lecture.2.thermodynamics.pdf, Slides of Law

Download lecture.2.thermodynamics.pdf and more Slides Law in PDF only on Docsity! 1 ESS55 Prof. Jin-Yi Yu Lecture 2: Atmospheric Thermodynamics Ideal Gas Law (Equation of State) Hydrostatic Balance Heat and Temperature Conduction, Convection, Radiation Latent Heating Adiabatic Process Lapse Rate and Stability ESS55 Prof. Jin-Yi Yu The Ideal Gas Law An equation of state describes the relationship among pressure, temperature, and density of any material. All gases are found to follow approximately the same equation of state, which is referred to as the “ideal gas law (equation)”. Atmospheric gases, whether considered individually or as a mixture, obey the following ideal gas equation: P = ρ R T pressure Density=m/V temperature (degree Kelvin) gas constant (its value depends on the gas considered) ESS55 Prof. Jin-Yi Yu Gas Constant The ideal gas law can be applied to the combination of atmospheric gases or to individual gases. The value of gas constant for the particular gas under consideration depends on its molecular weight: Rgas = R* / Mgas where R* = universal gas constant = 8314.3 J deg-1 kg-1 The gas constant for dry atmospheric air is: Rair = R* / Mair = 8314.3/28.97 = 287 J deg-1 kg-1 (Mair ≅ 0.80*MN2 + 0.20*MO2 = 0.80*28 + 0.2*32 = 28.8) The gas constant for water vapor is: Rvapor = R* / Mvapor = 8314.3/18.016 = 461 J deg-1 kg-1 ESS55 Prof. Jin-Yi Yu Applications of the Gas law Question: Calculate the density of water vapor which exerts a pressure of 9 mb at 20°C. Answer: Use the ideal gas law: Pv= ρRvT and Pv = 9 mb = 900 Pa (a SI unit) Rv = R* / Mv = 461 J deg-1 kg-1 T = 273 + 20 (°C) = 293 K. So we know the density of water vapor is: ρ = Pv/ (RvT) = 900 / (461*293) = 6.67 x 10-3 kg m-3 (from Atmospheric Sciences: An introductory Survey) 2 ESS55 Prof. Jin-Yi Yu Virtual Temperature Moist air has a lower apparent molecular weight that dry air. The gas constant for 1 kg of moist air is larger than that for 1 kg of dry air. But the exact value of the gas constant of moist air would depend on the amount of water vapor contained in the air. It is inconvenient to calculate the gas constant for moist air. It is more convenient to retain the gas constant of dry air and use a fictitious temperature in the ideal gas equation. This fictitious temperature is called “virtual temperature”. This is the temperature that dry air must have in order to has the same density as the moist air at the same pressure. Since moist air is less dense that dry air, the virtual temperature is always greater than the actual temperature. ESS55 Prof. Jin-Yi Yu How to Calculate Virtual Temperature? Where T: actual temperature p: actual (total) pressure = pd + e pd: partial pressure exerted by dry air e: partial pressure exerted by water vapor ε = Rd/Rv = 0.622 ESS55 Prof. Jin-Yi Yu Hydrostatic Balance in the Vertical vertical pressure force = gravitational force - (dP) x (dA) = ρ x (dz) x (dA) x g dP = -ρgdz dP/dz = -ρg (from Climate System Modeling) The hydrostatic balance !! ESS55 Prof. Jin-Yi Yu What Does Hydrostatic Balance Tell Us? The hydrostatic equation tells us how quickly air pressure drops wit height. The rate at which air pressure decreases with height (∆P/ ∆z) is equal to the air density (ρ) times the acceleration of gravity (g) 5 ESS55 Prof. Jin-Yi Yu The First Law of Thermodynamics This law states that (1) heat is a form of energy that (2) its conversion into other forms of energy is such that total energy is conserved. The change in the internal energy of a system is equal to the heat added to the system minus the work down by the system: ∆U = Q - W change in internal energy (related to temperature) Heat added to the system Work done by the system ESS55 Prof. Jin-Yi Yu Therefore, when heat is added to a gas, there will be some combination of an expansion of the gas (i.e. the work) and an increase in its temperature (i.e. the increase in internal energy): Heat added to the gas = work done by the gas + temp. increase of the gas ∆H = p ∆α + Cv ∆T volume change of the gas specific heat at constant volume (from Atmospheric Sciences: An Intro. Survey) ESS55 Prof. Jin-Yi Yu Heat and Temperature Heat and temperature are both related to the internal kinetic energy of air molecules, and therefore can be related to each other in the following way: Q = c*m*∆T Heat added Specific heat = the amount of heat per unit mass required to raise the temperature by one degree Celsius Mass Temperature changed ESS55 Prof. Jin-Yi Yu Specific Heat (from Meteorology: Understanding the Atmosphere) 6 ESS55 Prof. Jin-Yi Yu How to Change Air Temperature? Add (remove) heat to (from) the air parcel (diabatic processes) (1) Conduction: requires touching (2) Convection: Hot air rises (3) Advection: horizontal movement of air (4) Radiation: exchanging heat with space (5) Latent heating: changing the phase of water Without adding (removing) heat to (from) the air parcel (1) Adiabatic Process: Expanding and compressing air ESS55 Prof. Jin-Yi Yu Conduction Conduction is the process of heat transfer from molecule to molecule. This energy transfer process requires contact. Air is a poor conductor. (with low thermal conductivity) Conduction is not an efficient mechanisms to transfer heat in the atmosphere on large spatial scales. (from Meteorology: Understanding the Atmosphere) ESS55 Prof. Jin-Yi Yu Convection