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Energy Density of Nuclear & Organic Fuels

The Enthalpy (or Latent Heat) of Vaporisation (symbol ∆Hvap)

There is a reason for delving a bit more deeply into this Subject that Involves Enthalpy and Entrropy; and that is; that it was a subject area that I skimmed over many years ago;and now is as good a time as any to revise and update my knowledge and understanding.
My Interest in the Early '60's was in, amongst other things, resonance and Lasers.
Now I am interested in Laser Ignition and Resonant breaking of Interatomic bonds to enable the Seperation of Gasses within Fuel Molecules; and this subject area is of relevance!
More on that later, in another section under "Power Generation".

Another reason is that as a very famous Physicist declared,"It's all about 'Resonance"... or Richard Feynman used words to that effect!!
And another reason is because in The Tables I have used below to compare The Specific or Energy Densities of Various Fuels Nuclear and Organic: I have used The Term"Energy Density" (or Rather those who created the original Tables did). where "Specific Energy" would have been a better choice.
Although this little snippet of information does, at least, explain the slight conflict of adefinitions... "The unit of energy in the International System of Units (SI) is the joule (J). Also defined is a corresponding 'intensive energy density', called 'specific internal energy', which is either relative to the mass of the system, with the unit J/kg, or relative to the amount of substance with unit J/mol (molar internal energy).

The Purpose is still valid, as there is consistency and Apples are compared, in value at least, with Apples!

Another Note, Remember that a Decimeter is 10cm and a cubic Decimeter contains 1000 cc's (cubic centimeters).

Now on with the Story about ENTHALPY (H)

The enthalpy of melting (ΔH°m) of zinc is 7323 J/mol, and the enthalpy of vaporization (ΔH°v) is 115330 J/mol.

The enthalpy of vaporization can be written as:
ΔH°v or ΔHvap=ΔUvap+p*ΔV
Where ΔUvap_Refers to the internal energy in the Liquid Phase (U) for vaporization to occur.
It is equal to the increased internal energy of the vapor phase compared with the liquid phase, plus the work done against ambient pressure.
The increase in the internal energy can be viewed as the energy required to overcome the intermolecular interactions in the liquid (or solid, in the case of sublimation).
Hence helium has a particularly low enthalpy of vaporization, 0.0845 kJ/mol, as the Van der Waals forces between helium atoms are particularly weak.
On the other hand, the molecules in liquid water are held together by relatively strong hydrogen bonds, and its enthalpy of vaporization, 40.65 kJ/mol, is more than five times the energy required to heat the same quantity of water from 0 °C to 100 °C (Cp = 75.3 J/K·mol).
Joule/mol*Kelvin(In SI unit) is defined as:
Unit J/K.mol
xpUnit Joule per Kelvin times mole
SI_unit kg.m+2.s-2.K-1.mol
Dim M+1L+2T-2K-1
where 'T' represents the Time Unit in seconds 's'

Care must be taken, however, when using enthalpies of vaporization to measure the strength of intermolecular forces, as these forces may persist to an extent in the gas phase (as is the case with hydrogen fluoride), and so the calculated value of the bond strength will be too low.
This is particularly true of metals, which often form covalently bonded molecules in the gas phase: in these cases, the enthalpy of atomization must be used to obtain a true value of the bond energy.

Specific Energy and Energy Density

U = ∑ (pi Ei )

in the range i = 1 to N

"TABLE 1 - Energy Released By Nuclear Reactions" TABLE 1 - Energy Released By Nuclear Reactions

"TABLE 2 Energy Density of Hydro-Carbon Fuel Types" TABLE 2 Energy Density of Hydro-Carbon Fuel Types

Now to Continue with our Study of ENTHALPY (H)

Internal Energy

Ref: Wikipedia with ref No's, where applicable, left to aid those interested.

The internal energy of a thermodynamic system is the energy contained within it.

It keeps account of the gains and losses of energy of the system that are due to changes in its internal state.[1][2]

The internal energy is measured as a difference from a reference zero defined by a standard state. The difference is determined by thermodynamic processes that carry the system between the reference state and the current state of interest.

The internal energy is an extensive property, and cannot be measured directly.

