What is the temperature about 10 or 15 feet below Mars' surface?

What is the temperature about 10 or 15 feet below Mars' surface?

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I was wondering this for a school paper I'm writing.

This is one of key questions that NASA's Mars InSight probe is trying to answer but it has only recently arrived and starting taking data and it will be a while before the data is analyzed and published in peer reviewed journals. The "mole" which would burrow below the surface and make the temperature measurements encountered some initial issues and NASA and the instrument's builders were running further tests and looking at those data before proceeding according to this mission press release.

For a term-paper kind of answer you don't actually need to wait for Mars InSight to tell you. 15 feet is deep enough for you to able to assume that the temperature will be the average of temperatures on the surface.

So first find a graph of the temperature on a typical Martian spring or autumn day, then work out the average temperature over the 25 hours. That is a good first guess.

I think that 15 feet is deep enough for variations across the year, between summer and winter, to be averaged out fairly effectively as well, though that is something you may want to discuss a little in your paper. This Wikipedia article about permafrost is worth reading to see how the Earth averages its own temperatures at depth over the course of a year.

On a planetary scale 15 feet is very shallow indeed, so the amount of heat flowing from the inside of Mars towards the surface will be tiny (this is what that InSight probe is measuring) and I would suggest mentioning it only in order to say that you are ignoring it.

Historic climate change on Mars might be detectable

Historical instances of extreme climate change on Mars could be detected through the measurement of subsurface temperatures, according to a new University of Stirling study.

Experts in Stirling's Planetary Ices Laboratory, located within the Faculty of Natural Sciences, believe that the technology used by the heat flow probe on the latest NASA mission to Mars might be able to identify "major" climate change events of the past.

The team—led by Dr. Nicholas Attree—say the findings of their research, which involved hypothetical modeling, could help to understand similar historical events on Earth, where historical climate changes are already being traced in borehole temperature measurements.

Dr. Attree and Stirling colleague Dr. Axel Hagermann are working on NASA's InSight mission, which landed on the Red Planet last November. The scientists are simulating data obtained by the Heat Flow and Physical Properties Probe (HP3), an instrument provided by the German Institute of Planetary Research in Berlin. Dr. Attree used numerical models to estimate the effect that historic freak climate changes might have on the heat flow measurements.

Dr. Attree explained: "HP3 will be digging down into the subsurface of Mars and recording temperatures and heat flow from the interior. The magnitude of the heat flow tells us about the Martian deep interior and helps to create formation and evolution models. If historical climate change has led to more or less excess heat stored in the subsurface, it could influence HP3's results."

The team considered a specific situation where cycles in Mars's orbit causes its atmosphere to collapse—or freeze—onto the poles. In these cases, the team found that thermal conductivity of the Martian soil decreases—and, in turn, excess heat could build up.

"We found that small changes caused by climate change are unlikely to be picked up by HP3," Dr. Attree continued. "However, it may be possible to detect very large changes—and this is important because we may be able to carry out similar measurements on other planets."

Dr. Hagermann added: "We have demonstrated that it is not only historical changes in air temperature but also changes in air pressure and thermal conductivity of the soil that could be detectable, which might also be relevant for Earth, where borehole temperature measurements have played an important part in reconstructing past climate."

Built by the German Aerospace Centre, the self-hammering HP3 probe is designed to burrow between three and five meters (10 to 16 feet) into the Martian soil—15 times deeper than any previous hardware on Mars—to measure the heat flow from the planet's interior. By combining the rate of heat flow with other InSight data, the team will be able to calculate how energy within the planet drives changes on the surface, such as planetary evolution and the shaping of mountains and canyons.

The latest paper, "Potential effects of atmospheric collapse on Martian heat flow and application to the InSight measurements," is published in Planetary and Space Science.

Latitude, Longitude, and Temperature

Students look at lines of latitude and longitude on a world map, predict temperature patterns, and then compare their predictions to actual temperature data on an interactive map. They discuss how temperatures vary with latitude and the relationship between latitude and general climate patterns.

Earth Science, Geography, Physical Geography


1. Discuss differing temperatures in different places.

Activate students’ prior knowledge by asking if students have relatives who live in places that are much warmer or cooler during June, July, and August than in the students’ hometown. Locate those places on a wall map or globe. On the board, make a Three-Column Chart or project the one provided. In the first column, list those places students named, and in the second column write whether the temperatures in those places are similar, cooler, and warmer than where you are located. Ask: How would you dress differently if visiting those places? In the third column, list clothing needed for those places in the summer months. Discuss students’ ideas for why the temperatures might vary. Tell students that in this activity they will make predictions about temperature patterns around the world.

2. Review the difference between lines of latitude and longitude on a world map.
Give each student a printed MapMaker 1-Page world map, and also project the map from the provided website. Have students point to and explain the difference between lines of latitude and longitude.

3. Create a legend that shows temperature.
List the temperatures below on the board. Make sure students know these temperatures are in degrees Fahrenheit, not degrees Celsius. Have students contribute their ideas for a color range for hot to cold temperatures. Help them determine the following typical color range where red is the hottest and violet is the coldest.
violet = 30° F and below
blue = 40° F
green = 50° F
yellow = 60° F
orange = 70° F
red = 80° F and higher

4. Have students draw the average temperatures around the world in June, July, and August.

Ask students to think about climate and temperature, and what areas they think are warmest or coldest. Give each student six crayons of the colors listed in the legend, and ask them to draw their best predictions of the average temperatures around the world in June, July, and August. Tell students that the purpose of this activity is to think about patterns of temperature around the world, so their predictions will not be exact.

