Exam 2 Answers - NAME EXAM II ATMO 335 OPEN BOOK 1 A 1 kg...

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NAME: EXAM II, ATMO 335, March 24, 2008. OPEN BOOK 1. A 1 kg parcel of dry air is initially at a temperature of 283 K and pressure 1000 hPa. It is transformed (quasi-statically and reversibly) in two steps. i) It is lifted adiabatically to a pressure of 800 hPa. ii) It is then heated at constant pressure by 10 kJ. a) What is T at the end of steps (i) and (ii)? T 0 = 283 K; T 1 = T 0 p p 0 0 . 286 = 265 . 5 K; T 2 = Q/c p + T 1 = 275 . 5 K b) What is Δ S at the end of steps (i) and (ii)? Δ 1 S = 0; Δ 2 S = R T 1 T 0 dQ T = R T 1 T 0 c p dT T = c p ln T 1 T 0 = 36 . 975 J K - 1 c) What is the potential temperature initially? θ 0 = 283 K since θ 0 = T 0 ( 1000 1000 ) κ d) What is the potential temperature at the ends of steps (i) and (ii)? i) θ 1 = θ 0 ; ii) θ 2 = T 2 (10 / 8) 0 . 286 = 293 . 6 K; 2. A parcel of air at 283 K and 1000 hPa has relative humidity r=0.50. a) What are the saturation vapor pressure and the saturation mixing ratio? e s = 2 . 58 × 10 9 exp( - 5422 / 283) = 12 . 33 hPa; w s = 0 . 622 e s / 1000 = 0 . 0077 kg kg - 1 b) What is the virtual temperature? T v = (1 + 0 . 60 ws × 0 . 50)283 = 283 . 65 K 1
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c) The parcel is embedded in dry air of the same temperature and pres- sure. Does it rise or sink? It rises because the moist air has less density than dry air at the same temperature and pressure.
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