Temperature Measure

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A Temperature Measure is a physical measure of a system's average kinetic energy .

[math]\displaystyle{ T = \left (\frac{\partial U}{\partial S} \right )_{V,N}  }[/math]
where [math]\displaystyle{ )_{V,N} }[/math] means that the number of particles (N) and volume (V) are assumed to be constants
[math]\displaystyle{ T=\frac{2}{3}\frac{E_k}{K_B}=\frac{1} {3} \frac{mv_\mathrm{rms}^2}{k_B} }[/math] 
where [math]\displaystyle{ k_B }[/math] is Boltzmann constant.



The coldest theoretical temperature is absolute zero, at which the thermal motion of atoms and molecules reaches its minimum - classically, this would be a state of motionlessness, but quantum uncertainty dictates that the particles still possess a finite zero-point energy. In addition to this, a real system or object can never be brought to a temperature of absolute zero by thermodynamic means. Absolute zero is denoted as 0 K on the Kelvin scale, −273.15 °C on the Celsius scale, and −459.67 °F on the Fahrenheit scale.
The kinetic theory offers a valuable but limited account of the behavior of the materials of macroscopic bodies, especially of fluids. It indicates the absolute temperature as proportional to the average kinetic energy of the random microscopic motions of those of their constituent microscopic particles, such as electrons, atoms, and molecules, that move freely within the material.


Temperature is an important quantity in thermodynamics and kinetic theory, appearing explicitly for example in the ideal gas law
[math]\displaystyle{ PV=nRT }[/math]
where P is the pressure, V is the volume, n is the number of moles, and R is the universal gas constant. Thermodynamically, temperature is given by the Maxwell relation:

[math]\displaystyle{ T = \left (\frac{\partial E}{\partial S} \right )_{V} }[/math]

where E is the energy, S is the entropy, and the partial derivative is taken at constant volume. The quantity [math]\displaystyle{ 1/kT }[/math], where k is Boltzmann's constant, arising frequently in thermodynamics is defined as [math]\displaystyle{ \beta=1/kT }[/math] a quantity sometimes known as thermodynamic beta.


  • (Hyperphysics Encyclopedia, 2005) ⇒ http://hyperphysics.phy-astr.gsu.edu/hbase/force.html#fordef
    • One approach to the definition of temperature is to consider three objects, say blocks of copper, iron and alumninum which are in contact such that they come to thermal equilibrium. By equilibrium we mean that they are no longer transferring any net energy to each other. We would then say that they are at the same temperature, and we would say that temperature is a property of these objects which implies that they will no longer transfer net energy to one another. We could say that A is at the same temperature as C even though they are not in contact with each other. This scenario is called the "zeroth law of thermodynamics" since this understanding logically precedes the ideas contained in the important First and Second Laws of Thermodynamics.
An important idea related to temperature is the fact that a collision between a molecule with high kinetic energy and one with low kinetic energy will transfer energy to the molecule of lower kinetic energy. Part of the idea of temperature is that for two collections of the same type of molecules that are in contact with each other, the collection with higher average kinetic energy will transfer energy to the collection with lower average kinetic energy. We would say that the collection with higher kinetic energy has a higher temperature, and that net energy transfer will be from the higher temperature collection to the lower temperature collection, and not vice versa. Clearly, temperature has to do with the kinetic energy of the molecules, and if the molecules act like independent point masses, then we could define temperature in terms of the average translational kinetic energy of the molecules, the so-called "kinetic temperature". The average kinetic energy of the molecules of an object is an important part of the concept of temperature and provides some useful intuition about what temperature is. If all matter just consisted of independently moving point masses that just experienced elastic collisions with each other, that would be an adequate picture of temperature(...)