{"id":463904,"date":"2026-08-18T11:34:18","date_gmt":"2026-08-18T18:34:18","guid":{"rendered":"https:\/\/climatescience.press\/?p=463904"},"modified":"2026-08-18T11:34:20","modified_gmt":"2026-08-18T18:34:20","slug":"comparing-equilibrium-kinetic-and-non-equilibrium-temperatures","status":"publish","type":"post","link":"https:\/\/climatescience.press\/?p=463904","title":{"rendered":"Comparing Equilibrium, Kinetic, and Non-Equilibrium Temperatures"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"318\" data-attachment-id=\"463910\" data-permalink=\"https:\/\/climatescience.press\/?attachment_id=463910\" data-orig-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?fit=2504%2C1100&amp;ssl=1\" data-orig-size=\"2504,1100\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;,&quot;alt&quot;:&quot;&quot;}\" data-image-title=\"0 Figure-1_Thermal-equilibrium-3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?fit=723%2C318&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=723%2C318&#038;ssl=1\" alt=\"\" class=\"wp-image-463910\" srcset=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=1024%2C450&amp;ssl=1 1024w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=300%2C132&amp;ssl=1 300w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=768%2C337&amp;ssl=1 768w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=1536%2C675&amp;ssl=1 1536w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=2048%2C900&amp;ssl=1 2048w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=640%2C281&amp;ssl=1 640w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=1200%2C527&amp;ssl=1 1200w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?w=1446&amp;ssl=1 1446w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?w=2169&amp;ssl=1 2169w\" sizes=\"auto, (max-width: 723px) 100vw, 723px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/andymaypetrophysicist.com\/2026\/08\/17\/comparing-equilibrium-kinetic-and-non-equilibrium-temperatures\/\">Andy May Petrophysicist<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">By <a href=\"https:\/\/andymaypetrophysicist.com\/author\/andymay2014\/\">Andy May<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"312\" data-attachment-id=\"463907\" data-permalink=\"https:\/\/climatescience.press\/?attachment_id=463907\" data-orig-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Comparing-Equilibrium-Kinetic-and-Non-Equilibrium-Temperatures.webp?fit=1173%2C506&amp;ssl=1\" data-orig-size=\"1173,506\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;,&quot;alt&quot;:&quot;&quot;}\" data-image-title=\"0 Comparing Equilibrium, Kinetic, and Non-Equilibrium Temperatures\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Comparing-Equilibrium-Kinetic-and-Non-Equilibrium-Temperatures.webp?fit=723%2C312&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Comparing-Equilibrium-Kinetic-and-Non-Equilibrium-Temperatures.webp?resize=723%2C312&#038;ssl=1\" alt=\"\" class=\"wp-image-463907\" srcset=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Comparing-Equilibrium-Kinetic-and-Non-Equilibrium-Temperatures.webp?resize=1024%2C442&amp;ssl=1 1024w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Comparing-Equilibrium-Kinetic-and-Non-Equilibrium-Temperatures.webp?resize=300%2C129&amp;ssl=1 300w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Comparing-Equilibrium-Kinetic-and-Non-Equilibrium-Temperatures.webp?resize=768%2C331&amp;ssl=1 768w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Comparing-Equilibrium-Kinetic-and-Non-Equilibrium-Temperatures.webp?resize=640%2C276&amp;ssl=1 640w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Comparing-Equilibrium-Kinetic-and-Non-Equilibrium-Temperatures.webp?w=1173&amp;ssl=1 1173w\" sizes=\"auto, (max-width: 723px) 100vw, 723px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">This is part 3 of a series on defining temperature. In&nbsp;<a href=\"https:\/\/andymaypetrophysicist.com\/2026\/08\/08\/defining-temperature\/\">part one<\/a>&nbsp;I covered various temperature definitions used and pointed out that \u201ctemperature,\u201d unmodified is only a measurement of an emergent statistical property with little meaning beyond that. It is important in physics and daily life, but not a primitive well defined property like mass or energy. In&nbsp;<a href=\"https:\/\/andymaypetrophysicist.com\/2026\/08\/12\/kinetic-temperature\/\">part two<\/a>&nbsp;I covered kinetic temperature, which is \u201cwhat we measure with a thermometer\u201d (Schroeder, 2000). In the original&nbsp;<a href=\"https:\/\/x.com\/cohler\/status\/2084920172242960880?s=20\">X discussion<\/a>&nbsp;that spurred me to write these posts, some argued that the \u201creal\u201d definition of \u201ctemperature\u201d was the thermodynamic equilibrium temperature. Of course this is not true. For nearly everyone on Earth, thermometers measure temperature.