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The energy–momentum relation is consistent with the familiar mass–energy relation in both its interpretations: E = mc 2 relates total energy E to the (total) relativistic mass m (alternatively denoted m rel or m tot), while E 0 = m 0 c 2 relates rest energy E 0 to (invariant) rest mass m 0.
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance, rather than energy per temperature increment per particle.
In classical mechanics, both the m 0 c 2 term and the high-speed corrections are ignored. The initial value of the energy is arbitrary, as only the change in energy can be measured and so the m 0 c 2 term is ignored in classical physics. While the higher-order terms become important at higher speeds, the Newtonian equation is a highly accurate ...
The Morse potential, named after physicist Philip M. Morse, is a convenient interatomic interaction model for the potential energy of a diatomic molecule.It is a better approximation for the vibrational structure of the molecule than the quantum harmonic oscillator because it explicitly includes the effects of bond breaking, such as the existence of unbound states.
Δ r G, Gibbs free energy change per mole of reaction, Δ r G°, Gibbs free energy change per mole of reaction for unmixed reactants and products at standard conditions (i.e. 298 K, 100 kPa, 1 M of each reactant and product), R, gas constant, T, absolute temperature, ln, natural logarithm, Q r, reaction quotient (unitless),
Assuming that the Earth is a sphere of uniform density (which it is not, but is close enough to get an order-of-magnitude estimate) with M = 5.97 × 10 24 kg and r = 6.37 × 10 6 m, then U = 2.24 × 10 32 J. This is roughly equal to one week of the Sun's total energy output.
Conservation of four-momentum gives p C μ = p A μ + p B μ, while the mass M of the heavier particle is given by −P C ⋅ P C = M 2 c 2. By measuring the energies and three-momenta of the daughter particles, one can reconstruct the invariant mass of the two-particle system, which must be equal to M.
The Hamiltonian of a system represents the total energy of the system; that is, the sum of the kinetic and potential energies of all particles associated with the system. . The Hamiltonian takes different forms and can be simplified in some cases by taking into account the concrete characteristics of the system under analysis, such as single or several particles in the system, interaction ...