5. Discuss with students what they drew and why.
Conduct a class discussion about the maps. First, ask students to explain what they drew and how the colors related to latitude and longitude. Then have them work in small groups and compare their maps to their classmates’ maps. Finally, ask students to work on their own to make lists of questions the activity raised for them.

6. Have students compare their maps to an accurate map of average temperatures around the world in June, July, and August.
Show students the National Geographic MapMaker Interactive with the data layer showing average surface air temperatures around the world in June, July, and August selected. Ask students to describe similarities and differences between their map and the interactive map, surprising or unexpected parts of the map, and questions that they have about the map.

7. Have students use what they’ve learned to determine how latitude and longitude are related to temperature.
In pairs, have students discuss and answer the following questions:

  • How is latitude related to temperature? (farther from equator = colder)
  • How is longitude related to temperature? (no relationship)

8. Make sure students understand the relationship between latitude and general climate patterns.
Regroup and discuss students' answers. Make sure students understand the general climate patterns that occur as latitude increases. Explain to students that the areas farther away from the Equator tend to be cooler. Point out that the general climate patterns might not show exceptions and variations as a result of elevation, ocean currents, precipitation, and other factors. Have students follow the line of latitude from their location to the east and west to determine variations around the world at that latitude.

9. Discuss with students the importance of latitude and longitude.
Have students share why latitude and longitude are helpful map tools. Prompt them to explain how latitude and longitude can help them to identify specific locations, as well as explain general climate patterns.

Informal Assessment

Have students point out lines of latitude and longitude on one of the outline maps. Then read aloud the following statements to the class, and ask them to write what they think you might be wearing if you were really in these places:

Solar Storm Damage on Earth

When a CME reaches Earth, it distorts Earth’s magnetic field. Since a changing magnetic field induces electrical current, the CME accelerates electrons, sometimes to very high speeds. These “killer electrons” can penetrate deep into satellites, sometimes destroying their electronics and permanently disabling operation. This has happened with some communications satellites.

Disturbances in Earth’s magnetic field can cause disruptions in communications, especially cell phone and wireless systems. In fact, disruptions can be expected to occur several times a year during solar maximum. Changes in Earth’s magnetic field due to CMEs can also cause surges in power lines large enough to burn out transformers and cause major power outages. For example, in 1989, parts of Montreal and Quebec Province in Canada were without power for up to 9 hours as a result of a major solar storm. Electrical outages due to CMEs are more likely to occur in North America than in Europe because North America is closer to Earth’s magnetic pole, where the currents induced by CMEs are strongest.

Besides changing the orbits of satellites, CMEs can also distort the signals sent by them. These effects can be large enough to reduce the accuracy of GPS-derived positions so that they cannot meet the limits required for airplane systems, which must know their positions to within 160 feet. Such disruptions caused by CMEs have occasionally forced the Federal Aviation Administration to restrict flights for minutes or, in a few cases, even days.

Solar storms also expose astronauts, passengers in high-flying airplanes, and even people on the surface of Earth to increased amounts of radiation. Astronauts, for example, are limited in the total amount of radiation to which they can be exposed during their careers. A single ill-timed solar outburst could end an astronaut’s career. This problem becomes increasingly serious as astronauts spend more time in space. For example, the typical daily dose of radiation aboard the Russian Mir space station was equivalent to about eight chest X-rays. One of the major challenges in planning the human exploration of Mars is devising a way to protect astronauts from high-energy solar radiation.

Figure 2. NOAA Space Weather Prediction Operations Center: Bill Murtagh, a space weather forecaster, leads a workshop on preparedness for events like geomagnetic storms. (credit: modification of work by FEMA/Jerry DeFelice)

Advance warning of solar storms would help us minimize their disruptive effects. Power networks could be run at less than their full capacity so that they could absorb the effects of power surges. Communications networks could be prepared for malfunctions and have backup plans in place. Spacewalks could be timed to avoid major solar outbursts. Scientists are now trying to find ways to predict where and when flares and CMEs will occur, and whether they will be big, fast events or small, slow ones with little consequence for Earth.

The strategy is to relate changes in the appearance of small, active regions and changes in local magnetic fields on the Sun to subsequent eruptions. However, right now, our predictive capability is still poor, and so the only real warning we have is from actually seeing CMEs and flares occur. Since a CME travels outward at about 500 kilometers per second, an observation of an eruption provides several days warning at the distance of Earth. However, the severity of the impact on Earth depends on how the magnetic field associated with the CME is oriented relative to Earth’s magnetic field. The orientation can be measured only when the CME flows past a satellite we have put up for this purpose. However, it is located only about an hour upstream from Earth.

Space weather predictions are now available online to scientists and the public. Outlooks are given a week ahead, bulletins are issued when there is an event that is likely to be of interest to the public, and warnings and alerts are posted when an event is imminent or already under way (Figure 2).

Fortunately, we can expect calmer space weather for the next few years, since the most recent solar maximum, which was relatively weak, occurred in 2014, and scientists believe the current solar cycle to be one of the least active in recent history. We expect more satellites to be launched that will allow us to determine whether CMEs are headed toward Earth and how big they are. Models are being developed that will then allow scientists to use early information about the CME to predict its likely impact on Earth.

