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A cloud is observed to commence formation at a temperature of −61° C and continues to cool due to emission of infrared radiation. a) Determine the partial pressure (Pa) and density of water vapour (mg/m³) in the air before cloud formation commenced. b) Determine the partial pressure (Pa) and density of water vapour (mg/m³) in the cloud when the temperature is -63° C. c) Calculate the ice water content (mg/m³) in the cloud when the temperature is −63º C.

A cloud is observed to commence formation at a temperature of −61° C and continues to cool due to emission of infrared radiation. a) Determine the partial pressure (Pa) and density of water vapour (mg/m³) in the air before cloud formation commenced. b) Determine the partial pressure (Pa) and density of water vapour (mg/m³) in the cloud when the temperature is -63° C. c) Calculate the ice water content (mg/m³) in the cloud when the temperature is −63º C.

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
Section: Chapter Questions
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A cloud is observed to commence formation at a temperature of-61° C and continues to cool due to emission of infrared radiation. a) Determine the partial pressure (Pa) and density of water vapour (mg/m³) in the air before cloud formation commenced. b) Determine the partial pressure (Pa) and density of water vapour (mg/m³) in the cloud when the temperature is -63° C. c) Calculate the ice water content (mg/m³) in the cloud when the temperature is −63° C. Use Table 1. Table 1. Saturated water vapour pressure and density. Temperature (°C) Saturated Water Vapour Pressure (Pa) -60 -61 -62 -63 -64 -65 1.100 0.9612 0.8382 0.7300 0.6349 0.5515 Saturated Water Vapour Density (mg/m³) 11.192 9.819 8.603 7.528 6.579 5.742
Transcribed Image Text:A cloud is observed to commence formation at a temperature of-61° C and continues to cool due to emission of infrared radiation. a) Determine the partial pressure (Pa) and density of water vapour (mg/m³) in the air before cloud formation commenced. b) Determine the partial pressure (Pa) and density of water vapour (mg/m³) in the cloud when the temperature is -63° C. c) Calculate the ice water content (mg/m³) in the cloud when the temperature is −63° C. Use Table 1. Table 1. Saturated water vapour pressure and density. Temperature (°C) Saturated Water Vapour Pressure (Pa) -60 -61 -62 -63 -64 -65 1.100 0.9612 0.8382 0.7300 0.6349 0.5515 Saturated Water Vapour Density (mg/m³) 11.192 9.819 8.603 7.528 6.579 5.742
Wien's displacement Law: Ap=2898/Tum Kirchoff's Law: absorptivity = emissivity Flux of solar Radiation at Earth: F, = T1370 Watts/m² Effective Radiating Temperature for the Earth (current climate): T₂ = 255 K Beer's Law: 1(x) = 1(0) exp[-x]; x = kpdx = fondx Optical cross section: k in Force of buoyancy: Fg = g kg Ideal Gas Law: P = pRT; R = 287 J Kg¹ K Ideal Gas Law: P = nkT; k=1.381x 1023 J/K Ideal Gas Law for Water Vapour: e=p, R, T; R = 461.5 J Kg¹ K-¹ Hydrostatic Equation:=-pg Barometric Law: P(z) = P(0) exp(-); H = RT/g; P. = 100 × 10³ Pa; g = 9.81 m/s² (Po-P) (T-T₂) P To dT Adiabatic Lapse Rate: dz or o in- m² molecule Cp = g First Law of Thermodynamics: &q= c₂ dT + P da or 8q = cp dT - 1 dp Specific Heat Capacity for Air: c=1005; CAPER -9.8 °C/km EL So LFC Potential Temperature: 0 = T Brunt-Vaisala Frequency, or Buoyancy Frequency: N² = 98 = 0 dz Latent Heat of Condensation for water: 2535 J/g Latent Heat of Sublimation for water: 2834 J/g Les Clausius-Clapeyron Equation: dT R₂T² Solution to C-C equation: () eso Joules kg-deg C = exp { (- Đ Saturated (Wet) Adiabatic Lapse Rate: I' at To 0 °C (273 K), eso = 611 Pa Equivalent Potential Temperature: 0 = 0 exp Adiabatic liquid/ice water content: x = - Velocity: v² v² = 2a(z-zo); a is acceleration (T-T₂) dinPo dT dz LWS 1+ L dws Cp dr Information (as provided on 2021 final exam) Earth-Sun mean distance: 149.598 x 10⁹ m Radius of Sun: 6.96 x 10³ m Radius of Earth: 6371 x 10³ m Effective temperature of Sun: 5770 K Cross sectional area of a sphere: R² Surface area of a sphere: 4R² Solid Angle: 2 = Area on sphere/R²; d = sine de do Albedo of the Earth: A = 0.3 Plank Function: B(A,T) = 2hc² hc As ekXT-1 Plank's constant: h = 6.626 × 10-³4 Js Boltzmann's constant: k = 1.381x 1023 J/K Speed of light: c = 3 x 10³ m/s Flux: F = f I cose d Watts m² μm-ST Watts m² Stephan's constant: = 5.67 × 108 Wm² K-4 Net flux upward or downward for isotropic radiation: F = al Stephan-Boltzmann Law: F = 6T4 -Aws(); or x = - Δρ. (mg) kg m³
Transcribed Image Text:Wien's displacement Law: Ap=2898/Tum Kirchoff's Law: absorptivity = emissivity Flux of solar Radiation at Earth: F, = T1370 Watts/m² Effective Radiating Temperature for the Earth (current climate): T₂ = 255 K Beer's Law: 1(x) = 1(0) exp[-x]; x = kpdx = fondx Optical cross section: k in Force of buoyancy: Fg = g kg Ideal Gas Law: P = pRT; R = 287 J Kg¹ K Ideal Gas Law: P = nkT; k=1.381x 1023 J/K Ideal Gas Law for Water Vapour: e=p, R, T; R = 461.5 J Kg¹ K-¹ Hydrostatic Equation:=-pg Barometric Law: P(z) = P(0) exp(-); H = RT/g; P. = 100 × 10³ Pa; g = 9.81 m/s² (Po-P) (T-T₂) P To dT Adiabatic Lapse Rate: dz or o in- m² molecule Cp = g First Law of Thermodynamics: &q= c₂ dT + P da or 8q = cp dT - 1 dp Specific Heat Capacity for Air: c=1005; CAPER -9.8 °C/km EL So LFC Potential Temperature: 0 = T Brunt-Vaisala Frequency, or Buoyancy Frequency: N² = 98 = 0 dz Latent Heat of Condensation for water: 2535 J/g Latent Heat of Sublimation for water: 2834 J/g Les Clausius-Clapeyron Equation: dT R₂T² Solution to C-C equation: () eso Joules kg-deg C = exp { (- Đ Saturated (Wet) Adiabatic Lapse Rate: I' at To 0 °C (273 K), eso = 611 Pa Equivalent Potential Temperature: 0 = 0 exp Adiabatic liquid/ice water content: x = - Velocity: v² v² = 2a(z-zo); a is acceleration (T-T₂) dinPo dT dz LWS 1+ L dws Cp dr Information (as provided on 2021 final exam) Earth-Sun mean distance: 149.598 x 10⁹ m Radius of Sun: 6.96 x 10³ m Radius of Earth: 6371 x 10³ m Effective temperature of Sun: 5770 K Cross sectional area of a sphere: R² Surface area of a sphere: 4R² Solid Angle: 2 = Area on sphere/R²; d = sine de do Albedo of the Earth: A = 0.3 Plank Function: B(A,T) = 2hc² hc As ekXT-1 Plank's constant: h = 6.626 × 10-³4 Js Boltzmann's constant: k = 1.381x 1023 J/K Speed of light: c = 3 x 10³ m/s Flux: F = f I cose d Watts m² μm-ST Watts m² Stephan's constant: = 5.67 × 108 Wm² K-4 Net flux upward or downward for isotropic radiation: F = al Stephan-Boltzmann Law: F = 6T4 -Aws(); or x = - Δρ. (mg) kg m³
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