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">There are a number of unique conditions required to measure a thermodynamic equilibrium temperature and a separate set of conditions to measure a kinetic (or thermometer) temperature, and they are not the same. While the kinetic temperature may be the same as the thermodynamic equilibrium temperature in a system at equilibrium, they are not the same thing. There is also another category of temperatures that are very different from kinetic or thermodynamic temperatures, called non-equilibrium temperatures. Non-equilibrium temperatures do not meet all the conditions required for kinetic and thermodynamic temperatures. Examples:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The particle velocity distribution may not be Maxwellian<\/li>\n\n\n\n<li>Different directions in the system may have different temperatures (anisotropic)<\/li>\n\n\n\n<li>Different system components may have different temperatures (electron vs ion temperature in plasmas)<\/li>\n\n\n\n<li>System pressure may not be isotropic<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Thermodynamic equilibrium temperature<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s briefly review what thermodynamic equilibrium temperature is, some illustrative plots are presented in figure 1.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"318\" data-attachment-id=\"463910\" data-permalink=\"https:\/\/climatescience.press\/?attachment_id=463910\" data-orig-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?fit=2504%2C1100&amp;ssl=1\" data-orig-size=\"2504,1100\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;,&quot;alt&quot;:&quot;&quot;}\" data-image-title=\"0 Figure-1_Thermal-equilibrium-3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?fit=723%2C318&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=723%2C318&#038;ssl=1\" alt=\"\" class=\"wp-image-463910\" srcset=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=1024%2C450&amp;ssl=1 1024w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=300%2C132&amp;ssl=1 300w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=768%2C337&amp;ssl=1 768w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=1536%2C675&amp;ssl=1 1536w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=2048%2C900&amp;ssl=1 2048w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=640%2C281&amp;ssl=1 640w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?resize=1200%2C527&amp;ssl=1 1200w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?w=1446&amp;ssl=1 1446w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?w=2169&amp;ssl=1 2169w\" sizes=\"auto, (max-width: 723px) 100vw, 723px\" \/><figcaption class=\"wp-element-caption\">Figure 1. An illustration of the definition of thermodynamic equilibrium temperature.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">At the top of figure 1 I show the formal mathematical definition of thermodynamic equilibrium temperature; it applies to the middle and right-hand plots. It is described in detail in&nbsp;<a href=\"https:\/\/andymaypetrophysicist.com\/2026\/08\/08\/defining-temperature\/\">post 1<\/a>. In the equation, T is temperature, U is the system internal energy, S is system entropy, \u2202U\/\u2202S is the partial derivative of internal energy with respect to entropy, N is the number of particles, and V is the volume.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Figure 1 illustrates how thermodynamic temperature arises from the geometry of the equilibrium state space. The left panel shows the equilibrium manifold in the thermodynamic state space. The horizontal axis is entropy , the vertical axis is volume , and the shading and contour lines represent internal energy . For this plot N (the number of particles) is held fixed. Entropy may be interpreted as the number of microscopic configurations compatible with the macroscopic constraints, although in equilibrium thermodynamics it is treated as a state variable. For a system with fixed internal energy, volume, and particle number (a \u201cmicrocanonical\u201d ensemble), the equilibrium state is the point on this manifold where entropy is maximized. This point is the red dot. The blue arrow projects this equilibrium point down to the -axis, indicating how the full two\u2011dimensional manifold reduces to a one\u2011dimensional slice when volume is held fixed.