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Flashcards in Chapter 6 - Thermal Energy Deck (48):

How was the Earth created?

From differentiating accretion of planetary dust.


How are elements with different densities dispersed in the Earth?

High density elements predominant in earth center, minerals with lower density predominant in outer crust.


Which six shells can we separate the Earth into? What are their phases?

Inner core (solid), outer core (liquid), lower mantle (liquid), transition zone (viscous), upper mantle (viscous) and crust (solid).


How come the inner core is solid, even though the temperature is higher than on the surface of the sun?

Because of the high pressure.


What is superrotation?

The fact that the inner core of the Earth rotates quicker (about 0.3-0.5 degrees / year) faster than the mantle. This adds up to one additional turn in about 1000 years.


Where is the earth magnetic field generated?

In the liquid outer core.


How do we divide the Earth crust?

Into oceanic crust (5-10 km) and continental crust (30-60 km).


Where does the crust "swim"?

On top of the asthenosphere, which is the upper part of the upper mantle.


How much oxygen does the crust contain?

About 50 at%.


How far have we been able to drill down into the crust?

12 km, in Russia.


What is the average energy flux through the Earth surface from below?

60 mW/m^2 (compare to 1000 W / m^2 incoming solar irradiation).


What are the sources of the earth heat flux?

1) 50% from continuous cooling of inner earth due to heat conduction.
2) 50% from decay of radioactive elements.


What is the average temperature of the inner earth?

2000K. This was the kinetic and potential energy transformed into heat during the accretion of the earth.


What is the thermal conductance of the crust?

lambda ≈ 2 W / Km


What is the thermal gradient through the crust (geothermal gradient)?`

dQ/dt = 60 mW / m^2 (heat flux), lambda = 2 W / K m (heat conductance)

=> ∆T / ∆x = dQ/dt * 1/lambda = 0.03 K /m = 3K / 100 m.


Where can we find strong deviations from the average heat flux of the earth?

At volcanic anomalies, where liquid magma reaches very close to the earth surface. Here dQ/dt can reach above 300 mW / m^2.


Which radioactive isotopes are the most important for the heat flux of the Earth? What kind of radiation are we talking about?

Alpha decay: 235U, 238U, 232Th
Beta decay: 40K.


What is the total heat generated by radioactive decays in the Earth?

The heat flux is about 3 µW / m^3, which amounts to about 30 mW / m^2. Total all over the world is then about 16TW.


What is the total stored thermal energy in the Earth?

99% of the Earth is hotter than 1000C. THis means that the total stored thermal energy is ≈ 3*10^15 TWh. This could supply the human consumption for 10^10 years (more than the Earth will exist).


What are the three main forms of geothermal power?

- Geothermal anomalies (high enthalpy sites)
- Hot-dry-rock process, aquifers
- Heat pumps


What are high enthalpy sites?

These are sites that exist close to volcanoes or special "hot spots". They consist of water-vapor mixtures (so-called "two-phase" mixture) with temperatures between 100-300 C. Pressures ranges between 10 and 100 bar, which makes the boiling point of water 300 C at the highest.

Even extinct volcanoes there can exist hot magma pipes for millions of years.

These sites can be used directly (for heating) or in combination with turbines to produce electricity.


Name one problem with high enthalpy sites.

The water is contaminated with sulfur, which gives unwanted corrosion and smell. For this we have to use closed heat exchangers.


What are low enthalpy sites?

These are sites characterized by temperatures below 100C. Requires use of aquifers, or can use the hot-dry-rock method which employs a region of fractured rock and water injection.


What is the Law of Darcy?

It describes the transport (perlocation) of water in porous media.

v = sigma_w * H/L

sigma_w is the hydraulic conductance, H is the height of water column above the flow region and L is the length of flow region.


How can one calculate the energy content of a cavern used for heat extraction with the HDR-method?

Q = ∆T * m * C_v,

where m is the mass of the rocks, ∆T is the temperature difference between hot reservoir and temperature after cooling, and C_v is the heat capacity of the rock.


If we make a HDR heat plant, and extract all the heat, how long before it is reheated?

It will take along time due to the low thermal conductance.

For the example with the granite cavern of 100 x 100 x 100 m, with a surface area of 6*10^4 m^2 and a temperature gradient of 1 K / m it would take 100 years.


What are heat pumps? Draw a schematic.

They are reversely operated heat engines. See schematic on page 5.


What is the efficiency of a heat pump?

It is Qw/W. Since we extract more heat than we use to compress the gas, the efficiency is always above 1. (if not, it would not make sense to do this).


