Lecture 05: Heat Engines in the Atmosphere

Slides:



Advertisements
Similar presentations
GLOBAL CLIMATES & BIOMES
Advertisements

Atmospheric Stability
Atmospheric Stability and Cloud Formation. RECAP Mechanical equilibrium: stable, unstable, neutral. Adiabatic expansion/compression: no heat exchange.
Tephigrams ENVI1400 : Lecture 8.
METO 637 Lesson 1. Fig Troposphere- literally means region where air “turns over” -temperature usually decreases (on average ~6.5°C/km) with.
Thermodynamics of the Atmosphere Ideal Gas Atmosphere contains N 2 + O 2 + Ar + CO 2 ± H 2 O - well mixed in turbosphere - ideal gas (unless saturated)
* Reading Assignments:
Thermal Structure of the Atmosphere: Lapse Rate, Convection, Clouds, Storms.
Air Pressure. State Variables Describe the “state” of the gas “Variable” means they can change Physicists use P, V, T, N and constant k Chemists use P,
Lapse Rates and Stability of the Atmosphere
Thermodynamics, Buoyancy, and Vertical Motion Temperature, Pressure, and Density Buoyancy and Static Stability Adiabatic “Lapse Rates” Convective Motions.
Chapter 4 Moisture and Atmospheric Stability. Steam Fog over a Lake.
Chapter 11 Section 2 State of Atmosphere. Temperature vs. Heat Temperature: measures the movement of molecules  Faster = Warmer  Slower = Colder  Measured.
Atmospheric Moisture Vapor pressure (e, Pa) The partial pressure exerted by the molecules of vapor in the air. Saturation vapor pressure (e s, Pa ) The.
Objectives Review Vocabulary
Atmospheric Properties II Martin Visbeck DEES, Lamont-Doherty Earth Observatory
Water in the Atmosphere Evaporation Condensation and Cloud Formation.
Properties of the Atmosphere
The Atmosphere and is its importance to the Earth.
Atmosphere Chapter 11.2 & 11.3.
The Atmosphere: Part 3: Unsaturated convection Composition / Structure Radiative transfer Vertical and latitudinal heat transport Atmospheric circulation.
CHEMISTRY CONCEPTS (LAST CLASS) CHEMICAL THERMODYNAMICS: steps don’t matter  final state – initial state CHEMICAL KINETICS: rates depend on series of.
Lab 6: Saturation & Atmospheric Stability
EARTH SCIENCE Prentice Hall EARTH SCIENCE Tarbuck Lutgens 
Temperature Structure of the Atmosphere Chapter 5.
EARTH SCIENCE Prentice Hall EARTH SCIENCE Tarbuck Lutgens 
Water in the Atmosphere Lab 5 October 5, Water Is Important!!!
11.2- State of the Atmosphere Moisture in the Atmosphere
Photo: Pamela R. Cox 2013 Elizabethtown, Kentucky.
Lecture 4 Precipitation (1)
Weather and Climate Unit Investigative Science. * Meteorologists describe properties of the atmosphere using the following descriptors: * Temperature.
Moisture  There are several methods of expressing the moisture content (water in vapor form) of a volume of air.  Vapor Pressure: The partial pressure.
The Earth’s Atmosphere. The Atmosphere Present Atm. N 2 (78%) O 2 (21%) Ar (1%) CO 2 (0.04%) H 2 O (varies) …others Early Atm. N 2 CO 2 H 2 O H 2 S HCN.
Weather / Meteorology Atmospheric Layers &Temperature.
STATE OF THE ATMOSPHERE Earth Science. Temperature vs. Heat  NOT THE SAME THING!!  Temperature measures how fast or slow molecules move around (their.
Chapter 18 Moisture, Clouds, and Precipitation When it comes to understanding atmospheric processes, water vapor is the most important gas in the atmosphere!
Monday’s lesson (At the end the lesson you will be able to…) Describe the changes in temperature with height through the lower layers of the atmosphere.
Stability and Introduction to the Thermodynamic Diagram
Chapter 11 Review Game!.
Atmosphere Section 1: Atmospheric Basics
Properties of the Atmosphere
Lesson 1 Task 1 Can you draw a fully labelled diagram to show the ‘day model’ of radiation balance in the earth’s energy budget in 5 minutes on these.
Stability and Cloud Development
5.01 Heating and Cooling of the Atmosphere
AICE EM: Atmosphere Key Content 2
Meteorology.
Atmospheric Stability
Chapter 11 The Atmosphere
Thermodynamics, Buoyancy, and Vertical Motion
What is air pressure and how does it affect us
Ch Atmosphere Atmosphere – 99% Nitrogen and Oxygen
Lab 2: Vertical Structure of the Atmosphere
Section 2: Properties of the Atmosphere
GLOBAL ENERGY BUDGET - 3 Atmosphere Basics.
Earth’s Atmosphere.
Stability and Cloud Development
Seasons and Atmosphere
Atmosphere
Chapter 11 Atmosphere Atmospheric composition; 78% Nitrogen 21% Oxygen
Section 2: Properties of the Atmosphere
Atmospheric Moisture Atmospheric moisture is a very important topic under the theme of climatic system. In this presentation, you can make use of photos.
Static flow and Its Application
5.01 Heating and Cooling of the Atmosphere
Atmospheric Stability and Cloud Formation
1. Transformations of Moist Air
Thermodynamics!.
Seasons and Atmosphere
Atmospheric Stability
Chapter 18: Water in the Atmosphere
Chapter 11 Atmosphere.
Presentation transcript:

