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In particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 10 28 eV (the Planck energy, corresponding to the energy equivalent of the Planck mass, 2.176 45 × 10 −8 kg) at which quantum effects of gravity become significant.
In 1900, Max Planck derived the average energy ε of a single energy radiator, e.g., a vibrating atomic unit, as a function of absolute temperature: [24] = / (), where h is the Planck constant, ν is the frequency, k is the Boltzmann constant, and T is the absolute temperature. The zero-point energy makes no contribution to Planck's original ...
Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times the Boltzmann constant k B = 1.38 × 10 −23 J K −1. The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because ln(1) = 0 .
a) Single possible configuration for a system at absolute zero, i.e., only one microstate is accessible. b) At temperatures greater than absolute zero, multiple microstates are accessible due to atomic vibration (exaggerated in the figure). At absolute zero temperature, the system is in the state with the minimum thermal energy, the ground state.
Absolute zero is the lowest limit of the thermodynamic temperature scale; a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value. The fundamental particles of nature have minimum vibrational motion, retaining only quantum mechanical, zero-point energy -induced particle motion.
The heat capacity must be zero at zero temperature in order for the above integral not to yield an infinite absolute entropy, thus violating the third law of thermodynamics. One of the strengths of the Debye model is that (unlike the preceding Einstein model) it predicts the proper mathematical form of the approach of heat capacity toward zero ...
One of the relations it resolved to is the enthalpy of vaporization at a provided temperature by measuring the slope of a saturation curve on a pressure vs. temperature graph. It also allows us to determine the specific volume of a saturated vapor and liquid at that provided temperature.
This formulation does not mention heat and does not mention temperature, nor even entropy, and does not necessarily implicitly rely on those concepts, but it implies the content of the second law. A closely related statement is that "Frictional pressure never does positive work." [55] Planck wrote: "The production of heat by friction is ...
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