The hope is that by the time of the next maximum, solar weather forecasting will have some of the predictive capability that meteorologists have achieved for terrestrial weather at Earth’s surface. However, the most difficult events to predict are the largest and most damaging storms—hurricanes on Earth and extreme, rare storm events on the Sun. Thus, it is inevitable that the Sun will continue to surprise us.


The Timing of Solar Events
A basic equation is useful in figuring out when events on the Sun will impact Earth:

Dividing both sides by v, we get

Check Your Learning

How many days would it take for the particles to reach Earth if the solar wind speed increased to

The Atmosphere

4.2 Atmospheric Stability

Air movement in the atmosphere is strongly influenced by atmospheric stability recall that in a lake, stability occurs when higher temperatures and thus lower water density near the lake surface inhibit vertical mixing ( Section 2.2.2 ). Similarly, the degree of stability resulting from the vertical temperature profile of the atmosphere can either enhance or suppress vertical mixing of air and the chemicals contained in it. In a lake, the essentially incompressible water column is in a condition of neutral stability when water is at a constant temperature throughout in contrast, in the atmosphere, due to the compressibility of air, neutral stability occurs when the vertical temperature gradient which is actually measured (the actual lapse rate) is equal to the adiabatic lapse rate . The adiabatic lapse rate is the rate at which the temperature of an air parcel changes in response to the compression or expansion associated with elevation change, under the assumption that the process is adiabatic, i.e., no heat exchange occurs between the given air parcel and its surroundings. This is the same phenomenon that is responsible for the warmth of a tire pump after use the pump barrel becomes warmest at the air outlet, where the highest compression occurs. (Friction, which also causes heat, is more evenly distributed along the barrel.) Adiabatic heating through air compression causes a sufficient temperature to ignite diesel fuel in diesel engines and tinder in the slam-rod fire starter (fire piston). Adiabatic compression also is largely responsible for the high temperatures experienced by spacecraft during reentry into the atmosphere, sometimes with disastrous consequences when heat-shielding material is compromised.

4.2.1 The Dry Adiabatic Lapse Rate

The adiabatic lapse rate for a dry atmosphere, which may contain water vapor but which has no liquid moisture present in the form of fog, droplets, or clouds, is approximately 9.8 °C/1000 m (5.4 °F/1000 ft). A parcel of air placed in an insulated but expandable container and raised in height by 1000 m would become 9.8 °C cooler than its initial temperature ( Fig. 4.5 ). This value, borne out by experiment, is predictable on the basis of the atmospheric pressure profile and thermodynamic principles.

Figure 4.5 . Illustration of the adiabatic lapse rate. As this air parcel is raised in altitude by 1000 m, the air pressure decreases and the parcel expands and cools by 9.8 °C (5.4 °F for an altitude increase of 1000 ft). Assuming no heat is lost or gained by the parcel (i.e., the process is adiabatic), its temperature will increase to its original value once the parcel is lowered to its original height.

In Section 4.1.1 , Eqs. (4.1) and (4.2) were used to estimate the relationship between air pressure and altitude, assuming temperature to be constant with height. Eqs. (4.1) and (4.2) also can be used to calculate the dry adiabatic lapse rate when combined with Eq. (4.7) , which is based on conservation of energy. Assuming an adiabatic process, heat flow into a rising air parcel is zero. Conservation of energy requires that the mechanical (pressure-volume) work performed by the air as it expands equal the decrease in the internal energy of the air, which is given by the product of its heat capacity Cv (energy per unit mass per degree) and the change in temperature,

where P is pressure [M/LT 2 ], h is height [L], ρ is density [M/L 3 ], Cv is heat capacity [L 2 /(T 2 · Kelvin)], and T is absolute temperature (K).

Equation (4.2) can be rearranged as

where MW is the molecular weight and R is the gas constant. (Note that V/n equals MW/ρ.) Differentiating Eq. (4.8) ,

Substituting Eqs. (4.7) and (4.10) into Eq. (4.9) gives

Equation (4.11) can be rearranged as

The quantity (Cv · MW) is the heat capacity expressed in units of energy per mole per degree, and equals (5/2) · R for diatomic gases. Thus,

It is important not to confuse the dry adiabatic lapse rate with the rate of change of temperature with height in a Standard Atmosphere. The latter represents average conditions in Earth’s atmosphere, where heating, mixing, and wet adiabatic processes also are occurring.

Actual temperature profiles are based on data obtained routinely by sondes, devices that measure temperature, pressure, and often water vapor content of the air. Sondes are usually carried by weather balloons but may be dropped from airplanes they transmit their data to ground stations as they travel vertically through the atmosphere. If the actual measured lapse rate of the atmosphere is less than 9.8 °C/1000 m, a parcel of air initially at a temperature equal to that of the surrounding air becomes warmer than the surrounding air on being pushed downward ( Fig. 4.6a ). By being warmer and therefore less dense than its surroundings, it experiences an upward force tending to restore it to its original height. (Forces that arise from density differences in a fluid are called buoyancy forces.) Likewise, if the parcel of air is pushed upward, its temperature decreases with height more rapidly than that of the surrounding air, so that it experiences a downward buoyant force, again tending to restore it to its original height. The net result is that vertical air movements, such as those associated with eddies, are suppressed by buoyant forces the atmosphere is stable, the lapse rate is sometimes termed weak lapse, and vertical transport of chemicals is suppressed.

