GEU 0047: MeteorologyLecture 02

Heat Energy

Temperature is our way of quantifying matter’s internal kinetic energy.

It is a macroscopic measurement of the average kinetic energy found in the random and microscopic motions (vibration, rotation, and collision) of countless atoms and molecules.

Temperature is related to heat energy.

Heat Energy

What is temperature?

using Kinetic temperature definition

it is a measure of the average translational kinetic energy associated with the disordered microscopic motion of atoms and molecules.

Here, Temp. is measured in Kelvin in the SI units.

K: Boltzman const. = 13.805 x 10-24 J deg-1K = nR; R is the gas law constant in units of 1.98 cal/deg mole

Temperature ConversionsCELCIUS

C = 5/9 (F-32)

Fahrenheit

F = (9/5 C) + 32

Absolute or Kelvin

K = C + 273

Boiling Point of WaterCelcius

C = 5/9 (F-32) C = 100

Fahrenheit

F = (9/5 C) + 32 F = (9/5 100) + 32 = 180 + 32

Absolute = 212or Kelvin

K = C + 273 K = 100 + 273 = 373

Freezing Point of WaterCelcius

C = 5/9 (F-32) C = 5/9 (32-32) = 0.0

Fahrenheit

F = (9/5 C) + 32 F = 32

Absolute or Kelvin

K = C + 273 K = 0 + 273 = 273

Analog Temperature Conversion Plot

C F K F K

-20 -4 253 9/5*C +32 C + 273

0 32 273

20 68 293

40 104 313

60 140 333

80 176 353

100 212 373

Celsius to Fahrenheit ConversionCelcius to Fahrenheit

-80-60-40-20

020406080

100120140160180200220240260280300320340360380400420

-40

-30

-20

-10 0

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20

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40

50

60

70

80

90

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0

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0

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Celsius

Fa

hre

nh

eit

Series1

Distribution of Speeds

Maxwell-Boltzman Velocity Distribution

E

E

ENotice that the above plot is not symmetric => probability kinetic energy ≠ average kinetic energy.

Temperature and Kinetic Energy

T = mwv2

= 4.0 x 10-5 Ks2/m2

v2 = average molecular speed (KE)

mw = molecular weight Atmospheric Molecule

28.01 N2

32.00 O2

18.02 H2O

44.01 CO2

28.96 Weighted Mean Composition

Molecular Velocity

For a cold day (-15 oC) what is the average speed of a nitrogen molecule as compared to a hot day (32 oC)

v2 = T / mw

= 258 / (4E-5 x 28.01)

vcold = 480 m/s

v2 = T / mw

= 305 / (4E-5 x 28.01)

vhot = 522 m/s

Day Ground TemperatureOfficial

Temperature

is read at a

height of

1.5 meter

above the

ground, in

the shade,

and out of

the wind.

Night Ground Temperature• The ground radiates away the daytime heat faster than the

air above it.

Air is a

very poor

conductor.

Air Turbulence• Air motion causes mixing, removing stagnant boundary air

Hence, larger temperature gradients are possible without the wind

Radiation Shield• Thick forest, or Clouds can provide a radiation shield

Thermal Insulation• Thick Forest, Low Clouds can provide a thermal blanket

Temperature DataMean Daily Temperature:

average over 24 hours

Mean Annual Temperature:

average of 12 months

Average mean daily Temp.:

average of mean daily

temperatures over 30 years

Annual Temperature Range:

Difference between largest

monthly mean and smallest

monthly mean temperature.

Growing Days• Number of days when the mean daily temperature is 1

degree above the base temperature for the particular crop.

Cooling Degree Days• Used to estimate energy and power consumption needs for

cooling indoor air during summer. Base Temp = 65oF

Heating Degree Days• Used to estimate energy and power consumption needs for

heating indoor air during winter. Base Temp = 65oF

Controls of Temperature (important)• Solar Insolation

– Date & Time

– Latitude

– Exposure (wind, humidity)

• Geographic– Land

– Water

• Oceanic– Currents

• Topography– Elevation

Heat Index (apparent temp. due to RH)

c.f. Table D.2 in Appendix D

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Relative humidity (RH)(important)

• Amount of water vapor Amount required for saturation

• Water vapor pressure

Saturation water vapor pressure

• Hence, RH depends on the ambient Temp (and Pressure)

Wind Chill (apparent temp. due to wind)• Wind Chill Equivalent Temperature

– If the air temperature is 10 。 F and the wind is 25 mph, the wind chill equivalent temperature is -29 。 F .