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This projection shows how the manifold reduces to the slice shown in the middle and right-hand illustrations. The middle panel shows the curveat fixed and . The equilibrium point lies on this curve. The right panel zooms in on the equilibrium point and shows the tangent line to the curve at equilibrium. The slope of this tangent, , is the thermodynamic equilibrium temperature. Thus, temperature is not a coordinate in the state space but a geometric property.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Kinetic Temperature<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/andymaypetrophysicist.com\/2026\/08\/12\/kinetic-temperature\/\">Kinetic temperature<\/a>&nbsp;was discussed in the last post, it is the conventional thermometer measured temperature. Whereas the thermodynamic temperature comes from the slope of the equilibrium surface U(S,V,N), Kinetic temperature comes from the average translational kinetic energy of the particles in the system being measured. It is defined through the velocity distribution of the particles, not through an equilibrium manifold. Figure 2 illustrates the development of kinetic temperature.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"233\" data-attachment-id=\"463913\" data-permalink=\"https:\/\/climatescience.press\/?attachment_id=463913\" data-orig-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-137.png?fit=2544%2C820&amp;ssl=1\" data-orig-size=\"2544,820\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;,&quot;alt&quot;:&quot;&quot;}\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-137.png?fit=723%2C233&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-137.png?resize=723%2C233&#038;ssl=1\" alt=\"\" class=\"wp-image-463913\" srcset=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-137.png?resize=1024%2C330&amp;ssl=1 1024w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-137.png?resize=300%2C97&amp;ssl=1 300w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-137.png?resize=768%2C248&amp;ssl=1 768w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-137.png?resize=1536%2C495&amp;ssl=1 1536w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-137.png?resize=2048%2C660&amp;ssl=1 2048w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-137.png?resize=640%2C206&amp;ssl=1 640w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-137.png?resize=1200%2C387&amp;ssl=1 1200w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-137.png?w=1446&amp;ssl=1 1446w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-137.png?w=2169&amp;ssl=1 2169w\" sizes=\"auto, (max-width: 723px) 100vw, 723px\" \/><figcaption class=\"wp-element-caption\">Figure 2. An illustration of how kinetic temperature is defined.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Comparing figure 1 to figure 2 shows that, while thermodynamic equilibrium temperature and kinetic temperature of a system at equilibrium might be equal, it is a superficial equality, the two temperatures are defined differently.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Thermodynamic temperature<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Defined on the&nbsp;<em>macroscopic equilibrium manifold<\/em>&nbsp;.<\/li>\n\n\n\n<li>Temperature is the&nbsp;<em>slope<\/em>&nbsp;.<\/li>\n\n\n\n<li>Requires equilibrium and a well\u2011defined entropy.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Kinetic temperature<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Defined from&nbsp;<em>microscopic particle motion<\/em>.<\/li>\n\n\n\n<li>Temperature is proportional to the&nbsp;<em>average translational kinetic energy<\/em>.<\/li>\n\n\n\n<li>Does not require entropy or equilibrium surfaces.<\/li>\n\n\n\n<li>Emerges from the&nbsp;<em>velocity distribution<\/em>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Kinetic temperature arises from statistical mechanics rather than equilibrium thermodynamics.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Non-equilibrium temperature<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">There are number of techniques for measuring temperatures in non-equilibrium systems, but the commonly used translational temperature in a shock front is a very good example. It illustrates how important it can be to measure non-equilibrium temperatures. It is defined from the non\u2011Maxwellian velocity distribution immediately behind a shock front. The shock front temperature is widely used in aerospace, combustion, and atmospheric entry and it differs from thermodynamic and kinetic temperature in almost every way.