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Assume that each target's incorporated flux is proportional to its applied power over this operating range, and that the same composition convention is used throughout. The calibration gives $F_A/F_B=0.35/0.65$ at equal powers. Holding the A target unchanged while making the two incorporated fluxes equal therefore requiresThe B power decreases because B originally supplies more material. This linear magnetron sputtering approximation neglects power-dependent yield, target condition, resputtering and changes in sticking probability. A second composition measurement is the experimental check.

specific energy is usable stored energy divided by device mass, commonly in Wh/kg; specific power is deliverable power per the same mass, in W/kg. The definition must specify whether packaging and inactive components count, and the discharge conditions must be comparable. On a Ragone plot with energy horizontal and power vertical, ordinary capacitors occupy high-power/low-energy territory, batteries tend toward higher energy and lower power, and supercapacitors bridge and overlap the two. These are broad regions rather than universal measured boundaries.

High specific energy means long operation for a given mass; high specific power means rapid delivery. Their ratio is a characteristic duration: $t_{\mathrm{h}}=e_s/p_s$ when the preceding units are used, or $t_{\mathrm{s}}=3600e_s/p_s$. The diagonal lines in the sketch keep that unit conversion explicit. A cell's rated energy and peak pulse power need not be available simultaneously throughout discharge.

A material exhibiting piezoelectricity converts cyclic mechanical stress into electric charge; its mechanical and electrical boundary conditions jointly set the extractable energy. piezoelectric ceramics such as lead zirconate titanate are stiff and often have large charge coefficients and electromechanical coupling, but are brittle and can be difficult to match to large-strain flexible motion. piezoelectric polymers such as polyvinylidene fluoride are compliant, light and compatible with flexible large-area films. Their lower charge coefficient is partly offset in voltage-sensitive applications by lower permittivity: the voltage coefficient is $g=d/ϵ$.

Ceramics often favor strong charge generation and coupling; polymers favor flexibility and strain accommodation. The larger open-circuit voltage of a low-capacitance film does not itself imply more useful power. For a simple fixed-stress comparison the electrical energy scale involves $d^2/ϵ$, while coupling also depends on mechanical compliance. At fixed imposed strain, different stiffnesses change the available mechanical energy. resonance tuning, fatigue, mechanical mounting, rectifier losses and load matching can reverse a simplistic material ranking; compare complete devices under the same actual vibration source.

At fixed temperature difference and constant internal resistance,Differentiation givesIt is positive below $R_L=R$ and negative above it, while power vanishes for an open or shorted load. Therefore the maximum power transfer theorem givesAt this point $I=V_{\mathrm{oc}}/(2R)$ and half the electromotive force drops across the load. Maximum electrical power is not generally maximum thermal-conversion efficiency. If changing current also changes the temperature difference because the thermal source has finite impedance, the fixed-$\Delta T$ optimization must be reconsidered.

A thermoelectric generator uses the Seebeck effect: a maintained temperature difference across suitable conductors produces an open-circuit electromotive force. For a pair of legs,when the effective Seebeck coefficient is approximately constant. Repeated p- and n-type legs are usually connected electrically in series and thermally in parallel.

Connecting a load lets part of the heat flowing from the hot side to the cold side become electrical power. Both a heat source and a cold-side heat-removal path are necessary: a uniformly warm device with no maintained temperature difference supplies no sustained output. Internal electrical resistance, heat leakage, contact losses and the finite temperature difference reduce the harvested power; the converter is a heat engine rather than a source of energy from temperature alone.

Above-gap photon absorption generates electrons and electron holes. A p-n junction's built-in field and carrier diffusion direct them toward selective contacts; their nonequilibrium populations can maintain separated quasi-Fermi levels and deliver electrical power. The equilibrium built-in voltage alone is not a battery supplying continuous power.

Choose diode current positive into the cell. An idealized characteristic isIllumination shifts the curve downward. At short circuit $I(0)=-I_{\mathrm{sc}}$; at open circuit $I(V_{\mathrm{oc}})=0$. Between those points, $V>0$ and $I<0$, so the delivered power $P=-VI$ is positive.

The solar-cell fill factor compares maximum delivered power with the open/short-circuit rectangle:Series resistance, leakage, recombination and temperature change the shape and hence the fill factor. Neither the short-circuit nor the open-circuit point itself delivers power.

The useful bandgap depends on the illumination spectrum, not only on whether the device is indoors or outdoors. The stipulated $1.45\mathrm{eV}$ gap gives a long-wavelength absorption threshold near $855\mathrm{nm}$; $1.7\mathrm{eV}$ gives about $729\mathrm{nm}$ using ${\lambda }_g\simeq 1240/E_g$ in nanometers.