Lecture 05: Heat Engines in the Atmosphere ENPh257: Thermodynamics Lecture 05: Heat Engines in the Atmosphere © Chris Waltham, UBC Physics & Astronomy, 2018

Adiabatic changes For a diatomic gas, 𝛾 > 1 𝑇 𝑉 𝛾−1 =constant On a PV diagram, adiabatic curves are steeper than isothermal hyperbolae, because 𝛾 > 1. See Fermi p.27: Solid lines - isothermal Dotted lines - adiabatic © Chris Waltham, UBC Physics & Astronomy, 2018

Example: the atmospheric lapse rate Convection currents in the troposphere continually transport air from sea level to higher altitudes and vice versa. The air is largely heated from below, as it is fairly transparent to solar radiation. Air is a poor conductor, so little heat is transferred between layers, and the transformations as air rises or falls can be considered adiabatic. First, we need to look at some hydrostatics. © Chris Waltham, UBC Physics & Astronomy, 2018 https://www.weather.gov/jetstream/energy

The atmosphere How and why does it change with altitude? Hydrostatics Consider a horizontal slab of air of thickness 𝑑𝑧, where 𝑧 is the altitude above the Earth’s surface. In a stable air mass the pressure below must be balanced by the weight of the slab and the pressure above. Consider a slab of air, area 𝐴, thickness Δ𝑧, with pressure below 𝑃 0 and pressure above, 𝑃 1 : Δ𝑧 © Chris Waltham, UBC Physics & Astronomy, 2018

The atmosphere The weight of the air, 𝜌ΑΔ𝑧𝑔 must be balanced by the upward buoyant force 𝑃 1 − 𝑃 0 𝐴= 𝐴𝛥𝑃 𝑑𝑃 𝑑𝑧 = −𝜌𝑔 This is the barometric equation. Apply the gas laws: 𝑑𝑃 𝑑𝑧 = − 𝑚𝑔 𝑅𝑇 𝑃 Here 𝑚 is the mean molar mass of air. © Chris Waltham, UBC Physics & Astronomy, 2018

Uniform temperature approximation If the temperature is constant with altitude (not a crazy approximation in absolute units): 𝑃 𝑧 =𝑃 0 exp⁡(− 𝑚𝑔𝑧 𝑅𝑇 ) For a mean surface temperature of 288 K, this gives a scale height 𝑅𝑇/𝑚𝑔 = 8.4 km. So at 11 km, typical cruising altitude for an airliner, the pressure would be: 𝑃 𝑧 =𝑃 0 exp⁡(− 11 8.4 ) = 0.27 𝑃 0 = 27 kPa (in reality the mean value here is 23 kPa). Note: ~ 40 kPa (6000 m) provides the absolute minimum partial pressure of oxygen to survive. Not too bad, but we can do better… © Chris Waltham, UBC Physics & Astronomy, 2018