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In a shock front, the particle velocity distribution is distorted. It often has a high\u2011energy tail, is anisotropic, and contains mode\u2011dependent temperatures, like translational, rotational, vibrational, and electron. The development of a shock front temperature is illustrated in figure 3. A shock front is the advancing edge of a shock wave, a propagating disturbance that moves faster than the speed of sound in a fluid and causes an abrupt, nearly discontinuous change in pressure, temperature, density, and other flow properties (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Shock_wave\">Wikipedia<\/a>).<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"261\" data-attachment-id=\"463915\" data-permalink=\"https:\/\/climatescience.press\/?attachment_id=463915\" data-orig-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-138.png?fit=2479%2C894&amp;ssl=1\" data-orig-size=\"2479,894\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;,&quot;alt&quot;:&quot;&quot;}\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-138.png?fit=723%2C261&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-138.png?resize=723%2C261&#038;ssl=1\" alt=\"\" class=\"wp-image-463915\" srcset=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-138.png?resize=1024%2C369&amp;ssl=1 1024w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-138.png?resize=300%2C108&amp;ssl=1 300w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-138.png?resize=768%2C277&amp;ssl=1 768w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-138.png?resize=1536%2C554&amp;ssl=1 1536w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-138.png?resize=2048%2C739&amp;ssl=1 2048w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-138.png?resize=640%2C231&amp;ssl=1 640w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-138.png?resize=1200%2C433&amp;ssl=1 1200w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-138.png?w=1446&amp;ssl=1 1446w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-138.png?w=2169&amp;ssl=1 2169w\" sizes=\"auto, (max-width: 723px) 100vw, 723px\" \/><figcaption class=\"wp-element-caption\">Figure 3. An illustration of how a shock-front non-equilibrium temperature is defined and computed.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The left illustration in figure 3 shows an example shock wave velocity space, it is clearly not at equilibrium. The middle illustration compares this distribution to a Maxwellian distribution in blue. The right illustration computes the shock front temperature using only the core region of the distribution.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The shock-front non-equilibrium temperature is only one of many. There are others, for example the brightness temperature used by Spencer and Christy (Spencer &amp; Christy, 1990) at the UAH to determine atmospheric temperature for several intervals.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Radiation (brightness) temperature<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">This temperature measurement is ubiquitous in the atmospheric sciences, astrophysics, and remote sensing. Whereas the previous examples of temperature measurements used either entropy or particle velocity to determine temperature, this measure uses brightness or radiation intensity (I) to determine temperature. In essence, brightness temperature is the temperature you would infer if you assumed the radiation intensity was coming from a blackbody. You simply take the measured intensity at a given frequency (I<sub>v<\/sub>), plug it into&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Planck%27s_law\">Planck\u2019s law<\/a>&nbsp;and solve for temperature. Crucially, it does not require the radiation field to be Planckian.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Brightness temperature is not necessarily the real temperature of the emitting body. A real radiation field may be a mixture of temperatures, and it may be far from equilibrium and if so, the spectrum is not a Planck curve. But, at any given frequency, radiation intensity always increases with temperature (see the right-hand plot in figure 4) and you can always find a unique temperature for any brightness. So, brightness temperature is valuable because it expresses radiance on a temperature scale, making radiative transfer relationships intuitive even when the radiation field is far from equilibrium. This is convenient in microwave remote sensing, such as that done at UAH.