The thermodynamic processes that define the internal energy are transfers of chemical substances or of energy as heat, and thermodynamic work.[3]

These processes are measured by changes in the system's extensive variables, such as entropy, volume, and chemical composition.

It is often not necessary to consider all of the system's intrinsic energies, for example, the static rest mass energy of its constituent matter.

When mass transfer is prevented by impermeable containing walls, the system is said to be closed and the first law of thermodynamics defines the change in internal energy as the difference between the energy added to the system as heat and the thermodynamic work done by the system on its surroundings.

If the containing walls pass neither substance nor energy, the system is said to be isolated and its internal energy cannot change.

The internal energy describes the entire thermodynamic information of a system, and is an equivalent representation to the entropy, both cardinal state functions of only extensive state variables.[4]
Thus, its value depends only on the current state of the system and not on the particular choice from many possible processes by which energy may pass to or from the system. It is a thermodynamic potential.

Microscopically, the internal energy can be analyzed in terms of the kinetic energy of microscopic motion of the system's particles from translations, rotations, and vibrations, and of the potential energy associated with microscopic forces, including chemical bonds.

The unit of energy in the International System of Units (SI) is the joule (J).

Also defined is a corresponding intensive energy density, called specific internal energy, which is either relative to the mass of the system, with the unit J/kg, or relative to the amount of substance with unit J/mol (molar internal energy).

Cardinal functions

The internal energy U, of a system depends on its entropy S, its volume V and its number of massive particles: U(S,V,{Nj}).

It expresses the thermodynamics of a system in the energy representation. As a function of state, its arguments are exclusively extensive variables of state. Alongside the internal energy, the other cardinal function of state of a thermodynamic system is its entropy S, as a function, S(U,V,{Nj}), of the same list of extensive variables of state, except that the entropy, S, is replaced in the list by the internal energy, U. It expresses the entropy representation.[4][5][6]

Each cardinal function is a monotonic function of each of its natural or canonical variables. Each provides its characteristic or fundamental equation, for example U = U(S,V,{Nj}), that by itself contains all thermodynamic information about the system. The fundamental equations for the two cardinal functions can in principle be interconverted by solving, for example, U = U(S,V,{Nj}) for S, to get S = S(U,V,{Nj}).

In contrast, Legendre transforms are necessary to derive fundamental equations for other thermodynamic potentials and Massieu functions.

The Entropy as a function only of extensive state variables is the one and only cardinal function of state for the generation of Massieu functions. It is not itself customarily designated a 'Massieu function', though rationally it might be thought of as such, corresponding to the term 'thermodynamic potential', which includes the internal energy.[5][7][8]

For real and practical systems, explicit expressions of the fundamental equations are almost always unavailable, but the functional relations exist in principle.

Formal, in principle, manipulations of them are valuable for the understanding of thermodynamics.

Description and definition

The internal energy U of a given state of the system is determined relative to that of a standard state of the system, by adding up the macroscopic transfers of energy that accompany a change of state from the reference state to the given state: ∆ U =ΣEi
where ∆ U denotes the difference between the internal energy of the given state and that of the reference state, and the Ei are the various energies transferred to the system in the steps from the reference state to the given state. It is the energy needed to create the given state of the system from the reference state.

From a non-relativistic microscopic point of view, it may be divided into microscopic potential energy;
Umicro pot, and microscopic kinetic energy, Umicro kin, components:
U = Umicro pot + Umicro kin

The microscopic kinetic energy of a system arises as the sum of the motions of all the system's particles with respect to the center-of-mass frame, whether it be the motion of atoms, molecules, atomic nuclei, electrons, or other particles. The microscopic potential energy algebraic summative components are those of the chemical and nuclear particle bonds, and the physical force fields within the system, such as due to internal induced electric or magnetic dipole moment, as well as the energy of deformation of solids (stress-strain). Usually, the split into microscopic kinetic and potential energies is outside the scope of macroscopic thermodynamics. Internal energy does not include the energy due to motion or location of a system as a whole. That is to say, it excludes any kinetic or potential energy the body may have because of its motion or location in external gravitational, electrostatic, or electromagnetic fields. It does, however, include the contribution of such a field to the energy due to the coupling of the internal degrees of freedom of the object with the field.

