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In the case of a monoatomic gas, the [[kinetic energy]] is:<br> | In the case of a monoatomic gas, the [[kinetic energy]] is:<br> | ||
:<math> E_t = \begin{matrix} \frac{1}{2} \end{matrix} mv^2 </math> | :<math> E_t = \begin{matrix} \frac{1}{2} \end{matrix} mv^2 </math> | ||
(Note that a calculation of the kinetic energy of a more complicated object, such as a molecule, is slightly more involved. | (Note that a calculation of the kinetic energy of a more complicated object, such as a molecule, is slightly more involved. Additional [[degrees of freedom (physics and chemistry)|degrees of freedom]] are available, so molecular rotation or vibration must be included.)<br><br> | ||
The second law of thermodynamics states that any two given systems when interacting with each other will later reach the same average energy per particle (and hence the same temperature). | The second law of thermodynamics states that any two given systems when interacting with each other will later reach the same average energy per particle (and hence the same temperature). | ||
In a mixture of particles of various mass, the heaviest particles will move more slowly than lighter counterparts, but will still have the same average energy. A [[neon]] atom moves slower relative to a [[hydrogen]] molecule of the same kinetic energy; a pollen particle moves in a slow [[Brownian motion]] among fast moving water molecules, etc. | In a mixture of particles of various mass, the heaviest particles will move more slowly than lighter counterparts, but will still have the same average energy. A [[neon]] atom moves slower relative to a [[hydrogen]] molecule of the same kinetic energy; a pollen particle moves in a slow [[Brownian motion]] among fast moving water molecules, etc. A visual illustration of this [http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm from Oklahoma State University] makes the point more clear. Particles with different mass have different velocity distributions, but the average kinetic energy is the same because of the [[ideal gas law]]. | ||
===Temperature of the vacuum=== | ===Temperature of the vacuum=== | ||
It is possible to use the zeroth law definition of temperature to assign a temperature to something we don't normally associate temperatures with, like a perfect vacuum. Because all objects emit [[black body]] radiation, a thermometer in a vacuum away from thermally radiating sources will radiate away its own thermal energy; decreasing in temperature indefinitely until it reaches the [[zero-point energy]] limit. At that point it can be said to be in equilibrium with the vacuum and by definition at the same temperature. If we could find a gas that behaved ideally all the way down to absolute zero the kinetic theory of gases tells us that it would achieve zero kinetic energy per particle, and thereby achieve absolute zero temperature. | It is possible to use the zeroth law definition of temperature to assign a temperature to something we don't normally associate temperatures with, like a perfect vacuum. Because all objects emit [[black body]] radiation, a thermometer in a vacuum away from thermally radiating sources will radiate away its own thermal energy; decreasing in temperature indefinitely until it reaches the [[zero-point energy]] limit. At that point it can be said to be in equilibrium with the vacuum and by definition at the same temperature. If we could find a gas that behaved ideally all the way down to absolute zero the kinetic theory of gases tells us that it would achieve zero kinetic energy per particle, and thereby achieve absolute zero temperature. Thus, by the zeroth law a perfect, isolated vacuum is at absolute zero temperature. Note that in order to behave ideally in this context it is necessary for the atoms of the gas to have no zero point energy. It will turn out not to matter that this is not possible because the second law definition of temperature will yield the same result for any unique vacuum state. | ||
More realistically, no such ideal vacuum exists. For instance a thermometer in a vacuum chamber which is maintained at some finite temperature (say, chamber is in the lab at room temperature) will equilibrate with the thermal radiation it receives from the chamber and with time reaches the temperature of the chamber. | More realistically, no such ideal vacuum exists. For instance a thermometer in a vacuum chamber which is maintained at some finite temperature (say, chamber is in the lab at room temperature) will equilibrate with the thermal radiation it receives from the chamber and with time reaches the temperature of the chamber. If a thermometer orbiting the Earth is exposed to a [[sunlight]], then it equilibrates at the temperature at which power received by the thermometer from the Sun is exactly equal to the power radiated away by thermal radiation of the thermometer. For a black body this equilibrium temperature is about 281 K (+8 °C). Earth average temperature (which is maintained by similar balance) is close to this temperature. | ||
A thermometer isolated from solar radiation (in the shade of the Earth, for example) is still exposed to thermal radiation of Earth - thus will show some equilibrium temperature at which it receives and radiates equal amount of energy. If this thermometer is close to Earth then its equilibrium temperature is about 236 K (-37 °C) provided that Earth surface is at 281 K. | A thermometer isolated from solar radiation (in the shade of the Earth, for example) is still exposed to thermal radiation of Earth - thus will show some equilibrium temperature at which it receives and radiates equal amount of energy. If this thermometer is close to Earth then its equilibrium temperature is about 236 K (-37 °C) provided that Earth surface is at 281 K. | ||
A thermometer far away from Solar system still receives [[Cosmic microwave background radiation]]. | A thermometer far away from Solar system still receives [[Cosmic microwave background radiation]]. Equilibrium temperature of such thermometer is about 2.725 K, which is the temperature of a photon gas constituting black body microwave background radiation at present state of expansion of Universe. This temperature is sometimes referred to as the temperature of space. | ||
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Sistema Anglosajón de Unidades: | Sistema Anglosajón de Unidades: | ||
* [[Grado Rankine]] (°R o °Ra). Escala con intervalos de grado equivalentes a la escala fahrenheit. Con el origen en | * [[Grado Rankine]] (°R o °Ra). Escala con intervalos de grado equivalentes a la escala fahrenheit. Con el origen en -459.67 °F (aproximadamente) | ||
=== Relativas === | === Relativas === | ||