Figure 4.6 . (a) A stable atmosphere. The actual, measured temperature profile of the atmosphere decreases at a rate less than the adiabatic rate. Thus, when this air parcel is pushed upward, perhaps by an eddy in a turbulent atmosphere, it enters warmer, and hence less dense, surroundings being cooler and denser, it sinks back down. This stable situation tends to suppress vertical mixing. (b) An unstable atmosphere. The same air parcel pictured in (a) is again pushed upward. This time, the temperature of the surrounding atmosphere decreases more rapidly with altitude than the adiabatic rate that the air parcel follows. As it rises, the air parcel enters air that is increasingly cooler and denser than itself and consequently it is pushed up further by buoyancy. Vertical mixing is thereby enhanced by unstable conditions.

Conversely, if the actual measured lapse rate is greater than 9.8 °C/1000 m, a parcel of air displaced upward from its initial height becomes warmer than its surroundings and therefore tends to rise ( Fig. 4.6b ). If pushed downward, the parcel becomes colder than its surroundings and therefore tends to keep sinking. In this case, buoyant forces amplify any initial upward or downward movement of the air parcel, thus creating an unstable atmosphere.

It might be inferred from the preceding discussion that, based on its average lapse rate, the Standard Atmosphere is stable with little vertical mixing yet, on average, the troposphere is reasonably well mixed. Tropospheric mixing occurs in part because of atmospheric variability although widespread areas of stable air exist, there are also areas where, even in a dry atmosphere, the actual lapse rate exceeds the adiabatic lapse rate. As described in the following section, moisture is also exceedingly important in causing tropospheric mixing.

4.2.2 The Wet Adiabatic Lapse Rate

Energy in the form of heat is required to convert liquid water into water vapor 589 calories are absorbed per gram of water evaporated at 15 °C. The evaporation of water thus removes large amounts of heat, a process that is important to transpiring plant leaves, sweating people, and steam boilers. In the atmosphere, this heat energy can be subsequently released upon condensation of water vapor into liquid water during the formation of clouds. When a parcel of air whose RH is 100% (i.e., it is at the dew point) is moved upward, adiabatic cooling causes its temperature to drop, resulting in its RH exceeding 100% and water condensing. The heat released by condensation mitigates the adiabatic cooling effect, resulting in the parcel of air being warmer than it would be based on dry adiabatic cooling. The rate at which adiabatic cooling occurs with increasing altitude for wet air (air containing clouds or other visible forms of moisture) is called the wet adiabatic lapse rate , the moist adiabatic lapse rate, or the saturated adiabatic lapse rate. The wet adiabatic lapse rate lies in the range of 3.6-5.5 °C/1000 m (2-3 °F/1000 ft), depending on temperature and pressure. Note that any actual lapse rate less than 9.8 °C/1000 m in dry air results in a stable atmosphere, whereas a wet atmosphere must have an actual lapse rate of less than 3.6-5.5 °C/1000 m to be stable.

Wet adiabatic lapse rates can be determined from Fig. 4.7 , which is a skew T-log P diagram, or adiabatic chart. On this chart, dry adiabats are lines having a nearly constant slope of 9.8 °C/1000 m (5.4 °F/1000 ft). The wet adiabats (also called moist or saturated adiabats) are curved and have slopes that not only vary with the temperature at which the adiabat originates but also change along the length of the adiabats. Note that the wet adiabats tend to approach the slope of the dry adiabats at low temperatures, at which the absolute amount of moisture in saturated air is small (see Table 4.3 ).

Figure 4.7 . A skew T-log P diagram, or adiabatic chart. On this chart all lines of temperature versus altitude for dry conditions (i.e., no condensation of water vapor) are nearly straight lines with a slope corresponding to the dry adiabatic lapse rate of 9.8 °C/1000 m (5.4 °F/1000 ft). These are called dry adiabats and slope upward to the left. Wet adiabats have a variable slope and appear as curved lines. Horizontal lines denote altitude lines of constant temperature slope upward to the right.

Frequently, both kinds of adiabats must be employed to follow the behavior of a parcel of air as it rises. A parcel of dry air may rise by its own buoyancy, or may be pushed up by orographic lifting, which occurs when winds meet mountains and are deflected upward. The temperature of the air parcel follows the dry adiabat until water vapor condensation is incipient with further cooling, condensation can occur. If it is assumed that supercooling (a nonequilibrium situation in which air cools below the dew point without condensation) does not occur, the parcel of air then moves upward following the corresponding wet adiabat. Conditional stability refers to conditions under which dry, stable air is pushed upward to its dew point and consequently becomes unstable.

In the formation of the puffy, fair-weather clouds known as cumulus clouds, solar heating of the ground warms the adjacent air, and bubbles of this warmed air rise due to buoyancy, their temperature decreasing with altitude according to the dry adiabatic lapse rate ( Fig. 4.8 ). At the altitude where the dew point is reached and condensation begins, a cloud forms, and the stability of the air decreases as the air begins to follow a wet adiabat. Instability can lead to extensive vertical development of the cloud and strong upward air currents within the cloud. On hot summer days, this can lead to the production of a late-afternoon thunderstorm.

Figure 4.8 . Cumulus cloud formation. Steps I-III illustrate the warming of near-surface air as the ground is heated by the Sun, and the subsequent rising of the heated bubble of air (a thermal in the parlance of glider pilots and soaring birds). In step IV, the rising bubble of air reaches its dew point, and a cloud begins to form. Thereafter, the rising air cools at a wet adiabatic lapse rate, which is less than the dry adiabatic lapse rate, and accentuates the tendency of the air to rise farther.

