Energy, Light, Temperature
A 1000 W microwave runs for 30 seconds.
How much energy does it use?
30000 Joules
1000 W × 30 s = 30,000 J.
Why do we divide the TSI by 4?
A planet intercepts sunlight over πR² but has surface area 4πR².
The composition of dry air is approximately:
20% N₂, 80% O₂
The dry lapse rate is:
10 K/km
The daytime sky is blue because:
Rayleigh scattering by molecules much smaller than the wavelength favors blue.
The peak emission wavelength of an object at 500 K.
6 μm
3000μm K / 500K = 6 μm
What does 255 K represent for the real Earth?
The temperature of the τ = 1 (approximately 5 km) layer that radiates to space.
Air at 1000 mb total pressure is 21% oxygen by number of molecules. The partial pressure of oxygen is:
210 mb
Share of molecules = share of pressure: 0.21 × 1000 = 210 mb.
The moist lapse rate is smaller than the dry one because:
Condensation releases about 3.5 K/km, so 10 − 3.5 = 6.5.
Who discovered the greenhouse gases and name 3 of which they discovered?
John Tyndall
Water Vapor, Carbon Dioxide, Methane
Why does a ripe red apple look red?
It scatters red light and absorbs the other visible colors.
Everyday colors are scattered sunlight. Using Wien's law on a scattered color is the trap.
A rocky planet with no atmosphere has TSI = 2720 W/m² and albedo 0.3. The sunlight it absorbs per m² of surface is:
476 W/m²
2720 / 4 = 680; 680 × (1 - 0.3) = 476 W/m²
Or
TSI = 2720 W/m² (twice Earth's) Therefore, 238 W/m² x 2 = W/m²
Relative humidity = 0.4 means:
RH = Pv / Pv*, so Pv < Pv*. Net evaporation.
A dry air parcel at 360 K rises 3 km. Its temperature is now:
330 K
3 x 10 = 30; 360 - 30 = 360 K
If more greenhouse gas raises the τ = 1 level by 1 km, the surface temperature changes by about:
Surface warms by the lapse rate times the height change: +6.5 K.
Two identical objects, one at 200 K and one at 400 K. The hotter one radiates how many times more power?
16 times.
Double T → 2⁴ = 16× the power.
A rocky planet with no atmosphere has TSI = 8192 W/m² and albedo 0.25. The planet's temperature is closest to:
400 K
8192 / 4 = 2048; 2048 × (1 - 0.25) = 1536 W/m²
Using Stefan-Boltzmann Law: 6 × (T/100)⁴ = 1536
1536 / 6 = 256 = 4⁴, so T/100 = 4 and T = 400 K.
Evaporation occurs when:
Water boils when:
Evaporation: Pv* > Pv
Boiling: Pv* exceeds the total pressure
Boiling needs the saturation vapor pressure to exceed the total pressure.
What is the cloud base? (MUST state all)
The height at which the rising air first condenses water vapor.
The height at which rising air hits a relative humidity of one.
The height at which the saturation vapor pressure first equals the rising air’s vapor pressure.
According to _________ Law, Earth's predicted temperature is ____ K. However, this temperature is too ____ compared to the actual temperature because:
How do we calculate Earth's actual surface temperature?
Stefan-Boltzmann, 255K, cold
255 K is the temperature at which earth radiates to space from τ = 1 at 5 km.
Earth's actual surface temperature: 288K
255 + 6.5 × 5 = 287.5 ≈ 288 K.
A surface emits 486 W/m². Its temperature is closest to:
300K
Using Stefan-Boltzmann Law: 6 × (T/100)⁴ = 486
486 / 6 = 81 = 3⁴, so T/100 = 3 and T = 300 K.
A planet identical to Earth in albedo (0.3) with no atmosphere orbits at twice Earth's distance. Its temperature is closest to (calculator OK):
177 K (180 K)
TSI Scales 1/(distance from sun)2; 1/(2)2 = 1/4
Planet's TSI = (1/4) x (Earth TSI = 1360) = 340
340 / 4 = 85; 85 × (1 - 0.3) = 59.5 W/m²
59.5 = 6 (T/100)4; 59.5 / 6 = 9.92; sqrt4 (9.92) = 1.77; 1.77 x 100 = 177 --> 180 K
Two suction cups of radius 10 cm are pressed together (use π ≈ 3). About what mass is needed to pull them apart?
300 kg
Area = 3 × (0.1)² = 0.03 m². 0.03 × 10,000 kg/m² = 300 kg.
The surface is 270 K and the air above is cloudy and follows the typical lapse rate. The temperature 6 km up is:
231 K
6 × 6.5 = 39; 270 − 39 = 231 K
Match the names and their accomplishments in the discovery of global warming:
James Hansen, Joseph Fourier, Svante Arrhenius, John Tyndall, Dave Keeling
First predicted global warming and made a calculation of Earth’s climate sensitivity? 1898
Identified the gases responsible for the greenhouse effect? 1854
Svante Arrhenius
John Tyndall
Joseph Fourier
James Hansen
Dave Keeling