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SO345: Atmospheric Thermodynamics

EQUATION OF STATE OF A PERFECT GAS . Combining Charles' and Boyle's Laws allows us to get a relationship between the basic variables of state without the restrictions of having to maintain either constant temperature or constant pressure conditions.. EQUATION OF STATE OF A PERFECT GAS . Ch

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SO345: Atmospheric Thermodynamics

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    1. SO345: Atmospheric Thermodynamics CHAPTER 4: EQUATION OF STATE OF A PERFECT GAS (IDEAL GAS LAW)

    2. EQUATION OF STATE OF A PERFECT GAS Combining Charles' and Boyle's Laws allows us to get a relationship between the basic variables of state without the restrictions of having to maintain either constant temperature or constant pressure conditions.

    3. EQUATION OF STATE OF A PERFECT GAS Charles' Law + Boyle's Law - - - - - - - -> a general gas law for ideal gases

    4. EQUATION OF STATE OF A PERFECT GAS For the generalized law, we do not need: isothermal (Boyles Law) or isobaric (Charles and Gay-Lussacs Law) conditions. We can show that any process can be duplicated in terms of a two-step process: isothermal and isobaric (i.e., given any initial states we can arrive at any final state by following a two-step isobaric and isothemal process) - see Appendix A.

    5. EQUATION OF STATE OF A PERFECT GAS The resultant general gas law is referred to as "the Equation of State" or Ideal Gas Law: p? = RT (Eq 4.1) where p is pressure, T is temperature (Kelvin) and R is a constant called the "specific gas constant".

    6. EQUATION OF STATE OF A PERFECT GAS Universal gas constant (R*) this represents the amount of energy needed per mole of gas to change the temperature of the gas by 1 K. R* = 8314 J/(kg-mole- K)

    7. EQUATION OF STATE OF A PERFECT GAS Specific Gas Constant (R) - each gas has its own unique constant value for R, where R = R*/m For example, the specific gas constant for dry air: Rd = 8314 J/(kg-mole- K)/28.9 kg/kg-mole = 287 J/(kg-0K) which is the amount of energy needed to change the temperature of 1 kg of dry air by 1 K.

    8. EQUATION OF STATE OF A PERFECT GAS The Equation of State may also be written as: p? = R*T (Eq 4.3) m

    9. EQUATION OF STATE OF A PERFECT GAS For dry air, there are two forms of the Equation of State: p? = RdT (Eq 4.4a) or p? = R*T (Eq 4.4b) md where: p = total pressure R* = universal gas constant ? = specific volume = 8.314 J/(mol-0K) Rd= specific gas constant (dry air) T = temperature in 0K = 287 J/(kg-0K) md = molecular wt of dry air

    10. EQUATION OF STATE OF A PERFECT GAS MOLECULAR WEIGHTS OF GAS MIXTURES Since the Equation of State for a general ideal gas is given as: p?= (R*/m)T, computations for individual gases like Nitrogen (N2) and Oxygen (O2) whose molecular weights can be directly taken from a periodic chart are straightforward. How do you determine the molecular weight of a gas mixture (i.e., dry air)?

    11. EQUATION OF STATE OF A PERFECT GAS Define a "mean molecular weight" governed by a "weighted harmonic mean": mean molecular weight = where: M = mass (Eq4.5) m = molecular weight (See Appendix B for this mean molecular weight formula).

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