geu 0047: meteorology lecture 02 heat energy. temperature is our way of quantifying matter’s...
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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
10
20
30
40
50
60
70
80
90
10
0
11
0
12
0
13
0
14
0
15
0
16
0
17
0
18
0
19
0
20
0
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