Wind chill = 35.74 + 0.6215 T - 35.75 V0.16 + 0.4275 T V0.16

T: air temp. (F) V: wind speed (mph)

Matter Phases

• In order of increasing Temperature (Energy):

– CRYSTAL Occurring at the coldest temperatures– SOLID– LIQUID – GAS– PLASMA Occurring at the highest temperatures

Matter Phases

• In order of decreasing Organization (Symmetry):

– CRYSTAL Highly Ordered– SOLID– LIQUID– GAS– PLASMA Highly Disorganized

Phase Transitions

State ChangesEnergy increased and absorbed by substance:

• SOLID to LIQUID Melting

• LIQUID to GAS Boiling

• SOLID to GAS Sublimation

Energy decreased and released by substance:

• GAS to SOLID Deposition

• GAS to LIQUID Condensation

• LIQUID to SOLID Freezing

Water CrystalsAtomic and Molecular Structures Lead to Macroscopic Order

Heat Energy must be absorbed by the solid to break the highly ordered ice crystals. Heat Energy is released by a liquid in order to crystallize.

Phase Diagram

Latent Heat

T = const

T = const

Latent Heat of Fusion (Lf)

Heat Energy required to convert solid to liquid

Latent Heat of Evaporation (Lv)

Heat Energy required toconvert liquid to gas.

Water Latent Heat ExchangeCondensation yield 6.75 times more heat energy than

Fusion (Evaporation require 6.75 times more heat energy than Melting).

For water, Lf = 80 Cal /gram; Lv = 540 Cal/gram

Heat/energy Units

• Calorie: the amount of heat required to raise the temperature of 1 gram of water by 1 degree Celsius.

• 1 cal. = 4.186 Joules

• (1 Food calorie = 1,000 calories = 4186 J)

(see Appendix A for more)

Specific Heat ( 比熱 )• Q = m c T Q = Heat Energy (human

perception)

m = mass

T = Temperature difference

c = specific heat responsible for the thermal properties of the substance (J/kg/oC)

• T = Q/mc

Specific Heat T = Q/mc

For a given amount of heat energy, say 10,000 Joules,

what is the temperature change for 1 kg of water and

1 kg of sand?

Csand = 838 J/kgoC

Cwater = 4180 J/kgoC

Tsand = 10,000/1(838) = 11.9 oC

Twater = 10,000/1(4180) = 2.4 oC

Northern Hemisphere

Southern Hemisphere.

Land Versus SeaLand masses in the

North cause more

temperature

variations than

in the South where

oceans keep

the temperature

more even and

moderate.

Melting T = Q/mc

Amount of heat energy needed to bring a 0.25 kg ice

block to a temperature of 50oC? (Starting Temp = 0oC

Ending Temp = 50oC)

Q = heat needed to make transition from ice to water + heat needed to heat water from 0 to 50 oC

Q = mLf + mcT

Melting T = Q/mc

Q = heat needed to make transition from ice to water

+ heat needed to heat water from 0 to 50 oC

Q = (250 g) (80 Cal/g) (4.186 J/Cal) +

(0.25 kg) (4180 J/kgoC) (50-0 oC)

= 83720 + 52250 = 135970 Joules

Can you calculate it ? (important)

The amazing water molecule

(Covalent bond)

(in electricity) (hydrogen bonding)

Plus

high heat capacity (thermal inertial) and solvent power

Liquid/gas state only

共價鍵結

Freezing

This latent heat energy is released when water droplets

freeze. Water vapor that condenses also gives off

latent heat. Both processes help heat the

atmosphere.

The opposite processes (melting or evaporation) cause

heat energy to be removed from the atmosphere.

CONDENSATION• Gas to Liquid (or Freezing, Liquid to Solid)

– ENERGY IS RELEASED, Gas has a higher internal energy than the liquid state.

– A WARMING PROCESS

EVAPORATION• LIQUID to GAS

– ENERGY IS REMOVED, Liquid has a lower internal energy than the gaseous state.

– A COOLING PROCESS

RadiationEnergy transport via electromagnetic waves

Convection

Energy transport by mass motion

ConductionEnergy transport by vibrational translation

The jostling of atoms andmolecules in close proximityin a solid, especially one withhigh conductivity.

電磁波譜

電磁波依波長可分為：• γ 射線、 x 射線、紫外線、可見光、紅外線與無線電波

--無線電波又可進一步細分成微波、超短波、短波和長波

--紅外線有時也細分為近紅外線、遠紅外線與次毫米波

電磁波示意圖

電磁波譜

• 不同波長的電磁波，表現出的特色有明顯的差異

• 物體溫度較高時，輻射頻率較高，波長較短，例如：紫外線

• 物體溫度較低時，輻射線頻率較低，波長較長，例如：紅外線

可見光

-- 人類眼睛可看到，其波長在 0.4 μm~0.7 μm ( 可見光 ) (1μm =10-6m)

-- 為什麼？ 與太陽輻射能量分佈有關-- 太陽輻射相當於 6000 K 物體的輻射 涵蓋波長範圍包括紫外射線、可見光、紅外線、微波、電視及電台波段

-- 最大能量集中在可見光

太陽短波輻射和地球長波輻射 (Fig. 2.8 of text)