Outdoor sunlight contains substantial visible and near-infrared power, so cadmium telluride can use a broader portion of that spectrum while retaining a useful output voltage. Its direct-gap absorption permits thin absorbers and large-area thin-film manufacture. Challenges include contacts and interfaces, collection and recombination, material supply and managing cadmium-containing material through fabrication and end-of-life handling.

Many indoor lamps concentrate their emission in the visible and provide little near-infrared power. A wider-gap absorber can then trade fewer lost useful photons for a higher attainable voltage and a smaller thermal dark-current penalty. Hydrogenated amorphous silicon has strong visible absorption, permits low-temperature large-area deposition and can suit low-power indoor devices. Disorder and defects restrict transport, and light-induced degradation and passivation stability must be controlled. Its larger gap forfeits more of the outdoor red/near-infrared spectrum.

These are suitability arguments, not guaranteed efficiencies. Indoor lamp spectra differ, and shunt leakage and recombination become particularly important at low light. Bandgap alone does not establish which finished device produces more power in every room.

Conducting organic materials can be attractive for flexible, lightweight and near-ambient heat harvesters; inorganic materials offer a wider established range of high-performance and high-temperature options. The appropriate comparison includes device geometry and durability as well as peak $ZT$.

Conducting polymers can have low lattice thermal conductivity, be solution processed and accommodate mechanically compliant large-area devices. Their carrier concentration and ordering can be modified through doping and processing. Contact resistance, environmental stability, reproducibility and obtaining stable complementary p- and n-type materials can limit practical modules. Their organic character does not imply that they remain stable at high temperature.

Inorganic thermoelectrics can provide high power factors, temperature stability and mature transport data over application-specific ranges. Some compositions are brittle, dense, expensive or contain elements requiring careful environmental management; they are not all interchangeable. Interfaces, thermal cycling and interconnects can dominate device lifetime.

An experimental example of organic optimization controlled the oxidation level of a conducting polymer to balance transport and its low thermal conductivity, showing that organics are not categorically excluded from thermoelectric performance improvements.^[ref] Material selection should use measured properties across the actual temperature interval and the achievable thermal gradient, not a blanket organic-versus-inorganic ranking.

If the voltage were held at $4.57\mathrm{V}$ for the entire ideal discharge, thenand the electrical power would beThese are constant-voltage estimates, not a determination of the actual energy from the fresh-cell open-circuit voltage. Under load the voltage depends on state of discharge, electric polarization and internal resistance. The physical result is $E=I{\int }_0^{t_f}{V}_{\mathrm{load}}(t)dt$, and $P(t)=I{V}_{\mathrm{load}}(t)$. The supplied single open-circuit value does not specify that voltage curve; practical delivered energy will generally be lower than the simple estimate.

Absorbed photons with energy at least the band gap generate electron–hole pairs. The built-in field of the p-n junction separates carriers generated in or reaching the depletion region; minority carriers generated nearby can diffuse into that collection region. Selective contacts carry electrons and holes into an external circuit before they recombine.

Define positive electric current into the positive-voltage terminal. In the ideal illuminated-diode model,The dark curve has $I_{\mathrm{ph}}=0$; illumination shifts it downward. At short circuit $I\simeq -I_{\mathrm{ph}}$; at open circuit $I=0$ and $V=V_{\mathrm{oc}}$. Between them the illuminated cell lies in quadrant IV and supplies power $P_{\mathrm{out}}=-VI>0$. The maximum power point maximizes the area of the rectangle with sides $V$ and $-I$:It is neither the open-circuit point nor the short-circuit point, both of which supply zero power.

At fixed spectrum and temperature, photocurrent is approximately proportional to irradiance, so the magnitude of short-circuit current increases nearly linearly. In the ideal model,so open-circuit voltage rises only logarithmically with irradiance. More incident optical power generally raises the maximum electrical power, within the device's thermal and resistive limits.

Increasing temperature strongly increases the dark saturation electric current. In silicon this normally reduces open-circuit voltage and maximum power, despite a small increase in short-circuit current associated with the temperature dependence of absorption and band gap. The thermal-voltage factor alone is insufficient to predict the sign; the temperature dependence of $I_0$ matters.

maximum power point tracking adjusts the load seen by the cell as irradiance and temperature change. A controlled DC–DC converter can transform the external load so that operation stays near the changing maximum of $-VI$, instead of at the generally suboptimal intersection with a fixed load. It matches operating conditions and cannot generate additional energy beyond the photovoltaic output.

