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SO345: Atmospheric Thermodynamics

THERMODYNAMIC FUNDAMENTALS . How can we thermodynamically describe a system? We can describe a system thermodynamically by the following properties or variables:masscompositionvolumepressuretemperature . THERMODYNAMIC FUNDAMENTALS . Two caveats:We will confine ourselves to energy processes in which the systems will generally not change composition or mass.Since composition does not change, we can omit that variable. Also, volume may be expressed in terms of a s29

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SO345: Atmospheric Thermodynamics

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    1. SO345: Atmospheric Thermodynamics CHAPTER 3: THERMODYNAMIC FUNDAMENTALS

    2. THERMODYNAMIC FUNDAMENTALS How can we thermodynamically describe a system? We can describe a system thermodynamically by the following properties or variables: mass composition volume pressure temperature

    3. THERMODYNAMIC FUNDAMENTALS Two caveats: We will confine ourselves to energy processes in which the systems will generally not change composition or mass. Since composition does not change, we can omit that variable. Also, volume may be expressed in terms of a specific volume (volume/mass).

    4. THERMODYNAMIC FUNDAMENTALS To allow us to describe systems independent of mass, this leaves us with the variables: specific volume (a = V/m) pressure (p) temperature (T) which we will refer to as our basic "Variables of State". The values of these variables describe completely the state of any given system. Any other variables which are functions of these basic variables of state are also variables of state.

    5. THERMODYNAMIC FUNDAMENTALS The technique of dividing volume by mass to get specific volume will be used for other thermodynamic variables. For example: W = work w = specific work U = internal energy u = specific int. energy So, the adjective "specific" will normally refer to "per unit mass“ [per unit mass quantities will be denoted by lower case letter symbols]

    6. THERMODYNAMIC FUNDAMENTALS TEMPERATURE MEASUREMENTS We basically know temperature as the "hotness" or "coldness" of an object. Technically, temperature is a measure of an object's average kinetic energy. The Celsius (or Centigrade) scale uses pure water as the reference substance at a pressure of one atmosphere: - ice/liquid thermal equilibrium exists at a good convenient value of 00C, - liquid/vapor thermal equilibrium exists at a good convenient value of 1000C.

    7. THERMODYNAMIC FUNDAMENTALS TEMPERATURE MEASUREMENTS The Fahrenheit scale bases the ice/liquid and liquid/vapor equilibrium points at 32 0F and 212 0F respectively. Based on these thermal equilibrium references, one can derive the following Celsius-Fahrenheit relationships: [T]º F = (9/5)[T]ºC + 32 º F (Eq 3.2a) [T]º C = (5/9) ([T]ºF - 32 º F) (Eq 3.2b)

    8. THERMODYNAMIC FUNDAMENTALS PRESSURE MEASUREMENTS Pressure (p) is the measure of the force (F) acting perpendicularly on a unit surface area (A): p = F/A (Eq 3.3) Pressure has dimensions of [ Pa ] = [N / m2] = [kg/ (m ·s2) ] A common pressure unit you may be used to is pounds (force) per square inch. Torricelli invented a type of measuring device for atmospheric pressure (barometer), and was able to determine the atmospheric pressure in terms of the height of mercury (Hg) in a vacuum tube.

    9. Fig 3.1 Basic principle of Torricelli’s barometer

    10. THERMODYNAMIC FUNDAMENTALS PRESSURE MEASUREMENTS Basic principle of Torricelli's barometer. When the reference zero pressure is based on the atmospheric pressure value, it is referred to as gauge pressure. For example, the reading your tire pressure gauge gives is gauge pressure. The absolute pressure value would be found from the simple formula: P absolute = P gauge + P atmospheric (Eq 3.4)

    11. THERMODYNAMIC FUNDAMENTALS PRESSURE MEASUREMENTS Atmospheric (or barometric) pressure measurements are based on the absolute zero pressure reference. The standard pressure for one atmosphere (1 atm) has been assigned the values of: 1 atm = 14.7 lb per square inch = 29.92 inches of Hg = 760.0 millimeters of Hg = 1013.25 millibars

    12. THERMODYNAMIC FUNDAMENTALS PRESSURE MEASUREMENTS The millibar (mb) is a unit of pressure commonly used by meteorologists, while the Pascal (Pa) is used by physicists; 1 bar = 106 dyne/cm2 (cgs) 1 bar = 10 5Nt/m2 (mks) 1 bar = 1000 mb [Note: 1 bar (1000 mb) is close to the value of 1 standard atmosphere (1013 mb)].

    13. THERMODYNAMIC FUNDAMENTALS PRESSURE MEASUREMENTS The unit hectopascal (1 hPa = 100 Pa) can sometimes be found in meteorology articles, 1 mb = 1 hectopascal We will now look at the development of two basic ideal gas laws.

    14. THERMODYNAMIC FUNDAMENTALS BASIC GAS LAWS Boyle’s Law Goal: Find the relationship between ? and p for an isothermal process

    15. THERMODYNAMIC FUNDAMENTALS BASIC GAS LAWS Boyle’s Law Conditions: dry air temperature constant (isothermal) Experiment: with temperature (T) fixed, measure different values of specific volume (?) corresponding to different values of pressure (p)

    16. THERMODYNAMIC FUNDAMENTALS BASIC GAS LAWS Boyle’s Law . Fig. 3.3

    17. THERMODYNAMIC FUNDAMENTALS BASIC GAS LAWS Boyle’s Law From Fig 3.3, specific volume (a) is inversely proportional to pressure (p), or p1a1 = p2a2 = constant (Eq 3.8)

    18. THERMODYNAMIC FUNDAMENTALS BASIC GAS LAWS Charles & Gay-Lussac’s Law Goal: Find a relationship between ? and T The experiment reveals a linear relationship as shown in Figure 3.2:

    19. THERMODYNAMIC FUNDAMENTALS BASIC GAS LAWS Charles & Gay-Lussac’s Law Conditions: - dry air - pressure kept constant (isobaric) Experiment: - with pressure (p) fixed, determine the different values of specific volume (?), corresponding to different values of temperature (T).

    20. THERMODYNAMIC FUNDAMENTALS BASIC GAS LAWS Charles & Gay-Lussac’s Law Fig. 3.2 a vs T in Charles’ experiment

    21. THERMODYNAMIC FUNDAMENTALS BASIC GAS LAWS vs T in Charles experiment If temperature measurements were made in the Celsius scale, the intersection of the data curve with the T axis (where ? theoretically becomes zero) occurs at -273 0C. The relationship would be in the form: ?a1/(T1 +273) = ?a2/(T2 +273) = constant [T in 0Celsius] (Eq3.5)

    22. THERMODYNAMIC FUNDAMENTALS BASIC GAS LAWS To simplify calculations, an absolute temperature scale can be devised so that the value 273 need not be added to each of the Celsius readings. This is the reason for the Kelvin temperatures Tabs having the formula: Tabs = [T] ºC + 273 (Eq 3.6)

    23. THERMODYNAMIC FUNDAMENTALS BASIC GAS LAWS This results in a simpler formula for Charles' Law: ?a1/T1 = ?a2/T2 = constant (Eq 3.7) This clearly shows that the specific volume of dry air is directly proportional to absolute temperature.

    24. THERMODYNAMIC FUNDAMENTALS BASIC GAS LAWS Though Charles' and Boyle's Gas Laws may be useful at times, its utility is limited to the particular cases of constant pressure or constant temperature. Our next step is to explore the general situation (arbitrary values of p, T, and ? ) and develop an equation describing the relationship between these variables of state.

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