可見光•我們看到的色彩大多不是物體本身放射出來，而是反射陽光或照明設備

例如：紅色的書皮--是書皮反射陽光中的紅色，吸收其他顏色

--將書帶到暗房就看不到書--事實上，書也一直放射輻射，但因為溫度太低，放射的是紅外線，因而人類無法看到書的「本色」！

可見光

• 人類眼球結構的發展顯然與太陽輻射分佈有關。如果人類是穴居動物，我們的「可見光」可能就必須定義在紅外線波段！！

Blackbody radiation ( 黑體輻射 )

黑體是一種理想物體或狀況自然界中大部分固體或液體都近乎黑體高溫物體幾乎在每個波段都會輻射能量每一曲線的峰值也因為溫度的不同而改變

普朗克定律 (Planck’s law)

• 太陽輻射大多來自表面的光球部分，其能量 : Eλ隨波長變化，可用普朗克定律 (Planck’s law) 描述：

λ：波長 (m) ， T：溫度 (K)

兩個常數 : C1=3.74×10-16 W m2，C2=1.44×10-2 m K

黑體在不同溫度下所輻射出的能量頻譜 (Fig. 2.9)

?

?

?

韋恩定律 ( 或汾因定律 )(Wien’s law)

微分普朗克定律，就可求得發射能量峰值的波長 λmax

溫度越高， λmax 越短。 太陽溫度 6000K ， λmax = 0.5 μm

地球溫度 300K ， λmax 約等於 10 μm　

)()(

2897max m

KT

史蒂芬 - 波玆曼定律

若對普朗克定律積分，則得到史蒂芬 -波玆曼定理 (Stefan-Boltzman law) ：

E =σ T 4

史蒂芬 - 波玆曼常數 σ = 5.67×10-8 W m-2 K-4

溫度 600 K 的物體放射出的能量，是溫度 300 K 物體的 16 倍 !!

長波輻射與短波輻射

• 太陽溫度 6000K ，地球溫度 300K

• 兩個星球的輻射波譜，重疊部份幾乎可以忽略

• 一般稱太陽輻射稱為短波輻射 (short wave radiation) ，地球輻射為長波輻射(long wave radiation) 、地表輻射(terrestrial radiation) 或紅外輻射(infrared radiation)

Energy Balance

370

Earth Albedo• Reflection and Absorption of Incoming Solar Energy

Energy Budget

• Sunbeam (1365-1372 W/m2) = 100 % at the top of atmosphere

– 30 % reflected and scattered back out to space (411 W/m2)• Earth’s surface (4%)

• Clouds (20%)

• Atmosphere (6%)

– 19 % absorbed by Earth’s atmosphere (260.3 W/m2)

– 51 % heats Earth’s surface directly (698.7 W/m2)

沒有大氣的地球輻射平衡 (c.f. Ahrens ， p.42 ， Figure 2.12)

假設地球沒有大氣層•地球接收的太陽短波輻射等於放射出去的長波輻射•則地球平均溫度約為 -18oC

Te4 = S(1-A)/4

地球： A = 0.3, S = 1367 W/m2

Te = 255K

輻射平衡與地球溫度

實際上能量的平衡，除了輻射能量以外，還有其他因素

地球 - 大氣間的能量平衡示意圖

A Green HouseGlass is transparent to visible wavelengths (SW)

but opaque to infrared wavelengths (LW).

Atmosphere AbsorptionAtmospheric

Absorption

Energy Transformations• Radiant Solar Energy (1367 W/m2)

• Heat Energy (Gas Kinetic Energy Increased)

• Water Evaporation (Latent Heat)

• Air Convection (Potential Energy Increased)

• Water Condensation (Latent Heat Released)

• Precipitation (Converting Potential to Kinetic Energy)

• Erosion (Kinetic Energy causes Erosion Deformation)

• Reservoirs (Potential Energy of a Dam)

• Hydroelectric Power (Conversion of PE to KE to Electrical Energy)

Aurora

Magnetic Field

Particles Spiraling• Charged particles and a Magnetic Field (simulations)

http://www.phy.ntnu.edu.tw/java/emField/emField.html

Magnetosphere• Solar Wind (charged particles) and Earth’s Magnetic Field

S.-P. Weng 76

閃焰

Auroral Probability Zones• Number of Nights per Year Experiencing Northern Lights

http://www.pfrr.alaska.edu/~pfrr/AURORA/

Auroral Ionization Ring

Arkansas Aurora 2003-11-20

Arkansas Aurora 2003-11-20

Arkansas Aurora 2003-11-20

Summary• Temperature and Kinetic Energy• Temperature Scales

– Kelvin

– Celsius

– Fahrenheit

• Physical Changes of State– Latent Heat

– Specific Heat

• Energy Balance and Heating– Radiation, Convection, Conduction

– Albedo

– Greenhouse Effect

• Aurora