The illuminated area and incident power areA $412\mathrm{nm}$ photon has energy $hc/\lambda =4.821\times 10^{-19}\mathrm{J}=3.01\mathrm{eV}$, above the silicon band gap. With one collected electron per photon,Use the ideal-diode approximation with ideality factor $n=1$, negligible shunt leakage and the same dark diode parameters under illumination. At $300\mathrm{K}$, $V_T=k_{B}T/q=0.025852\mathrm{V}$. The measured dark point then fixesAt open circuit the forward diode electric current balances the photocurrent:This is below the $1.1\mathrm{eV}$ band gap expressed per elementary charge. Excess photon energy does not translate directly into terminal voltage; much of it thermalizes.

The paper does not explicitly specify an ideality factor. If it is not taken as unity, one dark operating point cannot determine both $I_0$ and $n$. The corresponding family isThus $0.625\mathrm{V}$ is a stated-model estimate, not a parameter-free inference from that one measurement.

Three standard approaches are piezoelectric, electromagnetic and electrostatic energy harvesting.

In all three cases the output is constrained by the available mechanical input and damping. Nanoscale dimensions alone do not supply an energy advantage.

With conventional electric current defined into the positive terminal, an ideal junction hasThe reverse-bias branch tends to $-I_0$ before breakdown. In forward bias the electric current rises exponentially; a visibly sharp “turn-on” is a convenient operating description rather than a discontinuity in the equation. A powered LED emits in quadrant I, where $V>0$, $I>0$ and the device absorbs electrical power $VI$. Strong reverse breakdown lies outside the ideal curve below.

Each equation is stored thermal energy changing at the rate “input minus output”. Define the three heat capacities $C_j=M_j{c}_j$, and introduce the internal heat-transfer ratesIn the fuel balance, $C_F{\dot{\overline{T}}}_F$ is accumulation, $P$ is thermal power generation and $Q_{FM}$ is transfer to the neutron moderator. In the moderator balance, $Q_{FM}$ enters, $Q_{MC}$ leaves and $C_M{\dot{\overline{T}}}_M$ is accumulation. In the coolant balance, $Q_{MC}$ enters, $C_C{\dot{\overline{T}}}_C$ is accumulation and $2W_C{c}_C({\overline{T}}_C-T_i)$ is net energy carried away by flowing coolant.

The factor two follows the model's arithmetic-mean approximation ${\overline{T}}_C=(T_i+T_o)/2$, since the advective energy removal is $W_C{c}_C(T_o-T_i)$. The parameters $R_1$ and $R_2$ are effective thermal resistances, in $\mathrm{K}{\mathrm{W}}^{-1}$, for fuel-to-moderator and moderator-to-coolant transfer. They summarize the relevant geometry and heat-transfer mechanisms; they are not heat capacities.

At a steady state, all three accumulation terms vanish. The fuel balance gives $Q_{FM}=P$, the moderator balance then gives $Q_{MC}=P$, and the coolant balance equates that input to its advective output. ThereforeEach successive region adds the temperature drop needed to carry the same thermal power through its thermal resistance. Summing the original balances cancels both internal transfers, providing the independent total energy balance $P=W_C{c}_C(T_o-T_i)$.

The average moderator temperature is $725{}^{\circ }\mathrm{C}$. First the mean coolant temperature in the lumped thermal model isAt a steady state, the same thermal power crosses both thermal resistances. If $R_1=R_2$, thenThusIn particular $R_1=R_2=(800-650)/(2P)=3.17797\times 10^{-7}\mathrm{K}{\mathrm{W}}^{-1}$ at the specified state.

The coolant mass flow rate is approximately $983\mathrm{kg}{\mathrm{s}}^{-1}$. All thermal power leaves in the steady coolant energy rise:With the stated constant specific heat capacity,The $100{}^{\circ }\mathrm{C}$ difference equals a $100\mathrm{K}$ difference. Thermal power is used directly; no electrical conversion efficiency enters.

Differentiate the family of steady states, keeping $T_i$, $W_C$, $c_C$, $R_1$ and $R_2$ fixed. A quasistatic process uses the temperature responses from part (b):Apply the chain rule to reactor reactivity along that family, weighting each response by its temperature coefficient of reactivity. Collecting terms gives the power coefficient of reactivityIts unit is inverse power. If the thermal resistances, coolant flow or inlet condition varied appreciably with power, their derivatives would contribute additional terms; those changes are excluded by the stipulated constant-parameter model.

The power coefficient is approximately $-2.28\times 10^{-11}{\mathrm{W}}^{-1}$, or $-2.28\times 10^{-5}\mathrm{M}{\mathrm{W}}^{-1}$. From part (c),Substituting in the power coefficient of reactivity givesThe negative sign means that a slow increase in thermal power produces a decrease in reactor reactivity along this family. This is a restoring thermal feedback control effect despite the positive moderator coefficient. A negative quasistatic slope alone does not prove stability of every transient: the separate heat capacities, transport delays and neutron-population dynamics matter for a time-dependent stability analysis.