Convection is heat transfer by mass motion of a fluid (such as air or water). Convection is produced when the heated fluid moves away from the heat source and carries energy with it. Convection is an efficient mechanism of heat transfer for the atmosphere in some regions (such as the tropics) but is an inefficient mechanism in other regions (such as the polar regions). (from Meteorology: Understanding the Atmosphere) ESS55 Prof. Jin-Yi Yu Advection Advection is referred to the horizontal transport of heat in the atmosphere. Warm air advection occurs when warm air replaces cold air. Cold air advection is the other way around. This process is similar to the convection which relies on the mass motion to carry heat from one region to the other. Advection can be considered as one form of convection. (from Meteorology: Understanding the Atmosphere) 7 ESS55 Prof. Jin-Yi Yu Radiation Radiation is heat transfer by the emission of electromagnetic waves which carry energy away from the emitting object. The solar energy moves through empty space from the Sun to the Earth and is the original energy source for Earth’s weather and climate. ESS55 Prof. Jin-Yi Yu Latent Heating Latent heat is the heat released or absorbed per unit mass when water changes phase. Latent heating is an efficient way of transferring energy globally and is an important energy source for Earth’s weather and climate. (from Meteorology: Understanding the Atmosphere) 80 cal/gm 600 cal/gm 680 cal/gm ESS55 Prof. Jin-Yi Yu Latent Heat of Evaporation The latent heat of evaporation is a function of water temperature, ranging from 540 cal per gram of water at 100°C to 600 cal per gram at 0°C. It takes more energy to evaporate cold water than evaporate the same amount of warmer water. ESS55 Prof. Jin-Yi Yu Adiabatic Process If a material changes its state (pressure, volume, or temperature) without any heat being added to it or withdrawn from it, the change is said to be adiabatic. The adiabatic process often occurs when air rises or descends and is an important process in the atmosphere. 10 ESS55 Prof. Jin-Yi Yu Absolutely Stable Atmosphere (from Meteorology Today) ESS55 Prof. Jin-Yi Yu Absolutely Unstable Atmosphere (from Meteorology Today) ESS55 Prof. Jin-Yi Yu Conditionally Unstable Atmosphere (from Meteorology Today) ESS55 Prof. Jin-Yi Yu Day/Night Changes of Air Temperature At the end of a sunny day, warm air near the surface, cold air aloft. In the early morning, cold air near the surface, warm air aloft. The later condition is called “inversion”, which inhibits convection and can cause sever pollution in the morning. End of Day Night (from Is the Temperature Rising?) 11 ESS55 Prof. Jin-Yi Yu Stability and Air Pollution Neutral Atmosphere (Coning) Stable Atmosphere (Fanning) Unstable Atmosphere (Looping) Stable Aloft; Unstable Below (Fumigation) Unstable Aloft; Stable Below (Lofting) (from Is the Temperature Rising?) ESS55 Prof. Jin-Yi Yu Potential Temperature (θ) The potential temperature of an air parcel is defined as the the temperature the parcel would have if it were moved adiabatically from its existing pressure and temperature to a standard pressure P0 (generally taken as 1000mb). θ= potential temperature T = original temperature P = original pressure P0 = standard pressure = 1000 mb R = gas constant = Rd = 287 J deg-1 kg-1 Cp = specific heat = 1004 J deg-1 kg-1 R/Cp = 0.286 ESS55 Prof. Jin-Yi Yu Importance of Potential Temperature In the atmosphere, air parcel often moves around adiabatically. Therefore, its potential temperature remains constant throughout the whole process. Potential temperature is a conservative quantity for adiabatic process in the atmosphere. Potential temperature is an extremely useful parameter in atmospheric thermodynamics. ESS55 Prof. Jin-Yi Yu Adiabatic Chart The expression of potential temperature can be modified into: T = (constant * θ) P 0.286 (from Atmospheric Sciences: An Intro. Survey) (from The Physics of the Atmospheres) 12 ESS55 Prof. Jin-Yi Yu(from Meteorology Today) ESS55 Prof. Jin-Yi Yu Water Vapor In the Air Evaporation: the process whereby molecules break free of the liquid volume. Condensation: water vapor molecules randomly collide with the water surface and bond with adjacent molecules. (from Understanding Weather & Climate) Saturation ESS55 Prof. Jin-Yi Yu How Much Water Vapor Is Evaporated Into the Atmosphere Each Year? On average, 1 meter of water is evaporated from oceans to the atmosphere each year. The global averaged precipitation is also about 1 meter per year. ESS55 Prof. Jin-Yi Yu How Much Heat Is Brought Upward By Water Vapor? Earth’s surface lost heat to the atmosphere when water is evaporated from oceans to the atmosphere. The evaporation of the 1m of water causes Earth’s surface to lost 83 watts per square meter, almost half of the sunlight that reaches the surface. Without the evaporation process, the global surface temperature would be 67°C instead of the actual 15°C. 15 ESS55 Prof. Jin-Yi Yu (from Meteorology Today) Adiabatic Chart: P and T ESS55 Prof. Jin-Yi Yu Adiabatic Chart: Dry Adiabatic / θ (from Meteorology Today) ESS55 Prof. Jin-Yi Yu Adiabatic Chart: Moist Adiabatic (from Meteorology Today) ESS55 Prof. Jin-Yi Yu Adiabatic Chart: Mixing Ratio (from Meteorology Today) 16 ESS55 Prof. Jin-Yi Yu An Example ESS55 Prof. Jin-Yi Yu Applications of Adiabatic Chart (from Meteorology Today)