Example 4.2

On a summer afternoon, air heated over a plowed field 1000 m above sea level has a temperature of 25 °C and RH of 80%. At what altitude does the rising air begin to form a cloud? What is the air temperature 2000 m above the cloud base (inside the cloud)? What is the average wet adiabatic lapse rate in this portion of the cloud?

As shown in Table 4.3 , at 25 °C the vapor pressure of water is 23.8 mm Hg. Therefore, in air at 25 °C with 80% RH, the partial pressure of water vapor is

Condensation will begin when the air is cooled to the temperature at which the vapor pressure of water is 19 mm Hg (from Table 4.3 , approximately 21 °C).

Use Fig. 4.7 , beginning at 25 °C and 1000 m, and follow the slope of the dry adiabats until the air parcel reaches 21 °C, which occurs at an altitude of approximately 1500 m. (Strictly, it must cool a bit more, because the expansion of the rising air causes the partial pressure of water to decrease somewhat.) Thereafter, the air follows a wet adiabat at 3500 m (2000 m above the cloud base) the temperature is approximately 12 °C. The average wet adiabatic lapse rate in the bottom 2000 m of cloud is therefore 9 °C/2000 m, or 4.5 °C/1000 m.

4.2.3 Mixing Height

Many common meteorological processes influence the actual lapse rate and thus the stability of the atmosphere. Even the daily cycle of daytime heating by the Sun and nighttime cooling produces periods of instability and stability in the atmosphere. As previously mentioned, during the day solar radiation warms the ground, which in turn warms air near the ground surface. Such air tends to rise by buoyant forces until it reaches a height where its temperature, and hence its density, are equal to those of the surrounding air. This height is called the mixing height between this height and the ground lies a layer of air (often called the boundary layer ) within which atmospheric mixing is aided by buoyancy. Mixing height for a given location can be inferred from simple graphic construction, in which the actual atmospheric temperature profile is intersected by a line originating at the surface temperature and having a slope equal to the adiabatic lapse rate . If urban air quality studies are being conducted, but only a rural atmospheric temperature profile is available, an estimate for urban surface temperature can be made by increasing the rural surface temperature by 5 °C ( Fig. 4.9 ).

Figure 4.9 . Urban mixing height is estimated graphically, using a measured temperature profile from a nearby rural area. It is assumed that the upper portions of this 1200 GMT (700 EST) profile are applicable for both the morning and afternoon mixing height estimates. Correcting the urban surface temperature by adding 5 °C to the rural surface temperature gives a somewhat higher morning mixing height than if the rural surface temperature were used. The afternoon maximum surface temperature (Tmax) in the urban area is used to estimate the maximum daytime mixing height.

At night, cooling of the land surface lowers the temperature of the air close to the ground and decreases the actual lapse rate, in many cases creating an inversion, a layer of atmosphere in which the actual lapse rate is negative air becomes warmer with increased altitude. Nighttime inversion development is favored by clear skies that radiate little longwave radiation downward to offset the loss of heat by longwave radiation upward from the ground surface. Nighttime inversions trap pollutant chemicals in a stable layer of atmosphere and lead to lowered air quality near the ground surface. Diagrams showing atmospheric stability effects on a plume of smokestack emissions are presented in Fig. 4.10 .

Figure 4.10 . Emission of pollutants from a smokestack, a typical continuous source, under a variety of meteorological conditions. The dry adiabatic lapse rate is represented as a dashed line and the actual measured lapse rate as a solid line in the left panels. Vertical mixing is strongest when the adiabatic lapse rate is less than the actual measured lapse rate and the atmosphere is unstable (top). Weak lapse, reflecting the existence of a stable atmosphere, results in less vertical mixing. An inversion, in the third panel from the top and in part of the last three panels, results in a highly stable atmospheric layer in which relatively little vertical mixing occurs.


Thermal radiation is the emission of electromagnetic waves from all matter that has a temperature greater than absolute zero. [3] Thermal radiation reflects the conversion of thermal energy into electromagnetic energy. Thermal energy is the kinetic energy of random movements of atoms and molecules in matter. All matter with a nonzero temperature is composed of particles with kinetic energy. These atoms and molecules are composed of charged particles, i.e., protons and electrons. The kinetic interactions among matter particles result in charge acceleration and dipole oscillation. This results in the electrodynamic generation of coupled electric and magnetic fields, resulting in the emission of photons, radiating energy away from the body. Electromagnetic radiation, including visible light, will propagate indefinitely in vacuum.

The characteristics of thermal radiation depend on various properties of the surface from which it is emanating, including its temperature, its spectral emissivity, as expressed by Kirchhoff's law. [3] The radiation is not monochromatic, i.e., it does not consist of only a single frequency, but comprises a continuous spectrum of photon energies, its characteristic spectrum. If the radiating body and its surface are in thermodynamic equilibrium and the surface has perfect absorptivity at all wavelengths, it is characterized as a black body. A black body is also a perfect emitter. The radiation of such perfect emitters is called black-body radiation. The ratio of any body's emission relative to that of a black body is the body's emissivity, so that a black body has an emissivity of unity (i.e., one).

Absorptivity, reflectivity, and emissivity of all bodies are dependent on the wavelength of the radiation. Due to reciprocity, absorptivity and emissivity for any particular wavelength are equal – a good absorber is necessarily a good emitter, and a poor absorber is a poor emitter. The temperature determines the wavelength distribution of the electromagnetic radiation. For example, the white paint in the diagram to the right is highly reflective to visible light (reflectivity about 0.80), and so appears white to the human eye due to reflecting sunlight, which has a peak wavelength of about 0.5 micrometers. However, its emissivity at a temperature of about −5 °C (23 °F), peak wavelength of about 12 micrometers, is 0.95. Thus, to thermal radiation it appears black.