What is the working principle of a heat pump? Draw a schematic.

1) Evaporation of working medium. Heat of evaporation Qc is taken from the environment.
2) Compression by mechanical work, W, close to adiabatic.
3) Liquiefaction of working medium by giving the heat of condensation Qw to environment.
4) Decrease of pressure in a throttle.

See schematic on page 6.


What are typical efficiencies of heat pumps, and what does it depend on?

eta = 2-6.

Depends on the temperature spread Tw-Tc. This leads to a divergence between avilable heating power and the necessary heating power (works better when we don't need it).


In a heat pump, what can be the cold reservoir Tc?

The surrounding air, ground water or soil (typical power extraction 10-40 W/m^2).


What are typical working medium used in heat pumps?

Propane, NH3, CO2. CFC gases used before, but illegal now.


How are photons absorbed? Draw a schematic.

Photons excite electrons through Coulombic forces. The excited electron than undergoes an electron-phonon coupling where a phonon mode is excited. See page 7 for schematic.


What are the principal processes occuring for incoming photons?

Reflection: coherent process at a defined interface described by Fresnel equations.

Scattering: incoherent process by photon interaction with atoms or molecules (Rayleigh-scattering, Mie-scattering).

Absorption: incoherent process via transformation of photons into excited electrons and/or phonons.

Transmission: part of incoming flux is neither reflected, scattered or absorbed.


Which energy conservation equation holds for incoming photons on a material?

R + S + A + T = 1.


How is the Lamber-Beer law defined? What does it tell us?

PHI(x) = (1-R)PHI_0 exp[-alhpa x]

with alpha = alpha[E_photon] being the absorption coefficient. PHI(X) is the photon flux at depth x in an absorber, PHI_0 is the incoming photon flux.

It tells us how much of the photon flux still remains after having travelled a distance x in the absorber.


Which of the photon interaction processes are important for solar thermal energy?

All of them.

Absorption: ideal absorbers have A = 1 for all wavelength., selective absorbers have A = 1 for wavelengths under a critical wavelength, and A = 0 above.

Reflection: mirrors have R = 1, A= 0 and are used for concentration of solar radiation. R = 0 for perfect antireflex coating, but here it is decoupled from A.

Scattering: at the surface or in materials and environment.


What is a problem regarding the emissivity of a black body with a finite temperature, when speaking about solar thermal energy?

The fact that it always emits radiation, even without incoming radiation. The hotter it gets, the more it radiates.


How does the amount of scattered light change when we change the angle of incidence?

The amount of Rayleigh and Mie scattering that occurs when we change from normal incidence to 5% increases a lot. This is diffuse radiation, and cannot be concentrated.


What things does the average irradiation depend upon?

Time of year and latitude.


What type of trackers can we install?

1-axis trackers, that tracks the sun over the course of the day.
2-axis trackers, that also tracks the sun depending on time of year.


What are the main applications of solar thermal energy?

i) Architecture (winter garden, low energy house)
ii) Non-concentrating solar collectors.
iii) Concetrating solar recievers


How are non-concentrating solar collectors best realized?

By combining glass windows (selective transmission) with selective absorbers (prevents emission losses since emission is low, which it is because absorption is very low in the IR-range).


Why are selective absorbers good?

Because they absorb in the frequency range of the incoming photons, but they do not absorb in the frequency range of IR. This is important since, through Kirchhoff's law of radiation, the emissivity is large when the absorption is large. The typical range the absorber would emit would be in the IR-range, and since the absorption is low here, the emissivity is also low.


Give examples of some frequently used selective absorbers. What are their typical absorption data?

Black chromium, black nickel and TiNOx.

Typical values:
for lambda 3µm: A = 5-10%, T = 0, R = 90-95%.


What are concentrating solar recievers?

They use concentrated sunlight, concentrated by linear or parabolic mirrors, to heat a working media (steam, Stirling engines, phase change salts) to high temperatures of 400-1000 C.


What is the maximum concentration for point focussing?

This is given by the opening angle of sun as seen from Earth.

alpha = arcsin R_sun / R_SE = 16' = 0.27 deg = 0.0046 rad

Maximum concentration is given by

C_max = 1/alpha^2 = 46211.

For one-axis linear concentration, this is given as:

C_max, lin = sqrt(C_max) = 215


What does the maximum concentration of point focussing determine?

It determines the maximum reachable absorber temperature, assuming ideal thermal isolation and e = 1.

C * SC = sigma T^4

T = (C*SC/sigma)^1/4 => T = 5780 K (same as surface of sun)