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  1. What kind of energy is converted by our digestive system.  How efficient is our digestive system compared to other living beings?  Answer

  2. A closed system is one in which no mass crosses the boundaries of your system.  An isolated system is one in which no mass and no energy crosses the boundary.  What is an open system?  What is a steady state system?  Is a steady state (time invariant) energy conversion process reversible?  Answer

  3. What if the device in Q2 was isentropic? Adiabatic?  Answer

  4. Friction produces heat, and heat flow produces entropy. I understand this.  But I have read that entropy is generated when two or more substances are mixed?  Why? Answer

  5. Is there any theoretical limitation to wind energy conversion efficiency? Answer

  6. Is there any theoretical limitation to solid-state solar energy conversion efficiency? Answer

  7. Is there any any obvious similarity between the relationship contained in the Euler characteristics of a polyhedra and the Gibbs phase rule.  Why do they appear to be so similar with non-dimensional quantities comprising the variable in the equations?  Is there a topological connection? Answer

    Euler Rule:  Any convex polyhedron's surface has a Euler (Euler-Poincare) characteristic (E-V+2= F).  Here V, E, and F are respectively the numbers of vertices (corners), edges and faces in the given polyhedron.                                                                        Gibbs Rule:  If F is the number of degrees of freedom, C is the number of components and P is the number of phases in thermodynamic equilibrium with each other then the Gibbs Phase Rule applies  to non-reactive multi-component heterogeneous systems in thermodynamic equilibrium.  This is given by the equality (C-P+2= F) which looks very similar to the Euler rule.  To answer the question of similarity, please not hesitate to use the Borsuk-Ulam theorem (an amazing topological theorem with symmetry implications).  Regardless, it must be noted that there is no definite answer for this question yet.
  8. Why is energy conserved?  Answer:   This is a consequence of Emmy Noether's theorem on symmetry and the principle of least action.  The principle of least action also appears to shed light on the postulate of shape selection (from


Answer to Q1:   Yes we are able to processes some cooked foods better than most other organisms. However this is a complex question and there is not one simple answer.  Regardless the short answer is that humans convert chemical energy through complex biological processes into heat and work.   Our digestive systems which converts what we eat into energy and other compounds, have evolved over time.  In our digestive system we break-down complex molecules (food) into substances like sugar, which when combined with oxygen produces mass, heat and work types of energy exchanges within our body.  

Answer to Q2 :  No.   Steady-state Processes do not have to be reversible for open systems. An open system is a control volume where mass is input and/or output from the control volume as well as energy.   When one imagines a system contained in a control volume which shows time invariant properties i.e. it is at steady state, new entropy can be continuously generated and dispersed through the boundaries of the control volume in a manner that ensures that other thermodynamic properties like Temperature, Pressure, Volume, Energy, and Entropy are measured to remain constant within the control volume.   Such a process is however not a reversible process.  Reversible implies that no new entropy is generated.  A  reversible processes for an open system is one that maximizes the amount of work produced because it does not create new entropy.   However, in reality, open systems are difficult to make fully reversible; although such an approximation is often used for solving engineering problems.   Note that the entropy is not a conserved property unlike mass and energy which are conserved properties (at least for velocities that do not approach the speed of light). 

Answer to Q3:  For a reversible steady- state thermally isentropic cyclic process, the change in enthalpy is equal to the maximum work that can be extracted (or conversely for a pump or refrigerator it is the minimum work that is required to run the device for the required objective).   Regardless, the thermal efficiency limit is set by the Second Law and cannot be violated in any scenario.    For a fluid exchanging energy in a open cyclic thermal device (bound by a control volume) and one which is which is adiabatic and has no changes to the control volume shape or size with time - one can obtain close to isentropic approximations; but not always a strict steady state condition when comparing the input and outlet thermodynamic properties of the fluid entering and leaving the device. 

Answer to Q4:  The first type of entropy generation is called thermal entropy generation.   A mixing process also creates new entropy by the generation of configurational entropy.  Essentially the specific heat, after mixing, changes in comparison to the unmixed state.  Entropy generation is used as a marker when shapes are created.  Nature's clever way of process-path and shape selection is called the MEPR principle. The acronym MEPR (sometimes just called MEP) stands for 'Maximum Entropy Production Rate'.

Answer to Q5:  Yes it is about 59.5%.  The limit comes from the fact that air has to push through with a certain velocity to the other side of the windmill.  Conserve momentum and mass.

Answer to Q6:  This is the most engaging of all the six questions.  Although often cloaked in quantum terms, the issue simply lies in the second law of thermodynamics.  It is generally known that the hotter a body becomes, the more heat it radiates.  Simultaneously the peak radiation frequency downshifts.  Power per unit volume is related to kT (see below).  T is in Kelvin, kB=1.380 6488×10−23 J/K is the Boltzmann constant.  The second law sets limit on maximum available work between two temperatures.

For the explanation below, T is in Kelvin, kB=1.380 6488×10−23 J/K is the Boltzmann constant, h is the Planck constant=6.62606957(29)×10−34J.s.   A lower case c=299,792,458 m/s is the common symbol that is used to denote the velocity of e.m radiation (light).  Lambda {\lambda ) is the wavelength (m) and \nu is the frequency (1/s). 


A  famous equation called the Plancks equation shows that the power per unit volume is related to Temperature of a unit area of a surface The sun temperature is 5778K (see calculation below).  This is only a modestly high temperature when compared to other more-active stars recognized in distant galaxies.  The heat generated by the Sun is from nuclear fusion processes inside our Sun (yes a lot of entropy is also generated).  The earth surface is at ~300K.  The theoretical Carnot efficiency (this is the maximum allowed efficiency) between a source of heat at at a temperature Thot to a sink at a temperature Tcold is equal to (1-Thot/Tcold).   Therefore about 94.8% efficiency should be possible for converting to work from sunlight falling on earth.  Unfortunately sunlight falls in a mid range of the electromagnetic spectrum and has a wide variation of frequencies in the optical frequency range, from low frequency red region to the high frequencies like (blue - ultraviolet) region.    Not all frequencies are easily absorbed by receptor materials (solar cells).   There is thus an additional limit on the best possible direct work conversion from solar radiation.  The best efficiencies reported so far for solar cells is about 44% with sunlight (not very close to the 94.8% mentioned above). The average amount of sunlight  incident on earth is about 1300W/m2 . The sun may be considered to be a black-body.  Radiance and spectral radiance are measures of the quantity of radiation that passes through or is emitted from a surface and falls within a given solid angle in a specified direction. The SI unit of radiance is watts per steradian per square metre (W·sr−1·m−2), while that of spectral radiance is W·sr−1·m−2·Hz−1 or W.·sr−1·m−3 depending on if the spectrum is a function of frequency or of wavelengthYou may not have previously encountered the unit sr.  It is the solid angle subtended at the center of a unit sphere by a unit area on its surface. Assume a sphere of radius r, any portion of its surface with area A = r2 will be one steradian.  The surface area of a sphere is 4.pi.r2.  This gives 4.pi = 12.56637 steradians The radiation spectrum and temperature relationships are discussed below.  For a well define space that has equilibrium e.m radiation i.e.a wave that has a electric and magnetic fields, the energy U is given by:

 U = \frac{\varepsilon_0}{2} \mathbf{E}^2 + \frac{1}{2\mu_0} \mathbf{B}^2

E is the electric field and B is the magnetic field.    The SI unit for U is Joules.

From this equation and other laws of physics and statistics not described here, one may now derive the spectral energy densities as a function of frequency uv(T) or as a function of wavelength uλ(T):

    \frac{U}{L^3} = \int_0^\infty u_\nu(T)\, d\nu,


u_\nu(T) = {8\pi
 h\nu^3\over c^3}{1\over e^{h\nu/k_\mathrm{B}T} - 1}.

and L3 defines a volume. 

Assume B is the spectral radiance with the units of W·sr−1·m−2·Hz−1.  B is a function of frequency or wavelength and is given by the Plank expressions:


B_\nu(T) = \frac{ 2 h \nu^3}{c^2} \frac{1}{e^\frac{h\nu}{k_\mathrm{B}T} - 1},\text{ or }\,B_\lambda(T) =\frac{2 hc^2}{\lambda^5}\frac{1}{ e^{\frac{hc}{\lambda k_\mathrm{B}T}} - 1}

For radiation emitted by an ideal black body at temperature T, spectral radiance is described by Planck's law formulation, while the integral of radiance over the hemisphere into which it radiates, in W/m2, is described by the Stefan-Boltzmann law formulation.


Electric and magnetic fields store energy. In a vacuum, the (volumetric) energy density (in SI units) is given by


u_i(T) = \frac{4\pi}{c} B_i(T).

Planck's law can also be written in terms of the spectral energy density (ui) by multiplying Bv by 4p/c:

{U\over V} = \frac{4 \sigma T^4}{c}.

Where V is volume.

The constant 4σ/c is called the radiation constant. Note that s (sigma) is the Stefan-Boltzmann constant.  The energy density is related to temperature that corresponds to the equilibrium radiation.

Note that the energy density is related to both i.e. the wave properties (frequency) and the temperature in the two expressions above.  The energy density units are the same as pressure i.e. J/m3.   

In the limit of low frequencies (i.e. long wavelengths), Planck's law can be approximated as:

B_\nu(T) \approx \frac{2 \nu^2 }{c^2}\,k_\mathrm{B} T or \qquad B_\lambda(T) \approx \frac{2c}{\lambda^4}\,k_\mathrm{B} T.

In the limit of high frequencies (i.e. small wavelengths) Planck's law can be approximated as

B_\nu(T) \approx \frac{2 h \nu^3}{c^2}\,e^{-\frac{h \nu}{k_\mathrm{B}T}}

A very useful law emerges from the spectral density expression called Wein's displacement Law.  Wein's displacement Law states that there is an inverse relationship between the wavelength of the peak of the emission of a black body ( \lambdamax ) and its temperature (T). 

\lambdamax. T= W-constant

where λmax is the peak wavelength,  T is the absolute temperature of the black-body, and the W-constant in the equation above is called Wien's displacement Law constant which is equal to 2.8985×10−3 m·K = 2.8985 mm·K = 2,897,768.5 nm·K.

Sun Temperature: The sun may be considered to be a black-body.  The maximum (peak) emission wavelength of e.m. waves from the sun, peaks at a wavelength of ~501.5 nm (yellow).  The sun surface temperature can be calculated from the Wien's displacement law which gives the temperature as equal to (2,897,768.5 nm·K/501.5nm) = 5778 K.  Note: The sun's surface is not uniform (the surface is all turbulent plasma) therefore this calculated temperature is an average based on the maximum emission wavelength observed.  In the body of literature about the Sun's temperature one may find other temperatures that are reported but they will all be close to 5778K.  Inside the sun i.e. close to its core, temperatures exceeding several million (close to 15 million) degrees Kelvin are expected that enables fusion of hydrogen into helium. For correctness one must note that helium and hydrogen both fuse in the core.   The gamma rays generated from this fusion process take an enormous amount of time to finally transmit energy from the core of the sun, to the surface of the  surface.  The range of frequencies emanating from the surface of the sun, that travel at the speed of light are not the same as those generated from the fusion process.  Interaction with the dense mantle changes the range of frequencies that get transmitted.   Some energy (a very small amount) is also transferred into space by neutrinos that seemingly pass through the dense mantle of the sun without much difficulty.  Neutrinos travel also at speeds that approach the speed of light.


Human Body Energy Radiation and Temperature:  The human body radiates approximately ~100W on the average.  The normal human average temperature is 37C but varies with time of day and age. The thermometer measurement under the tongue correlates with the core body temperature.  Variations exist for time of the day, age and perhaps also the gender as per some published studies.  For thermal detection with imaging methods let us assume that a 32C-37C temperature is require to be detected.    Application of Wien's Displacement Law to the human body emission in such a range, results in a peak close to 9microns (micrometers).  Consequently any thermal imaging device developed for detecting humans should be constructed to be the most sensitive sensitive in the 6–15 micron wavelength range of detection.  This wavelength-range is beyond the visible spectrum (long IR range).

Bond Energy:  Visible light is a small part of the entire electromagnetic spectrum (i.e. waves that have electric and corresponding magnetic fields).  The velocity c (m/s) of any electromagnetic wave is the the same in vacuum for all frequencies and wavelengths.    \nu is the frequency with units (1/s).  The wavelength is given by c/ \nu and because c is constant in any medium - the wavelength and frequency are inversely proportional.  A higher peak-frequency corresponds to a higher temperature radiation and can give much better carnot efficiencies when converted to work (Rule: The best possible second law efficiencies come from the hottest possible source temperature for the same sink temperature).   The frequency spectrum of sunlight corresponds to an average surface temperature of the sun of about ~5778K.  One may note that the common chemical bond energies correspond to energy levels in the e.m spectrum that are in the Infrared region of the e.m spectrum.  From the two radiations laws above we note that this corresponds to a temperature of about 1000-10000K.  Nuclear bonds are stronger than chemical bonds with corresponding e.m. wave-energies that indicate the temperature to be in ~10000K-100000K range.   Check out the e-ion ideation brochure to simulate some aspects of this answer.

Standard Model of Matter:  For the description of the structure of matter on the scale of elementary particles we use the Standard Model, which is a theoretical framework formulated back in the 1970's.  The particles considered as "elementary", play various roles in the construction of matter.  Bosons are carriers of forces: photons are related to electromagnetic interactions, eight types of gluons are responsible for strong interactions, and W+, W– and Z0 bosons mediate weak interactions. It is now imagined (and somewhat tested) that matter is formed by particles called fermions, which are divided into quarks and leptons. In the Standard Model, there are six types of quarks (down, up, strange, charm, top and bottom) and six types of leptons (electrons, muons, taons and their three corresponding neutrinos) as well as twelve antiparticles associated with them. The Higgs boson provides particles with mass (except to the gluons and photons).

IR Spectrum Devices:  Somewhere in the range of 600C to 800C, the blackbody spectrum encroaches enough in the the visible to be seen as a dull red glow.  At temperatures in the 50oC range (body to normal room temperatures) almost all of the radiated energy from the body or wall is in the infrared part of the spectrum. The wavelengths predominantly in this part of the spectrum is of the order of (1000nm = 1 micron) and above. The lower the temperature, the peak shifts to higher wavelength and as shown above could be mostly off the visible scale below 600oC.  Thus the human body mostly loses radiation (heat) by emitting in the infra-red (IR) region, invisible to the eye.   A typical human body controls its body temperature with a natural automatic regulation process and attempts to keep t around 37oC.   An average human-body emits about 100W of radiation at 37oC.  This number increases with vigorous exercise.   Detecting human body movement requires sensors that are particularly sensitive in the IR regions.   Night vision goggle have this type of feature that accentuates IR and converts it to a visible frequency which the eye can detect.  Almost all surface heating involves IR. Each quanta of IR has a lower frequency compared to UV.  As the frequency increases towards UV radiation the waves penetrate more as they have more energy.  The energy of a photon depends on the wavelength.  This is why UV shades are recommended  because UV has a shorter wavelength than IR. Note that the radiation power of a surface increases with temperature and with the emissivity in a non-linear manner.  Note also the general trend of emissivity of a materials is to increase as a function of temperature.  However emissivity and reflectance are not simple properties.  Radiation is absorbed via mechanisms that involve allowed quantum states.  The dielectric constant has a real and imaginary component and directly impacts reflectance.  Therefore oddities are noted in reflectance measurements e.g. reflectance for a shiny metal can often decreases with peak temperature or increase (with wavelength).  Emissivity is associated with high temperature measurements (>300K), reflectance with low (<300K) temperature measurements. Note that photons are not conserved.

Visible Spectrum Devices:  Solar and UV panels can be of two types (1) those that absorb all radiation (black body) in the solar spectrum and (2) that selectively absorb in order to stimulate electron activity in semiconductors.  These are classified as visible spectrum devices.  Oxynitride, carbonitride, nitride and carbide coatings of transition metals and also of aluminium, titanium or zirconium made by the Cascade e-ion or D-e-ion devices often give antimicrobial propertes.  They are also used for wavelength controlled surface devices for solar energy enhanced absorption (the MHI trade name is GoldenBlue(TM).  MHI's patented high emissivity and controlled boson, fermion, photon stimulators are the key to the next generation of power producing surfaces.  See also duburr page for Golden/Blue surfaces/ microstructures for iron, zirconium and titanium alloys.  Surfaces can be manipulated to absorb some wavelengths and reflect the others.  As noted above, Kirchoffs law applies, however the amount transmitted or reflected at various wavelengths can be manipulated with transparent coatings e.g. of glass or gold plating or the more recently rediscovered copper-tin mirror materials.  For example, a black body in the visible spectrum range can be covered with a layer (glass) which is trasparent in the visble range but opaque in the UV or IR range. Such layering techniques are used for hot water solar heaters, for example.

In the visible spectrum, the units of lumens (amount of light in the visible range) and lux are used to calculate/infer the illumination which normally pertains only to the visible spectrum objectives.  Here the efficiency of the device for the objective of providing illumination is defined by the luminous efficacy η in lumens per watt of the device (lm/W).  The illuminance Ev in lux (lx) is equal to the power P in watts (W), multiplied the luminous efficacy η, divided by the surface area A (m2):  Ev(lx) = P(W) × η(lm/W) / A(m2) .   Note that red is a higher wavelength radiation compared to violet.  In terms of wavelength, the graphic below for the energy of photon (shown in eV) would range from 720 microns to 390 microns (left to right).

Color:  The reflection color from an object for sunlight depends on the intensity (including angle), polarization, photonic band gap, refractive index (real and imaginary parts) and other properties. The reflection or refraction of individual wavelength is often not the same for all surfaces or thin films. Separation properties are utilized for thin film devices.  Thin films have many commercial applications including as partially transparent or anti-reflection coatings, mirrors, and on optical filters.  For graded and compositionally variant films, the colors yield considerable important information.  Thin film interference is a phenomena associated with films which determines colors.  Such interference partially explains the colors of nitrideded surfaces, tempered colors and also the color of the wings of butterflies!  The reflected, partially reflected, or refracted wave (depending on polarization) may interact and thus reveal information about the surface(s) from which individual frequency components are reflected, like the thickness of the film, or the effective refractive index of the film medium. 


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