The distribution of power that a black body emits with varying frequency is described by Planck's law. At any given temperature, there is a frequency fmax at which the power emitted is a maximum. Wien's displacement law, and the fact that the frequency is inversely proportional to the wavelength, indicates that the peak frequency fmax is proportional to the absolute temperature T of the black body. The photosphere of the sun, at a temperature of approximately 6000 K, emits radiation principally in the (human-)visible portion of the electromagnetic spectrum. Earth's atmosphere is partly transparent to visible light, and the light reaching the surface is absorbed or reflected. Earth's surface emits the absorbed radiation, approximating the behavior of a black body at 300 K with spectral peak at fmax. At these lower frequencies, the atmosphere is largely opaque and radiation from Earth's surface is absorbed or scattered by the atmosphere. Though about 10% of this radiation escapes into space, most is absorbed and then re-emitted by atmospheric gases. It is this spectral selectivity of the atmosphere that is responsible for the planetary greenhouse effect, contributing to global warming and climate change in general (but also critically contributing to climate stability when the composition and properties of the atmosphere are not changing).

The incandescent light bulb has a spectrum overlapping the black body spectra of the sun and the earth. Some of the photons emitted by a tungsten light bulb filament at 3000 K are in the visible spectrum. Most of the energy is associated with photons of longer wavelengths these do not help a person see, but still transfer heat to the environment, as can be deduced empirically by observing an incandescent light bulb. Whenever EM radiation is emitted and then absorbed, heat is transferred. This principle is used in microwave ovens, laser cutting, and RF hair removal.

Unlike conductive and convective forms of heat transfer, thermal radiation can be concentrated in a tiny spot by using reflecting mirrors, which concentrating solar power takes advantage of. Instead of mirrors, Fresnel lenses can also be used to concentrate radiant energy. (In principle, any kind of lens can be used, but only the Fresnel lens design is practical for very large lenses.) Either method can be used to quickly vaporize water into steam using sunlight. For example, the sunlight reflected from mirrors heats the PS10 Solar Power Plant, and during the day it can heat water to 285 °C (558 K 545 °F).

Surface effects Edit

Lighter colors and also whites and metallic substances absorb less of the illuminating light, and as a result heat up less but otherwise color makes little difference as regards heat transfer between an object at everyday temperatures and its surroundings, since the dominant emitted wavelengths are nowhere near the visible spectrum, but rather in the far infrared. Emissivities at those wavelengths are largely unrelated to visual emissivities (visible colors) in the far infra-red, most objects have high emissivities. Thus, except in sunlight, the color of clothing makes little difference as regards warmth likewise, paint color of houses makes little difference to warmth except when the painted part is sunlit.

The main exception to this is shiny metal surfaces, which have low emissivities both in the visible wavelengths and in the far infrared. Such surfaces can be used to reduce heat transfer in both directions an example of this is the multi-layer insulation used to insulate spacecraft.

Low-emissivity windows in houses are a more complicated technology, since they must have low emissivity at thermal wavelengths while remaining transparent to visible light.

Nanostructures with spectrally selective thermal emittance properties offer numerous technological applications for energy generation and efficiency, [4] e.g., for cooling photovoltaic cells and buildings. These applications require high emittance in the frequency range corresponding to the atmospheric transparency window in 8 to 13 micron wavelength range. A selective emitter radiating strongly in this range is thus exposed to the clear sky, enabling the use of the outer space as a very low temperature heat sink. [5]

Personalized cooling technology is another example of an application where optical spectral selectivity can be beneficial. Conventional personal cooling is typically achieved through heat conduction and convection. However, the human body is a very efficient emitter of infrared radiation, which provides an additional cooling mechanism. Most conventional fabrics are opaque to infrared radiation and block thermal emission from the body to the environment. Fabrics for personalized cooling applications have been proposed that enable infrared transmission to directly pass through clothing, while being opaque at visible wavelengths, allowing the wearer to remain cooler.

There are 4 main properties that characterize thermal radiation (in the limit of the far field):

  • Thermal radiation emitted by a body at any temperature consists of a wide range of frequencies. The frequency distribution is given by Planck's law of black-body radiation for an idealized emitter as shown in the diagram at top.
  • The dominant frequency (or color) range of the emitted radiation shifts to higher frequencies as the temperature of the emitter increases. For example, a red hot object radiates mainly in the long wavelengths (red and orange) of the visible band. If it is heated further, it also begins to emit discernible amounts of green and blue light, and the spread of frequencies in the entire visible range cause it to appear white to the human eye it is white hot. Even at a white-hot temperature of 2000 K, 99% of the energy of the radiation is still in the infrared. This is determined by Wien's displacement law. In the diagram the peak value for each curve moves to the left as the temperature increases.
  • The total amount of radiation of all frequency increases steeply as the temperature rises it grows as T 4 , where T is the absolute temperature of the body. An object at the temperature of a kitchen oven, about twice the room temperature on the absolute temperature scale (600 K vs. 300 K) radiates 16 times as much power per unit area. An object at the temperature of the filament in an incandescent light bulb—roughly 3000 K, or 10 times room temperature—radiates 10,000 times as much energy per unit area. The total radiative intensity of a black body rises as the fourth power of the absolute temperature, as expressed by the Stefan–Boltzmann law. In the plot, the area under each curve grows rapidly as the temperature increases.
  • The rate of electromagnetic radiation emitted at a given frequency is proportional to the amount of absorption that it would experience by the source, a property known as reciprocity. Thus, a surface that absorbs more red light thermally radiates more red light. This principle applies to all properties of the wave, including wavelength (color), direction, polarization, and even coherence, so that it is quite possible to have thermal radiation which is polarized, coherent, and directional, though polarized and coherent forms are fairly rare in nature far from sources (in terms of wavelength). See section below for more on this qualification.

