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Mass near the M87* black hole is converted into a very energetic astrophysical jet, stretching five thousand light years. In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement.
Specific volume is the volume occupied by a unit of mass of a material. [1] In many cases, the specific volume is a useful quantity to determine because, as an intensive property, it can be used to determine the complete state of a system in conjunction with another independent intensive variable. The specific volume also allows systems to be ...
If the calorically perfect gas approximation is used, then the ideal gas law may also be expressed as follows = where is the number density of the gas (number of atoms/molecules per unit volume), = / is the (constant) adiabatic index (ratio of specific heats), = is the internal energy per unit mass (the "specific internal energy"), is the ...
The equilibrium state of a thermodynamic system is described by specifying its "state". The state of a thermodynamic system is specified by a number of extensive quantities, the most familiar of which are volume, internal energy, and the amount of each constituent particle (particle numbers). Extensive parameters are properties of the entire ...
However, in the thermodynamic limit (i.e. in the limit of infinitely large system size), the specific entropy (entropy per unit volume or per unit mass) does not depend on . The entropy is thus a measure of the uncertainty about exactly which quantum state the system is in, given that we know its energy to be in some interval of size δ E ...
Total energy is the sum of rest energy = and relativistic kinetic energy: = = + Invariant mass is mass measured in a center-of-momentum frame. For bodies or systems with zero momentum, it simplifies to the mass–energy equation E 0 = m 0 c 2 {\displaystyle E_{0}=m_{0}c^{2}} , where total energy in this case is equal to rest energy.
The density of states related to volume V and N countable energy levels is defined as: = = (()). Because the smallest allowed change of momentum for a particle in a box of dimension and length is () = (/), the volume-related density of states for continuous energy levels is obtained in the limit as ():= (()), Here, is the spatial dimension of the considered system and the wave vector.
The state volume function (used to calculate entropy) is given by v ( E ) = ∑ H i < E 1. {\displaystyle v(E)=\sum _{H_{i}<E}1.} The microcanonical ensemble is defined by taking the limit of the density matrix as the energy width goes to zero, however a problematic situation occurs once the energy width becomes smaller than the spacing between ...