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">However, that said, brightness temperature can equal physical temperature, or be very close to it, when the emitting medium is optically thick and in local thermodynamic equilibrium (LTE) at that frequency. The O\u2082 microwave bands from the atmosphere are close to this ideal, which is why UAH can treat brightness temperature as physical temperature after instrument corrections and calibration. UAH made a very good choice when they picked the oxygen microwave bands (~50-60 GHz) to use in their work. Oxygen molecules (O<sub>2<\/sub>) in the atmosphere are well mixed and behave like a blackbody in local thermodynamic equilibrium. Thus, the brightness temperatures in the O<sub>2<\/sub>&nbsp;frequencies are very close to the real atmospheric temperature.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The satellite radiation measurements must be corrected for various instrument effects and orbital drift, and the satellites contain a two-point internal calibration to make their calculation of brightness temperature more accurate. Periodically the instrument is pointed to space (about 2.7K) and then to a warm target inside the satellite with a known temperature and these readings are used as part of the process of calibrating the brightness temperature to real temperatures (Spencer &amp; Christy, 1990). These calibration points and the instrument corrections are good enough that both UAH and RSS use the final brightness temperature as is, they don\u2019t try and calibrate the brightness temperatures to any ground-based data, but they do use the ground-based data to estimate the accuracy at chosen points, mainly weather balloon launch sites. The accuracy is quite good (Christy et al., 2018). The development of brightness temperature is illustrated in figure 4.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"244\" data-attachment-id=\"463917\" data-permalink=\"https:\/\/climatescience.press\/?attachment_id=463917\" data-orig-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-139.png?fit=2476%2C833&amp;ssl=1\" data-orig-size=\"2476,833\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;,&quot;alt&quot;:&quot;&quot;}\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-139.png?fit=723%2C244&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-139.png?resize=723%2C244&#038;ssl=1\" alt=\"\" class=\"wp-image-463917\" srcset=\"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-139.png?resize=1024%2C345&amp;ssl=1 1024w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-139.png?resize=300%2C101&amp;ssl=1 300w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-139.png?resize=768%2C258&amp;ssl=1 768w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-139.png?resize=1536%2C517&amp;ssl=1 1536w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-139.png?resize=2048%2C689&amp;ssl=1 2048w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-139.png?resize=640%2C215&amp;ssl=1 640w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-139.png?resize=1200%2C404&amp;ssl=1 1200w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-139.png?w=1446&amp;ssl=1 1446w, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/image-139.png?w=2169&amp;ssl=1 2169w\" sizes=\"auto, (max-width: 723px) 100vw, 723px\" \/><figcaption class=\"wp-element-caption\">Figure 4. The development of a brightness temperature.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The left panel in figure 4 shows an equilibrium Planck curve versus frequency in black and a distorted brightness (I) versus frequency (<em>v<\/em>) curve in red. The distortion could be due to the lack of equilibrium or other complicating factors, like optical thinness, mixtures of temperatures, or anisotropic radiation fields. Real spectrums are more like the red distorted curve than the black Planckian curve. The middle panel zooms into a portion of the left plot and computes two brightness temperatures at two different frequencies. The two estimated temperatures are far from the Planckian curve. Finally, the right-hand plot inverts the Planck curve and shows a new plot of brightness versus temperature for one frequency. The curve is monotonic, with temperature increasing as brightness increases.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">While the brightness temperature is not always equal to actual temperature, it can be very close, as it is in the UAH oxygen brightness measurements discussed above.