization of water depends on the temperature. Latent heat of water at 20ºC is 2.45 MJ/kg. A common relationship is:

  15. Thermodynamics. Change of Phase and Latent Heat Common types of phase change include fusion, freezing, (liquid to solid), melting (solid to liquid), vaporization(liquid to vapor or gas); condensation (gas or vapor to liquid), and sublimation (solid directly to vapor and vapor to solid –in some places the last process is called deposition-). When a phase change appears there is no temperature change when the thermal energy is being transferred to the body in which the phase change is occurring. In the case of a phase change, the specific heat (or capacity) is infinitum. http://www.usatoday.com/weather/wwatphse.htm

  16. Thermodynamics. Change of Phase and Latent Heat. Water http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html

  17. Thermodynamics. Evaporation Evaporation Ordinary evaporation is a surface phenomenon - some molecules have enough kinetic energy to escape. If the container is closed, an equilibrium is reached where an equal number of molecules return to the surface. The pressure of this equilibrium is called the saturation vapor pressure. In order to evaporate, a mass of water must collect the large heat of vaporization, so evaporation is a potent cooling mechanism. Evaporation heat loss is a major climatic factor and is crucial in the cooling of the human body. http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html

  18. Thermodynamics. Evaporation vs. Boiling http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html

  19. Thermodynamics. Thermal expansion Thermal expansion. When the temperature of an object increase, the object usually increase Do holes expand?

  20. Thermodynamics. Thermal Expansion. Case of Water Volume of 1 g of water at atmospheric pressure versus temperature. The minimum volume, which corresponds to the maximum density, occurs at 4ºC. [ Supercooled water is water that is cooled below the normal freezing point without solidifying. It is showed in the figure] Discuss the expansion of water in the case of freezing (or fusion) -liquid to solid (ice)-. See the density of ice and the density of liquid water

  21. Thermodynamics. Phase Diagramas. Case of Water The diagram P-T for water at a constant volume. The pressure and temperature scales are not linear.

  22. Thermodynamics. Heat Transfer Heat Transfer The spontaneous transfer of heat energy is from a high temperature object to a lower temperature object. Heat Transfer focus on the energy rate that is being transferred and on the mechanism of transport. • Thermal energy is transferred from one place to another by three types of processes. The driving force of heat transfer flow is always the difference of temperature: • Conduction, In this case, the mechanism of heat energy transport is the interactions among atoms or molecules (collisions), although there is no mass motion. It is the case of heat transfer in opaque solids • Convection, heat energy is transported by direct mass transport. Convective currents are in charge of the transport • Radiation; heat energy is transferred through space in the form of electromagnetic waves [ or photons] that move at light speed. Sun´s energy In all cases we can write: rate of net heat transfer = difference of temperatures/ resistance

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