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Quiz 4

Quiz 4. Solved Problems 1 & 2 of quiz #4. Chapter 7 – Moist Air. Reversible Saturated Adiabatic Ascent The system under consideration is a parcel of cloud that rises and expands adiabatically and reversibly, indicating that all condensed water is kept (a closed system).

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Quiz 4

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  1. Quiz 4 Solved Problems 1 & 2 of quiz #4.

  2. Chapter 7 – Moist Air • Reversible Saturated Adiabatic Ascent • The system under consideration is a parcel of cloud that rises and expands adiabatically and reversibly, indicating that all condensed water is kept (a closed system). • Since it is adiabatic and reversible, the process is isentropic. • What we derive here is valid for an ice cloud as well. • The expression for the entropy of this system is

  3. Chapter 7 – Moist Air • Reversible Saturated Adiabatic Ascent • If we divide by md and note that the entropy S = const, • Where wt,w = mt/md = wsw + mw/mdand the subscript w indicates saturation values (except in mw). • If we differentiate the expression, we get • This equation describes the saturated adiabatic process. • If T and pd are independent variables, wsw = esw/pdand esw = f (T), so the equation determines a curve in T, pdplane.

  4. Chapter 7 – Moist Air • Reversible Saturated Adiabatic Ascent • We can make several assumptions to get an approximate and somewhat simpler form of the equation • Assume wt,w < cpdand esw < pd. This yields • Next assume that lvvaries slowly with T, we differentiate • Use of the approximate form is good to within a few percent.

  5. Chapter 7 – Moist Air • Pseudo-adiabatic Ascent • In saturated adiabatic ascent, the equations depend on wt. • While the saturation vapor mixing ratio, wsw, is determined, the liquid water mixing ratio, mw/mdis arbitrary. • This creates the situation where on a T, pdiagram where saturation is just reached, there will be an infinite number of reversible saturated adiabats passing through, each differing ever so slightly from each other, depending on the amount of liquid water in the parcel. • This dilemma can be avoided with a simple assumption.

  6. Chapter 7 – Moist Air • Pseudo-adiabatic Ascent • We assume that all the condensed liquid water (or ice) falls out of the parcel as soon as it appears. • This is a process of saturated expansion, but the system is now open and irreversible. • It is called a pseudo-adiabatic process and gives unique curves through each T, p point on a diagram. • Assume that mw = 0 and wt,w = ww, yielding • The cooling is slightly greater in pseudo-adiabatic than in reversible expansion for the same change in pressure.

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