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Besides brightness temperature, there are other non-equilibrium temperature measurements, these include:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Vibrational temperature<\/strong>: Used for combustion and plasmas. It depends upon internal state populations and is defined with Boltzmann plots of excited populations of particles.<\/li>\n\n\n\n<li><strong>Electron temperature<\/strong>: Used in plasmas, determined from the slope of a distorted, often non-Maxwellian energy distribution. It is defined by the high energy tail of the electron energy distribution.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Discussion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The key point is that the term \u201ctemperature\u201d is just a measurement arbitrarily scaled with increasing energy. It has little meaning, until the type of temperature is specified with a modifier, like \u201cthermodynamic,\u201d \u201ckinetic,\u201d \u201cshock-front,\u201d \u201cbrightness,\u201d etc. In everyday usage, \u201ctemperature\u201d is assumed to be a temperature measured with a thermometer, which is a kinetic temperature, not a thermodynamic equilibrium temperature as some argued in the subject&nbsp;<a href=\"https:\/\/x.com\/cohler\/status\/2084920172242960880?s=20\">X thread<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Temperature does not have one definition or one meaning, either in physics or everyday use of the word. The examples discussed and illustrated above all have very different meanings and definitions. All are useful temperature measurements, but they do not all fit into one definition.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>The illustrations were all made with R, the programs can be downloaded&nbsp;<\/em><a href=\"https:\/\/andymaypetrophysicist.com\/wp-content\/uploads\/2026\/08\/R-code-for-illustrations.zip\"><em>here<\/em><\/a><em>.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>H\/T to Mike Chillit who suggested I make the illustrations to make the definitions clearer.<\/em><\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Works Cited<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Christy, J. R., Herman, B., Sr., R. P., Klotzbach, P., McNider, R. T., Hnilo, J. J., . . . Douglass, D. (2010). What Do Observational Datasets Say about Modeled Tropospheric Temperature Trends since 1979?&nbsp;<em>Remote Sensing, 9<\/em>, 2148-2169.&nbsp;<a href=\"https:\/\/doi.org\/10.3390\/rs2092148\">https:\/\/doi.org\/10.3390\/rs2092148<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Christy, J. R., Spencer, R. W., Braswell, W. D., &amp; Junod, R. (2018). Examination of space-based bulk atmospheric temperatures used in climate research.&nbsp;<em>International Journal of Remote Sensing, 39<\/em>(11), 3580\u20133607.&nbsp;<a href=\"https:\/\/doi.org\/10.1080\/01431161.2018.1444293\">https:\/\/doi.org\/10.1080\/01431161.2018.1444293<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Schroeder, D. V. (2000).&nbsp;<em>Thermal Physics.<\/em>&nbsp;San Francisco: Addison Wesley Longman.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Spencer, R., &amp; Christy, J. (1990). Precise Monitoring of Global Temperature Trends from Satellites.&nbsp;<em>Science, 247<\/em>. Retrieved from&nbsp;<a href=\"https:\/\/science.sciencemag.org\/content\/247\/4950\/1558.abstract\">https:\/\/science.sciencemag.org\/content\/247\/4950\/1558.abstract<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>There are a number of unique conditions required to measure a thermodynamic equilibrium temperature and a separate set of conditions to measure a kinetic (or thermometer) temperature, and they are not the same. While the kinetic temperature may be the same as the thermodynamic equilibrium temperature in a system at equilibrium, they are not the same thing. <\/p>\n","protected":false},"author":121246920,"featured_media":463910,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_seo_schema_type":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"There are a number of unique conditions required to measure a thermodynamic equilibrium temperature and a separate set of conditions to measure a kinetic (or thermometer) temperature, and they are not the same. While the kinetic temperature may be the same as the thermodynamic equilibrium temperature in a system at equilibrium, they are not the same thing.","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[691844788,691844682,691844681],"class_list":["post-463904","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized","tag-brightness-temperature","tag-kinetic-temperature","tag-thermodynamic-temperature","fallback-thumbnail"],"jetpack_publicize_connections":[],"jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/paxLW1-1WGk","jetpack-related-posts":[{"id":462757,"url":"https:\/\/climatescience.press\/?p=462757","url_meta":{"origin":463904,"position":0},"title":"Kinetic Temperature","author":"uwe.roland.gross","date":"08\/13\/2026","format":false,"excerpt":"Kinetic temperature can be measured in gases, liquids, and solids. However, in liquids and solids, the relationship between kinetic energy and temperature becomes more complicated because molecular motion is constrained by bonds and intermolecular forces.","rel":"","context":"In \"kinetic temperature\"","block_context":{"text":"kinetic temperature","link":"https:\/\/climatescience.press\/?tag=kinetic-temperature"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Maxwell-Boltzmann_distribution.svg_.webp?fit=1200%2C960&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Maxwell-Boltzmann_distribution.svg_.webp?fit=1200%2C960&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Maxwell-Boltzmann_distribution.svg_.webp?fit=1200%2C960&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Maxwell-Boltzmann_distribution.svg_.webp?fit=1200%2C960&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Maxwell-Boltzmann_distribution.svg_.webp?fit=1200%2C960&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":461410,"url":"https:\/\/climatescience.press\/?p=461410","url_meta":{"origin":463904,"position":1},"title":"Defining Temperature","author":"uwe.roland.gross","date":"08\/09\/2026","format":false,"excerpt":"Plasmas may have an electron temperature or an ion temperature. NMRs have a spin temperature. Electronic circuits have a noise temperature. These temperatures are meaningful and important especially when the system is far from equilibrium.","rel":"","context":"In \"Atmospheric physics\"","block_context":{"text":"Atmospheric physics","link":"https:\/\/climatescience.press\/?tag=atmospheric-physics"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-ChatGPT-Defining-Temperature.png?fit=1200%2C800&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-ChatGPT-Defining-Temperature.png?fit=1200%2C800&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-ChatGPT-Defining-Temperature.png?fit=1200%2C800&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-ChatGPT-Defining-Temperature.png?fit=1200%2C800&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-ChatGPT-Defining-Temperature.png?fit=1200%2C800&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":369201,"url":"https:\/\/climatescience.press\/?p=369201","url_meta":{"origin":463904,"position":2},"title":"Energy Imbalance Part II \u2013 An Addendum","author":"uwe.roland.gross","date":"03\/09\/2025","format":false,"excerpt":"First, there was some question about what a radiometer would see if pointed down at the surface. Figure 1 is educational in several ways. It is from the SURFRAD site at Desert Rock, Nevada on June 22, 2024. The four curves correspond to total downward solar radiation, total upward solar\u2026","rel":"","context":"In \"Atmosphere\"","block_context":{"text":"Atmosphere","link":"https:\/\/climatescience.press\/?tag=atmosphere"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/03\/0-Energy-Imbalance.jpeg?fit=1200%2C818&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/03\/0-Energy-Imbalance.jpeg?fit=1200%2C818&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/03\/0-Energy-Imbalance.jpeg?fit=1200%2C818&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/03\/0-Energy-Imbalance.jpeg?fit=1200%2C818&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/03\/0-Energy-Imbalance.jpeg?fit=1200%2C818&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":390189,"url":"https:\/\/climatescience.press\/?p=390189","url_meta":{"origin":463904,"position":3},"title":"Climate Model Assumptions Contrary to Balloon\u00a0Data","author":"uwe.roland.gross","date":"07\/22\/2025","format":false,"excerpt":"Recently Michael Connolly presented the evidence contradicting assumptions built into GCMs (Global Climate Models).