Near-field and far-field Edit

The general properties of thermal radiation as described by the Planck's law apply if the linear dimension of all parts considered, as well as radii of curvature of all surfaces are large compared with the wavelength of the ray considered' (typically from 8-25 micrometres for the emitter at 300 K). Indeed, thermal radiation as discussed above takes only radiating waves (far-field, or electromagnetic radiation) into account. A more sophisticated framework involving electromagnetic theory must be used for smaller distances from the thermal source or surface (near-field thermal radiation). For example, although far-field thermal radiation at distances from surfaces of more than one wavelength is generally not coherent to any extent, near-field thermal radiation (i.e., radiation at distances of a fraction of various radiation wavelengths) may exhibit a degree of both temporal and spatial coherence. [6]

Planck's law of thermal radiation has been challenged in recent decades by predictions and successful demonstrations of the radiative heat transfer between objects separated by nanoscale gaps that deviate significantly from the law predictions. This deviation is especially strong (up to several orders in magnitude) when the emitter and absorber support surface polariton modes that can couple through the gap separating cold and hot objects. However, to take advantage of the surface-polariton-mediated near-field radiative heat transfer, the two objects need to be separated by ultra-narrow gaps on the order of microns or even nanometers. This limitation significantly complicates practical device designs.

Another way to modify the object thermal emission spectrum is by reducing the dimensionality of the emitter itself. [4] This approach builds upon the concept of confining electrons in quantum wells, wires and dots, and tailors thermal emission by engineering confined photon states in two- and three-dimensional potential traps, including wells, wires, and dots. Such spatial confinement concentrates photon states and enhances thermal emission at select frequencies. [7] To achieve the required level of photon confinement, the dimensions of the radiating objects should be on the order of or below the thermal wavelength predicted by Planck's law. Most importantly, the emission spectrum of thermal wells, wires and dots deviates from Planck's law predictions not only in the near field, but also in the far field, which significantly expands the range of their applications.

Subjective color to the eye of a black body thermal radiator Edit

°C (°F) Subjective color [8]
480 °C (896 °F) faint red glow
580 °C (1,076 °F) dark red
730 °C (1,350 °F) bright red, slightly orange
930 °C (1,710 °F) bright orange
1,100 °C (2,010 °F) pale yellowish orange
1,300 °C (2,370 °F) yellowish white
> 1,400 °C (2,550 °F) white (yellowish if seen from a distance through atmosphere)

Selected radiant heat fluxes Edit

The time to a damage from exposure to radiative heat is a function of the rate of delivery of the heat. Radiative heat flux and effects: [9] (1 W/cm 2 = 10 kW/m 2 )

kW/m 2 Effect
170 Maximum flux measured in a post-flashover compartment
80 Thermal Protective Performance test for personal protective equipment
52 Fiberboard ignites at 5 seconds
29 Wood ignites, given time
20 Typical beginning of flashover at floor level of a residential room
16 Human skin: sudden pain and second-degree burn blisters after 5 seconds
12.5 Wood produces ignitable volatiles by pyrolysis
10.4 Human skin: Pain after 3 seconds, second-degree burn blisters after 9 seconds
6.4 Human skin: second-degree burn blisters after 18 seconds
4.5 Human skin: second-degree burn blisters after 30 seconds
2.5 Human skin: burns after prolonged exposure, radiant flux exposure typically encountered during firefighting
1.4 Sunlight, sunburns potentially within 30 minutes. Sunburn is NOT a thermal burn. It is caused by cellular damage due to ultraviolet radiation.

Thermal radiation is one of the three principal mechanisms of heat transfer. It entails the emission of a spectrum of electromagnetic radiation due to an object's temperature. Other mechanisms are convection and conduction.

Radiation heat transfer is characteristically different from the other two in that it does not require a medium and, in fact it reaches maximum efficiency in a vacuum. Electromagnetic radiation has some proper characteristics depending on the frequency and wavelengths of the radiation. The phenomenon of radiation is not yet fully understood. Two theories have been used to explain radiation however neither of them is perfectly satisfactory.

