MIDTERM EXAM SOLUTIONS Science A30 The Atmsphere March 0, 008 INSTRUCTIONS WRITE YOUR NAME ON EVERY PAGE. Exam will last 80 minutes. Cmplete the prblems directly n the exam. Extra paper available if needed. Yu may use ne page f ntes and a calculatr. Sectin I: / 4 /40 Sectin II: 11. a. /4 b. /5 c. /4 d. /5 /18 1. a. /4 b. /6 c. /6 d. /8 /4 13. a. /4 b. /6 c. /8 /18 TOTAL /0 1
Sectin I: Multiple chice (0 minutes) Clearly circle yur chice 4 pints each Name: 1. Buyancy frce is NOT a) always equal t the frce due t gravity acting n an bject b) equal t the weight f the displaced fluid c) required t determine the net vertical frce acting n an bject d) an imprtant frce in vertical mtin f the atmsphere. If an air parcel is traveling frm east t west in the Suthern Hemisphere, we expect it t a) stay n the same path and increase its speed b) stay n the same path and decrease its speed c) be deflected suthward by the Crilis frce d) be deflected nrthward by the Crilis frce 3. If a sea-breeze circulatin is established during mid-afternn, the pressure at an altitude well abve the surface is a) higher ver land b) higher ver the sea c) the same ver land and sea d) scillating between higher ver land and higher ver the sea 4. Suppse the pressure difference inside and utside f a sealed il drum is Pa. If the il drum s surface area is.0 m, what is the net frce acting n the surface f the il drum? a) 5.0 N b) N c) 0 N d) 7.5 N 5. In the Hadley cell, there is a) warm, mist air rising at 30º Nrth and Suth b) warm, mist air rising at the equatr c) cld, dry air rising at the ples d) mist air ascending in the Western Pacific and descending in the Eastern Pacific 6. Latent heat release frm cndensatin a) causes water vapr t reach saturatin b) remves heat frm the surrunding air c) adds heat t the surrunding air d) is the reasn that cluds frm 7. What is the saturatin vapr pressure f water if the relative humidity is 80% and the vapr pressure f water 1 mb? a) 15 mb b) 5 ºC c) 9.6 mb d) 13 mb e) nt enugh infrmatin
8. We may expect rain in a regin where there is a) stability and n vertical mtin b) strng hrizntal wind c) subsidence and dwnward mtin d) buyancy and upwards mtin Name: 9. What is the atmspheric pressure surrunding me if I ascend ne scale height abve sea level where the atmspheric pressure is 1.0 atm? a) 0.50 atm b) 0.37 atm c) 0.63 atm d).7 atm. The Hadley cell a) was first discussed in the 18 th century b) was advanced t explain the existence f trade winds near the equatr and westerlies at middle latitudes c) des nt extend t the ples due t the influence f the Crilis frce d) all f the abve 3
Sectin II: Shrt answer Shw all wrk t receive partial credit Name: 11. Munt Waialeale n the island f Kauai, Hawaii is ntable fr having the secnd highest average annual rainfall n Earth. (0 minutes) a) An air parcel abve the island has a temperature f 1ºC and water vapr pressure f 1 mb. Use the graph f the Clausius-Clapeyrn equatin (prvided n the frmula sheet) t estimate the dew pint (in units f ºC) and the relative humidity (in units f %) f this parcel. (4 pints) Dew pint ~ ºC RH 0 (1 mb / 4.5 mb) 49% b) Offshre air that is appraching the island at sea level has a temperature f 18ºC. Suppse the dew pint were 8ºC and (t make a quick estimate) is independent f altitude. As this air is pushed frm sea level up Munt Waialeale, at what altitude (in units f km) will a clud begin t frm? (5 pints) The parcel must cl at the adiabatic lapse rate, frm18 C t 8 C. Tfinal Tinitial 8 C 18 C Adiabatic lapse rate 9.8 K km Z Z Z 0 km Z final C 9.8 K km 1.0 km final initial final [3 pints] c) Des the lapse rate f the air parcel in part b change as it ascends abve the level where cluds begin t frm? Briefly explain. (4 pints) Yes The lapse rate f the parcel increases (becme less negative) nw fllwing the mist adiabatic lapse rate [1 pint] due t latent heat release frm cndensatin. [1 pint] d) Calculate the latent heat released (in units f J) if 1.8 3 kg f water vapr cndenses t frm a clud? (5 pints) 3 6 Latent heat released m L (1.8 kg) (.5 4.5 9 J J kg ) [3 pints] 4
