Let's stop ignoring the greenhouse effect and incorporate it into the previous problem in a very rough way. Assume the atmosphere is a single layer, a spherical shell around Earth, with an emissivity e 0.77 (chosen simply to give the light answer) at infrared wavelengths emitted by Earth and by the atmosphere. However, the atmosphere is transparent to the Sun's radiation (that is, assume the radiation is at visible wavelengths with no infrared), so the Sun's radiation leaches the surface. The greenhouse effect comes from the difference between the atmosphere transmission of visible light and its rather strong absorption of infrared. Note that the atmosphere's radius is not significantly different from Earth's, but since the atmosphere is a layer above Earth, it emits radiation both upward and downward, so it has twice Earth's area. There are three radiative energy transfers in this problem: solar radiation absorbed by Earth's surface; infrared radiation from the surface, which is absorbed by the atmosphere according to its emissivity; and infrared radiation from the atmosphere, half of which is absorbed by Earth and half of which goes out into space. Apply the method of the previous problem to get an equation for Earth 's surface and one for the atmosphere, and solve them for the two unknown temperatures, surface and atmosphere. a. In terms of Earth's radius, the constant σ , and the unknown temperature T s of the surface, what is the power of the infrared radiation from the surface? b. What is the power of Earth 's radiation absorbed by the atmosphere? c. In terms of the unknown temperature T e of the atmosphere, what is the power radiated from the atmosphere? d. Write an equation that says the power of the radiation the atmosphere absorbs from Earth equals the of the radiation it emits. e. Half of the power radiated by the atmosphere hits Earth. Write an equation that says that the power Earth absorbs from the atmosphere and the Sun equals the power that it emits. f. Solve your two equations for the unknown temperature of Earth. For steps that make this model less crude, see for example (https://openstaxcollege.org/l/21paulgormlec) by Paul O'Gorrnan.
Let's stop ignoring the greenhouse effect and incorporate it into the previous problem in a very rough way. Assume the atmosphere is a single layer, a spherical shell around Earth, with an emissivity e 0.77 (chosen simply to give the light answer) at infrared wavelengths emitted by Earth and by the atmosphere. However, the atmosphere is transparent to the Sun's radiation (that is, assume the radiation is at visible wavelengths with no infrared), so the Sun's radiation leaches the surface. The greenhouse effect comes from the difference between the atmosphere transmission of visible light and its rather strong absorption of infrared. Note that the atmosphere's radius is not significantly different from Earth's, but since the atmosphere is a layer above Earth, it emits radiation both upward and downward, so it has twice Earth's area. There are three radiative energy transfers in this problem: solar radiation absorbed by Earth's surface; infrared radiation from the surface, which is absorbed by the atmosphere according to its emissivity; and infrared radiation from the atmosphere, half of which is absorbed by Earth and half of which goes out into space. Apply the method of the previous problem to get an equation for Earth 's surface and one for the atmosphere, and solve them for the two unknown temperatures, surface and atmosphere. a. In terms of Earth's radius, the constant σ , and the unknown temperature T s of the surface, what is the power of the infrared radiation from the surface? b. What is the power of Earth 's radiation absorbed by the atmosphere? c. In terms of the unknown temperature T e of the atmosphere, what is the power radiated from the atmosphere? d. Write an equation that says the power of the radiation the atmosphere absorbs from Earth equals the of the radiation it emits. e. Half of the power radiated by the atmosphere hits Earth. Write an equation that says that the power Earth absorbs from the atmosphere and the Sun equals the power that it emits. f. Solve your two equations for the unknown temperature of Earth. For steps that make this model less crude, see for example (https://openstaxcollege.org/l/21paulgormlec) by Paul O'Gorrnan.
Let's stop ignoring the greenhouse effect and incorporate it into the previous problem in a very rough way. Assume the atmosphere is a single layer, a spherical shell around Earth, with an emissivity e 0.77 (chosen simply to give the light answer) at infrared wavelengths emitted by Earth and by the atmosphere. However, the atmosphere is transparent to the Sun's radiation (that is, assume the radiation is at visible wavelengths with no infrared), so the Sun's radiation leaches the surface. The greenhouse effect comes from the difference between the atmosphere transmission of visible light and its rather strong absorption of infrared. Note that the atmosphere's radius is not significantly different from Earth's, but since the atmosphere is a layer above Earth, it emits radiation both upward and downward, so it has twice Earth's area. There are three radiative energy transfers in this problem: solar radiation absorbed by Earth's surface; infrared radiation from the surface, which is absorbed by the atmosphere according to its emissivity; and infrared radiation from the atmosphere, half of which is absorbed by Earth and half of which goes out into space. Apply the method of the previous problem to get an equation for Earth 's surface and one for the atmosphere, and solve them for the two unknown temperatures, surface and atmosphere.
a. In terms of Earth's radius, the constant
σ
, and the unknown temperature Ts of the surface, what is the power of the infrared radiation from the surface?
b. What is the power of Earth 's radiation absorbed by the atmosphere?
c. In terms of the unknown temperature Te of the atmosphere, what is the power radiated from the atmosphere?
d. Write an equation that says the power of the radiation the atmosphere absorbs from Earth equals the of the radiation it emits.
e. Half of the power radiated by the atmosphere hits Earth. Write an equation that says that the power Earth absorbs from the atmosphere and the Sun equals the power that it emits.
f. Solve your two equations for the unknown temperature of Earth.
For steps that make this model less crude, see for example (https://openstaxcollege.org/l/21paulgormlec) by Paul O'Gorrnan.
Study of body parts and their functions. In this combined field of study, anatomy refers to studying the body structure of organisms, whereas physiology refers to their function.
A. The planet Venus is different from the earth in several respects: (a) it is
only 70 % as far from the sun, so the solar constant is 2800 W/m²; (b) its
thick clouds reflect 77% of all incident sunlight and (c) its atmosphere is
much more opaque to infrared light.
B.
(i) Estimate what the average surface temperature of Venus would be if it
had no atmosphere and did not reflect any sunlight.
(ii) Taking into account the reflectivity of the clouds, estimate the surface
temperature.
Use the theory of Earth's energy balance to discuss the greenhouse effect.
The next four questions use this description.
Our Sun has a peak emission wavelength of about 500 nm and a
radius of about 700,000 km. Your dark-adapted eye has a pupil
diameter of about 7 mm and can detect light intensity down to
about 1.5 x 10-11 W/m². Assume the emissivity of the Sun is equal
to 1.
First, given these numbers, what is the surface temperature of the
Sun in Kelvin to 3 significant digits?
5,796
(a) Cherry-red embers in a fireplace are at 850C and have an exposed area of 0.200 m2 and an emissivity of 0.980. The surrounding room has a temperature of 18.0C. If 50% of the radiant energy enters the room, what is the net rate of radiant heat transfer in kilowatts? (b) Does your answer support the contention that most of the heat transfer into a room by a fireplace comes from infrared radiation?
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
The Laws of Thermodynamics, Entropy, and Gibbs Free Energy; Author: Professor Dave Explains;https://www.youtube.com/watch?v=8N1BxHgsoOw;License: Standard YouTube License, CC-BY