In such a case, the field is included in the thermodynamic description of the object in the form of an additional external parameter.

For practical considerations in thermodynamics or engineering, it is rarely necessary, convenient, nor even possible, to consider all energies belonging to the total intrinsic energy of a sample system, such as the energy given by the equivalence of mass. Typically, descriptions only include components relevant to the system under study. Indeed, in most systems under consideration, especially through thermodynamics, it is impossible to calculate the total internal energy.[9] Therefore, a convenient null reference point may be chosen for the internal energy.

The internal energy is an extensive property: it depends on the size of the system, or on the amount of substance it contains.

At any temperature greater than absolute zero, microscopic potential energy and kinetic energy are constantly converted into one another, but the sum remains constant in an isolated system (cf. table). In the classical picture of thermodynamics, kinetic energy vanishes at zero temperature and the internal energy is purely potential energy. However, quantum mechanics has demonstrated that even at zero temperature particles maintain a residual energy of motion, the "zero point energy".

A system at absolute zero is merely in its quantum-mechanical ground state, the lowest energy state available. At absolute zero a system of given composition has attained its minimum attainable entropy.

The microscopic kinetic energy portion of the internal energy gives rise to the temperature of the system. Statistical mechanics relates the pseudo-random kinetic energy of individual particles to the mean kinetic energy of the entire ensemble of particles comprising a system. Furthermore, it relates the mean microscopic kinetic energy to the macroscopically observed empirical property that is expressed as temperature of the system.

While temperature is an intensive measure, this energy expresses the concept as an extensive property of the system, often referred to as the thermal energy,[10][11]

The scaling property between temperature and thermal energy is the entropy change of the system.

Statistical mechanics considers any system to be statistically distributed across an ensemble of N microstates. In a system that is in thermodynamic contact equilibrium with a heat reservoir, each microstate has an energy Ei and is associated with a probability pi. The internal energy is the mean value of the system's total energy, i.e., the sum of all microstate energies, each weighted by its probability of occurrence:

U = ∑ (pi Ei ) in the range i = 1 to N


Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle.[1] As well as atoms and molecules, the empty space of the vacuum has these properties. According to quantum field theory, the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields, whose quanta are fermions (i.e., leptons and quarks), and force fields, whose quanta are bosons (e.g., photons and gluons). All these fields have zero-point energy.[2] These fluctuating zero-point fields lead to a kind of reintroduction of an aether in physics[1][3] since some systems can detect the existence of this energy.

However, this aether cannot be thought of as a physical medium if it is to be Lorentz invariant such that there is no contradiction with Einstein's theory of special relativity.[1]

Physics currently lacks a full theoretical model for understanding zero-point energy; in particular, the discrepancy between theorized and observed vacuum energy is a source of major contention.[4]

Physicists Richard Feynman and John Wheeler calculated the zero-point radiation of the vacuum to be an order of magnitude greater than nuclear energy, with a single light bulb containing enough energy to boil all the world's oceans.[5]

Yet according to Einstein's Theory of General Relativity, any such energy would gravitate, and the experimental evidence from both the expansion of the universe, dark energy and the Casimir effect; shows any such energy to be exceptionally weak.

A popular proposal that attempts to address this issue is to say that the fermion field has a negative zero-point energy, while the boson field has positive zero-point energy; and thus these energies somehow cancel each other out.[6][7]

This idea would be true if supersymmetry were an exact symmetry of nature; however, the LHC at CERN has so far found no evidence to support it. Moreover, it is known that if supersymmetry is valid at all, it is at most a broken symmetry, only true at very high energies, and no one has been able to show a theory where zero-point cancellations occur in the low energy universe we observe today.[7]

This discrepancy is known as the "Cosmological Constant Problem" and it is one of the greatest unsolved mysteries in physics. Many physicists believe that "the vacuum holds the key to a full understanding of nature".[8]

Some Values of Enthalpies of Vaporisation
At Their Respective Boiling Points…

"A Mendeleev Table"with a Difference…. Lol…

And Below that.

The Enthalpies of vaporization of common substances, measured at their respective standard boiling points: