Answers

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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 heat and work types of energy exchanges within our body.

Answer to Q2 : No. Steady-state Processes's do not have to be reversible for open systems. Whyen one imagines a system contained in a control volume which shows time invariant properties i.e. is at steady state, you should be aware that entropy can yet be continuously generated and dispersed through the boundaries of the control volume in a manner that thermodynamic properties like Temperature, Pressure, Volume are measured to remain constant within the control volume. Reversible means 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 ( where mass is input and/or output from the control volume) are difficult to make fully reversible; although such an approximation is often used for solvingengineering problems. Note that the entropy is not a conserved property unlike mass and energy which are conserved properties (especially at 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. For a fluid exchanging open cyclic thermal device (bound by a control volume) 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 output thermodynamic conditions 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 comarison to the unmixed state. Entropy generation is used as a marker when shapes are created. Nature's clever way of process and shape selection is called the MEPR principle. The acronym MEPR (sometimes 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, and a peak radiation frequency for a given power per unit volume is related to kT. The second law sets limit on maximum available work between two temperatures. For the explanation below, T is in Kelvin, k_B=1.380 6488×10⁻²³ J/K is the Boltzmann constant, h is the Planck constant=6.62606957(29)×10⁻³⁴J.s. Lower case c=299,792,458 m/s is the velocity of e.m radiation (light).. Lamda { $\lambda$ ) is wavelength (m) and $\nu$ is the frequency (1/s). A famous equation called the Planks equation shows that 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 effciency) 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. 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 a black-body. An explanation about radiation spectrum and temperature is given below.

If B is the spectral radiance with the units of W·sr⁻¹·m⁻²·Hz⁻¹, then B is a function of frequency or wavelength and is given by:

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

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

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

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

You 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.

Note how the energy density is related to wave properties (frequency) and 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

Wein's displacement law states that there is an inverse relationship between the wavelength of the peak of the emission of a black body ( $\lambda$ _max ) and its temperature.

where λ_max is the peak wavelength, T is the absolute temperature of the black-body, and the constant in the equation above is called Wien's displacement constant 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 wavelenght of e.m. waves from the sun, peaks at a wavelength of 501.5 nm ( yellow - infrared range). The sun surface temperature can be calculated from the Wien's displacement law whch gives the temperature as equal to 2,897,768.5 nm·K/501.5nm = 5778 K. Note: The sun surface is not uniform (the surface is all plasma) so this calculated temperature is an average based on the maximum emission wavelenght observed. In the literature one may find other temperatures that are reported but they will al be close to 5778K. Inside the sun i.e. close to its core, temeratures exceeding a million of degrees Kelvin are expected that enables fusion of hydrogen into helium.

Human Body Energy Radiation and Temperature: The human body radiates approximately 100W on the average. The normal temperature is 32C. Application of Wien's Law to the human body emission results in a peak wavelength of

$\lambda_{\rm peak} = \frac{2.898\times 10^6 \ \mathrm{K} \cdot \mathrm{nm}}{305 \ \mathrm{K}} = 9.50 \ \mu\mathrm{m}.$

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 correponds 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 cin the Infrared region of the e.m spectrum. From the two laws above we note that this corresponds to a temperature of about 1000-10000K. Nuclear bond energies on the other hand correspond to wave energies that indicate the temperature to be ~10000K-100000K. Check out the e-ion ideation brochure to simulate some aspects of this answer.