First, the earlier theory which originated from the concept of a hypothetical medium referred as ether. Ether supposedly fills all evacuated or non-evacuated spaces. The transmission of light or of radiant heat are allowed by the propagation of electromagnetic waves in the ether. [10] Electromagnetic waves have similar characteristics to television and radio broadcasting waves they only differ in wavelength. [11] All electromagnetic waves travel at the same speed therefore, shorter wavelengths are associated with high frequencies. Since every body or fluid is submerged in the ether, due to the vibration of the molecules, any body or fluid can potentially initiate an electromagnetic wave. All bodies generate and receive electromagnetic waves at the expense of its stored energy [11]

The second theory of radiation is best known as the quantum theory and was first offered by Max Planck in 1900. [10] According to this theory, energy emitted by a radiator is not continuous but is in the form of quanta. Planck claimed that quantities had different sizes and frequencies of vibration similarly to the wave theory. [12] The energy E is found by the expression E = hν, where h is the Planck's constant and ν is the frequency. Higher frequencies are originated by high temperatures and create an increase of energy in the quantum. While the propagation of electromagnetic waves of all wavelengths is often referred as "radiation," thermal radiation is often constrained to the visible and infrared regions. For engineering purposes, it may be stated that thermal radiation is a form of electromagnetic radiation which varies on the nature of a surface and its temperature. [10] Radiation waves may travel in unusual patterns compared to conduction heat flow. Radiation allows waves to travel from a heated body through a cold nonabsorbing or partially absorbing medium and reach a warmer body again. [10] This is the case of the radiation waves that travel from the sun to the earth.

The interplay of energy exchange by thermal radiation is characterized by the following equation:

Reflectivity deviates from the other properties in that it is bidirectional in nature. In other words, this property depends on the direction of the incident of radiation as well as the direction of the reflection. Therefore, the reflected rays of a radiation spectrum incident on a real surface in a specified direction forms an irregular shape that is not easily predictable. In practice, surfaces are assumed to reflect in a perfectly specular or diffuse manner. In a specular reflection, the angles of reflection and incidence are equal. In diffuse reflection, radiation is reflected equally in all directions. Reflection from smooth and polished surfaces can be assumed to be specular reflection, whereas reflection from rough surfaces approximates diffuse reflection. [13] In radiation analysis a surface is defined as smooth if the height of the surface roughness is much smaller relative to the wavelength of the incident radiation.

In a practical situation and room-temperature setting, humans lose considerable energy due to thermal radiation in infra-red in addition to that lost by conduction to air (aided by concurrent convection, or other air movement like drafts). The heat energy lost is partially regained by absorbing heat radiation from walls or other surroundings. (Heat gained by conduction would occur for air temperature higher than body temperature.) Otherwise, body temperature is maintained from generated heat through internal metabolism. Human skin has an emissivity of very close to 1.0. [14] Using the formulas below shows a human, having roughly 2 square meter in surface area, and a temperature of about 307 K, continuously radiates approximately 1000 watts. If people are indoors, surrounded by surfaces at 296 K, they receive back about 900 watts from the wall, ceiling, and other surroundings, so the net loss is only about 100 watts. These heat transfer estimates are highly dependent on extrinsic variables, such as wearing clothes, i.e. decreasing total thermal circuit conductivity, therefore reducing total output heat flux. Only truly gray systems (relative equivalent emissivity/absorptivity and no directional transmissivity dependence in all control volume bodies considered) can achieve reasonable steady-state heat flux estimates through the Stefan-Boltzmann law. Encountering this "ideally calculable" situation is almost impossible (although common engineering procedures surrender the dependency of these unknown variables and "assume" this to be the case). Optimistically, these "gray" approximations will get close to real solutions, as most divergence from Stefan-Boltzmann solutions is very small (especially in most STP lab controlled environments).

If objects appear white (reflective in the visual spectrum), they are not necessarily equally reflective (and thus non-emissive) in the thermal infrared – see the diagram at the left. Most household radiators are painted white, which is sensible given that they are not hot enough to radiate any significant amount of heat, and are not designed as thermal radiators at all – instead, they are actually convectors, and painting them matt black would make little difference to their efficacy. Acrylic and urethane based white paints have 93% blackbody radiation efficiency at room temperature [15] (meaning the term "black body" does not always correspond to the visually perceived color of an object). These materials that do not follow the "black color = high emissivity/absorptivity" caveat will most likely have functional spectral emissivity/absorptivity dependence.

Calculation of radiative heat transfer between groups of object, including a 'cavity' or 'surroundings' requires solution of a set of simultaneous equations using the radiosity method. In these calculations, the geometrical configuration of the problem is distilled to a set of numbers called view factors, which give the proportion of radiation leaving any given surface that hits another specific surface. These calculations are important in the fields of solar thermal energy, boiler and furnace design and raytraced computer graphics.

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Davis lab/provided This composite image shows where the selenium atoms reside in the crystal of niobium diselenide, a transition metal dichalcogenide, using conventional scanned tunneling microscopy (left, in grey) and where the electron pairs are observed using scanned Josephson tunneling microscopy (right, in blue).

International Standard Atmosphere (ISA)

The International Standard Atmosphere “is intended for use in calculations and design of flying vehicles, to present the test results of flying vehicles and their components under identical conditions, and to allow unification in the field of development and calibration of instruments.” The use of this atmospheric model is also recommended in the processing of data from geophysical and meteorological observations. It is used as a standard against which one can compare the actual atmosphere and based on the values at mean sea level shown below. All values decrease with increase in altitude:

  • Pressure of 101.325 kPa at mean sea level (MSL).
  • Temperature of +15 °C at MSL
  • Density of 1.225 kg/m³ at MSL.

Short-Term Hibernation

Some animals, such as hummingbirds, undergo a short-term hibernation known as torpor. Their nightly torpor is an energy-saving mechanism, as their tiny bodies lose heat rapidly. They must feed constantly during the day to keep their body temperature up and maintain their incredibly fast metabolism. They eat two to three times their body weight every day! If they didn’t enter torpor at night they would die, since their bodies would lose too much heat due to their large surface area to volume ratio. They also lack the insulating down feathers that many birds have, resulting in heat loss.