1. In the figure belw, we bserve a pressure system ver the Great Lakes. (0 minutes) a) Assuming gestrphic balance, in what directin (clckwise r cunterclckwise) will the air travel arund this pressure system? Briefly explain. (4 pints) Cunterclckwise Lw pressure system in the Nrthern Hemisphere b) In the space belw, draw and label arrws representing the pressure gradient frce, Crilis frce and the directin f mtin f an air parcel lcated directly nrth f the pressure system s center. Assume gestrphic balance. (6 pints) Directin f mtin Crilis frce Pressure gradient frce Directin f mtin Crilis frce Pressure gradient frce c) Calculate the Crilis frce (in units f N) acting n a 1.0 kg parcel f air mving west t east at m s at 0º latitude and at 45ºN latitude. Briefly cmment n their difference. (6 pints) At 45 F mωv sin( λ ) (1.0 kg) (7.9 c At 0 N F mωv sin( λ) (1.0 kg) (7.9 c There is n Crilis frce at the equatr. -5-5 3 s ) ( m s ) sin(45 ) 1.03 N s ) ( m s ) sin(0 ) 0 N d) Given the circulatin due t the pressure system bserved abve, wuld yu expect warmer temperatures ver New England r Wiscnsin (lcated west f the Great Lakes)? Briefly explain. (8 pints) We wuld expect warmer weather ver New England. The cunterclckwise mtin f air arund the lw pressure system indicates that air arriving in New England is frm the Suth (hence warmer) whereas air arriving in Wiscnsin is frm the Nrth (hence clder). [6 pints] 5
13. The current (008) mixing rati f carbn dixide (CO ) in the atmsphere is 384 ppm and is increasing at a rate f 1.8 ppm per year. (0 minutes) a) If the rate f increase f CO remains unchanged, what will be the atmspheric CO mixing rati (in units f ppm) in the year 05? (4 pints) ppm 384 ppm + 1.8 17 yr 414.6 ppm 415 ppm yr [4 pints] b) Calculate the number density (in units f mlecules m -3 ) f CO in this lecture hall assuming the pressure and temperature in the rm are 1.01 5 Pa and 3ºC, respectively, and the CO mixing rati is 384 ppm. (6 pints) n n CO P kt (1.38 air 3 n air mixing rati 5-1.01 N m J mlecule K ) (3 + 73) K CO (.47 9.49 5 1 mleculesf CO J N m m.47-3 5 mlecules f air m -3 384 mlecules CO mlecules f air m ) 6 mleculesair -3 c) Cmpare the accumulatin rate f CO in the atmsphere (1.8 ppm yr ) t the emissin rate f CO frm fssil fuels cmbustin (8.0 9 tns carbn yr ). Briefly explain their difference in terms f prcesses happening in the envirnment? (8 pints) Accumulatin f CO (8.0 9 3.8 ppm yr in the atmsphere if all emitted CO tns carbn yr (expected) 1ppm CO ) 9.1 tns carbn emitted > (1.8 ppm yr bserved) stayed in the atmpshere Only abut half (47%) f the emitted CO frm fssil fuel cmbustin stays in the atmsphere. This discrepancy is explained by the fact that CO in the atmsphere is taken up by the bisphere and the ceans. [4 pints] 6
Frmulas: Fma where F frce (N), m mass (kg), a acceleratin (m s - ) PF/A where P pressure (N m - ), A area (m ) PVNkT where N number f mlecules PnkTρR'T where n number density (mlecules m -3 ) and ρ mass density (kg m -3 ) P(z)P(z )e -z/h where HR'T/gkT/(m air g ) and m air is the mass f an air mlecule (kg mlecule ) Em L where E energy (J) released/required fr phase change, m mass underging phase change Net vertical frce (ρ fluid - ρ bject ) V bject g RH0 (P w /P sat ) where P w is water vapr pressure and P sat is the saturatin vapr pressure Clausius-Clapeyrn Equatin: 1 1 P sat ( 6.11 mb) exp 5308 K 73 T Pressure gradient frce mδp/(ρδx) where ΔP is the change in pressure ver a distance Δx Crilis frce mωv sin(λ) where Ω7.9-5 s, v is wind speed, λ is latitude. Deflectin due t Crilis Δy (Δx) Ω sin(λ)/v Cnstants: g acceleratin due t gravity 9.81 m s - k Bltzmann's cnstant 1.38-3 J mlecule K R' Atmspheric gas cnstant 87.5 J Kg K L Latent heat f vaprizatin/cndensatin f water.5 6 J kg Dry adiabatic lapse rate 9.8 K km Cnversins and SI Units: Pressure: 1 atm 13 mb 1.013 5 N m - 1.013 5 Pa Mles: 1 mle 6.03 3 mlecules Temperature: T(K) T(ºC) + 73.15 CO : 1 ppm f CO.1 9 tns f carbn in the atmsphere Quantity SI Units Length Meter (m) Time Secnd (s) Mass Kilgram (kg) Temperature Kelvin (K) Velcity m s Acceleratin m s - Frce r Weight Newtn (N) kg m s - Pressure Pascal (Pa) N m - Energy r Wrk Jule (J) N m 7