Temperature Measure

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

• AKA: Thermodynamic Temperature.
• Context:
  • It can be defined in terms of entropy(S) and internal energy (U):

[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

• For an ideal gas, temperature depends directly on volume, V and [[gas pressure],, i.e. [math]\displaystyle{ T=PV/nR }[/math] , n is the number of moles of gas and R is the gas constant.
• It is proportional to the kinetic energy, [math]\displaystyle{ E_k }[/math], and, therefore, to the root-mean-square speed, [math]\displaystyle{ v_\mathrm{rms} }[/math], of particles in an ideal gas (see Maxwell–Boltzmann probability distribution):

[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 most commom units of measurement of temperature are Celsius (°C), Fahrenheit (°F), Kelvin (K).

• Example(s):
  • Effective Temperature.
  • Absolute Temperature.
• Counter-Example(s):
  • Pressure.
  • Entropy.
  • Density.
  • Heat.
• See: Thermodynamics, Heat, Temperature Scales, Baoltzmann Constant, Kinetic Energy, Gas Pressure, Ideal Gas Law, Maxwell–Boltzmann probability distribution.

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References

2015

• (Wikipedia, 2015) ⇒ https://www.wikiwand.com/en/Temperature
  • A temperature is an objective comparative measure of hot or cold. It is measured by a thermometer, which may work through the bulk behavior of a thermometric material, detection of thermal radiation, or particle kinetic energy. Several scales and units exist for measuring temperature, the most common being Celsius (denoted °C; formerly called centigrade), Fahrenheit (denoted °F), and, especially in science, Kelvin (denoted K).

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.

2005

• (Wolfram Science world , 1999) ⇒ http://scienceworld.wolfram.com/physics/Temperature.html
  • Temperature (sometimes called thermodynamic temperature) is a measure of the average kinetic energy of the particles in a system. Adding heat to a system causes its temperature to rise. While there is no maximum theoretically reachable temperature, there is a minimum temperature, known as absolute zero, at which all molecular motion stops. Temperatures are commonly measured in the Kelvin or Celsius scales, with Fahrenheit still in common use in the Unites States.

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.

2005

• (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(...)

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