\u00a0","rel":"","context":"In \"GCMs (Global Climate Models)\"","block_context":{"text":"GCMs (Global Climate Models)","link":"https:\/\/climatescience.press\/?tag=gcms-global-climate-models"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/07\/0AQN9nbDyHU0LwIGlrNivs7neeULFURmrYCNjU2sUa-7In0S9s9uH3RwlWmnv4EywL0l3z2VE27lla58a_F6AOunn5a6FclPxYnlSvUkqBGG_1XDH6OrF_Nm60hV9Zjik9buP_sbLfuik1LTdg1pzV28Ds20ttg-1.jpeg?fit=1200%2C1200&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/07\/0AQN9nbDyHU0LwIGlrNivs7neeULFURmrYCNjU2sUa-7In0S9s9uH3RwlWmnv4EywL0l3z2VE27lla58a_F6AOunn5a6FclPxYnlSvUkqBGG_1XDH6OrF_Nm60hV9Zjik9buP_sbLfuik1LTdg1pzV28Ds20ttg-1.jpeg?fit=1200%2C1200&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/07\/0AQN9nbDyHU0LwIGlrNivs7neeULFURmrYCNjU2sUa-7In0S9s9uH3RwlWmnv4EywL0l3z2VE27lla58a_F6AOunn5a6FclPxYnlSvUkqBGG_1XDH6OrF_Nm60hV9Zjik9buP_sbLfuik1LTdg1pzV28Ds20ttg-1.jpeg?fit=1200%2C1200&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/07\/0AQN9nbDyHU0LwIGlrNivs7neeULFURmrYCNjU2sUa-7In0S9s9uH3RwlWmnv4EywL0l3z2VE27lla58a_F6AOunn5a6FclPxYnlSvUkqBGG_1XDH6OrF_Nm60hV9Zjik9buP_sbLfuik1LTdg1pzV28Ds20ttg-1.jpeg?fit=1200%2C1200&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/07\/0AQN9nbDyHU0LwIGlrNivs7neeULFURmrYCNjU2sUa-7In0S9s9uH3RwlWmnv4EywL0l3z2VE27lla58a_F6AOunn5a6FclPxYnlSvUkqBGG_1XDH6OrF_Nm60hV9Zjik9buP_sbLfuik1LTdg1pzV28Ds20ttg-1.jpeg?fit=1200%2C1200&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":382563,"url":"https:\/\/climatescience.press\/?p=382563","url_meta":{"origin":463904,"position":4},"title":"Our Atmospheric Heat\u00a0Engine","author":"uwe.roland.gross","date":"06\/10\/2025","format":false,"excerpt":"A previous post presented Michel Thizon\u2019s description of gravity\u2019s effect on the mass of air functioning as a climate thermostat. Some years ago, Dr. Murry Salby wrote in detail about the troposphere operating as a heat engine and the stratosphere as a refrigerator.","rel":"","context":"In \"Atmospheric physics\"","block_context":{"text":"Atmospheric physics","link":"https:\/\/climatescience.press\/?tag=atmospheric-physics"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/06\/ChatGPT-Image-8.-Juni-2025-18_50_51.png?fit=1200%2C800&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/06\/ChatGPT-Image-8.-Juni-2025-18_50_51.png?fit=1200%2C800&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/06\/ChatGPT-Image-8.-Juni-2025-18_50_51.png?fit=1200%2C800&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/06\/ChatGPT-Image-8.-Juni-2025-18_50_51.png?fit=1200%2C800&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/06\/ChatGPT-Image-8.-Juni-2025-18_50_51.png?fit=1200%2C800&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":369252,"url":"https:\/\/climatescience.press\/?p=369252","url_meta":{"origin":463904,"position":5},"title":"R.I.P. Climate Back\u00a0Radiation","author":"uwe.roland.gross","date":"03\/10\/2025","format":false,"excerpt":"In connection with the greenhouse\u00a0effect,\u00a0the\u00a0second law of Thermodynamics\u00a0is particularly\u00a0interesting. \u00a0There are various equivalent\u00a0formulations for the second law of\u00a0thermodynamics which states that thermal\u00a0energy cannot be completely converted\u00a0into other forms of energy. \u00a0Rudolf\u00a0Clausius\u00a0was the first to formulate the\u00a0second\u00a0law in the form that heat does not flow\u00a0spontaneously from cold to hot\u00a0bodies.\u00a0\u00a0Later in 1865\u2026","rel":"","context":"In \"carbon dioxide (CO\u2082)\"","block_context":{"text":"carbon dioxide (CO\u2082)","link":"https:\/\/climatescience.press\/?tag=carbon-dioxide-co%e2%82%82"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/03\/0bg-05.jpg?fit=1200%2C800&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/03\/0bg-05.jpg?fit=1200%2C800&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/03\/0bg-05.jpg?fit=1200%2C800&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/03\/0bg-05.jpg?fit=1200%2C800&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2025\/03\/0bg-05.jpg?fit=1200%2C800&ssl=1&resize=1050%2C600 3x"},"classes":[]}],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/climatescience.press\/wp-content\/uploads\/2026\/08\/0-Figure-1_Thermal-equilibrium-3.webp?fit=2504%2C1100&ssl=1","_links":{"self":[{"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/posts\/463904","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/users\/121246920"}],"replies":[{"embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=463904"}],"version-history":[{"count":11,"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/posts\/463904\/revisions"}],"predecessor-version":[{"id":463921,"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/posts\/463904\/revisions\/463921"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=\/wp\/v2\/media\/463910"}],"wp:attachment":[{"href":"https:\/\/climatescience.press\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=463904"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=463904"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/climatescience.press\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=463904"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}