Dry adiabatic atmosphere At some critical value of 𝑑𝑇/𝑑𝑧 air becomes buoyant and remains so even as it cools adiabatically into the lower pressure environment aloft. The relationship between temperature and pressure during an adiabatic change is: 𝑃 1 𝛾 −1 𝑇=constant Differentiate: 𝑑𝑇 𝑑𝑃 = 𝑇 𝑃 1− 1 𝛾   © Chris Waltham, UBC Physics & Astronomy, 2018

Dry adiabatic atmosphere Applying this to the barometric equation gives the dry adiabatic lapse rate, Γ𝑑: Γ𝑑 = 𝑑𝑇 𝑑𝑧 = 𝑑𝑇 𝑑𝑃 𝑑𝑃 𝑑𝑧 =−𝜌𝑔 𝑇 𝑃 (1− 1 𝛾 ) We know 𝜌=𝑚𝑛/𝑉 and 𝑛=𝑃𝑉/(𝑅𝑇): Γ𝑑 = 𝑑𝑇 𝑑𝑃 𝑑𝑃 𝑑𝑧 =− 𝑚𝑔 𝑅 (1− 1 𝛾 ) Here 𝑚 is the mean molar mass of air, ≈ 28.9 The result is about 10 K/km (and constant, so it can only be an approximation). The value is the right order of magnitude, but plainly bigger than reality; the top of Grouse Mountain is not 10 C cooler than the city. © Chris Waltham, UBC Physics & Astronomy, 2018

Moist adiabatic atmosphere The “International Standard Atmosphere” (shown) has a lapse rate of 6.5 K/km. Local lapse rates vary with temperature and RH – can occasionally be negative (“Inversion”). The air temperature reaches dew point: cloud formation, release of latent heat, which lowers the lapse rate. Big subject, no time: Climate science Weather forecasting Aviation, etc. etc. http://www.srh.noaa.gov/jetstream/atmos/layers.html and http://www.engineeringtoolbox.com/international-standard-atmosphere-d_985.html https://en.wikipedia.org/wiki/Lapse_rate F. W. Taylor in Elementary Climate Physics (Oxford, 2005) p.58. © Chris Waltham, UBC Physics & Astronomy, 2018

Hurricanes as heat engines Hurricane Harvey, 2017 G$125 damage https://en.wikipedia.org/wiki/Atlantic_hurricane © Chris Waltham, UBC Physics & Astronomy, 2018

Hurricanes as heat engines Initiated by ocean temperatures > 26 C to a depth of 60 m. Moist air starts to rise at B Air dragged in from A, latent heat added isothermally. Coriolis force starts it spinning; heat is concerted to kinetic energy (work). Air cools adiabatically as it rises. Radiative cooling C to D (isothermal). Air falls and cools isothermally. “Super-Carnot” efficiency as heat source boosted by frictional heating. Contour colours indicate entropy density. © Chris Waltham, UBC Physics & Astronomy, 2018 Kerry Emanuel, Hurricanes: Tempests in a Greenhouse, Physics Today, August 2006.

Hurricanes as heat engines A simple calculation: For 𝑇1 = 200 K and 𝑇2 = 300 K, Carnot efficiency 𝜂 = 1/3. Saturated vapour pressure of water at 27 C is about 3 kPa, 3% of standard air pressure, about 2% of air by mass. Latent heat of vaporization of water is 2.4 MJ/kg, so latent heat available in this air is 48 kJ/kg. With a Carnot efficiency of 1/3, 16 kJ/kg is available for kinetic energy. Equate to ½ 𝑚𝑣2 gives 𝑣 = 175 m/s. Ignoring surface friction. Highest recorded is 96 m/s at surface (Hurricane Patricia, 2015) 87.2 kPa for Hurricane Patricia © Chris Waltham, UBC Physics & Astronomy, 2018