Climate and Energy Flashcards
What gases are the main contributors to the greenhouse effect?
Water vapour, CO2 and methane.
What is the equation for Black Body Radiation?
It is dependent on wavelength and temperature.
Intensity R: R (L, T) = 2hc2/L5 * 1/(ehc/LkT - 1)
Where L is wavelength and k is the Boltzmann constant.
What is the Stefan-Boltzmann law?
Total power F: F = σT4
Where σ is Stefan’s constant.
Around what wavelengths of light does CO2 absorb?
Around the Infrared spectrum, not visible light.
Similar for water vapour and other atmospheric gases, but not nitrogen.
What is the structure of the lower atmosphere?
Close to the surface is the troposphere, which is optically thick in IR, and temperature falls linearly with height (i.e. dT/dH ~ constant)
Above that (around 11km) is the lower stratosphere, which is optically thin in IR, and T is constant.
How does an increase in CO2 affect the tropopause (i.e. the top of the troposphere)?
It increases the height of the tropopause, which by dT/dH therefore increases temperature at the surface.
What is radiative forcing?
A change to the downward energy flux upon introducing, or perturbing, a particular mechanism of radiative transfer.
e.g. Increasing CO2 reduces outgoing radiation and provides positive forcing.
What methods are there of tracking CO2 levels over periods of time?
- Ice core analysis (oxygen isotopes and Deuterium to H ratio) (Medium accuracy)
- Geological analysis (low accuracy)
- Tree ring data
- Coral and shell growth rings
- Ground and space-based instuments (for recent data). (High Accuracy)
What is solar variation?
The effective strength of the sun changes over time, due to sunspots (short term) and orbital cycles (long term).
What effect do clouds and aerosols have on the greenhouse effect?
Sub-visible particles (e.g. organics and black carbon) and cloud cover increase the albedo of the Earth, leading to negative radiative forcing.
What is the indirect aerosol (Twomey) effect?
Cloud droplets form on aerosol seeds, leading to ‘whiter’, more long lived clouds, which increase Earth albedo.
What are some approaches to fixing climate change?
- Carbon pricing and trading
- Energy efficiency
- Investment in new technologies
- Education
- Climate engineering
How is a kilowatt-hour defined?
It is the energy equivalent of using a kilowatt of power for an hour.
What is the equation for heat capacity?
ΔQ = cΔT or c = dQ/dT
Where c is heat capacity.
What is the ideal gas equation?
pV = nRT
Where R is the gas constant, for n moles of gas.
What is the first law of thermodynamics?
Q = ΔU + W
What is the efficiency of a Carnot engine working between 2 temperatures, Tc and Th?
Efficiency µ = W/Q = 1 - Tc/Th
Where W = work done by the system, and Q = heat put into the system.
What is the equation for entropy, s?
Δs =ΔQreversible / T
What are the sources of energy loss in cars?
- Kinetic energy required to speed up
- Air resistance
- Rolling resistance
- Engine efficiency
What is the drag equation?
F = 1/2 rho v2 Cd A
Where rho is the mass density of the fluid (e.g air), v = velocity, Cd = drag coefficient, and A is the frontal area.
What is binding energy?
The energy required to break up a nucleus into respective nucleons.
In the semi-empirical mass formula, what are the meanings of the coefficients av, as, ac, aa, and ap?
- av: volume term : binding of each nucleon to its neighbours
- as: surface term: reduced binding for nucleons on the surface.
- ac: Coulomb term: electrostatic repulson between protons.
- aa: asymmetry term: Pauli exclusion principle prefers equal number of protons and neutrons.
- ap: pairing term: nucleons are particularly tightly bound in pairs.
What is the most stable element? Why?
Iron, as it has the highest binding energy per nucleon.
What is the process behind fission?
A fast moving neutron is absorbed by a large nucleus, giving it enough energy to overcome activation energy and split apart.
This creates 2 daughter nuclei, as well as some more fast-moving neutrons that go on to produce more fission events (chain reaction).
What is the 4-factor foumula for an infinite reactor?
Explain each term in the formula
k = µ e p f
Where k is the criticality of the reactor (i.e number of neutrons in (n+1)th fission stage / neutrons in nth fission stage,
µ = average number of fission neutrons released per thermal neutron absorbed,
e = fast fission factor (~1.02-1.08), due to fission contributions from fast neutrons, mainly on 238U.
p = resonance escape probability, the fraction of neutrons that escape capture as they slow to thermal velocities.
f = neutron utilisation factor, the fraction of thermal neutrons absorbed in the fuel rather than other structures (e.g. coolant)
How is reactivity rho defined in terms of k?
rho = k - 1 / k
What are delayed neutrons and what role to they play in reactivity?
Delayed neutrons are created ~13 seconds after a reaction. If B is the fraction of delayed neutrons (~0.65%), then if reactivity rho is 0 < rho < B, the reactor within safe operating condition, and if rho = B, the reactor is prompt critical.
What are the features of a Pressurised Water Reactor (PWR)?
- Most common reactor type.
- Fuel rods placed in water kept in liquid phase under high pressure, operating up to 325C.
- Heat exchanger / steam-generator, secondary circuits drive turbines.
- Fuel contained in pellets inside rods.
- Control rods are lowered into position.
- Negative void coefficient (moderation strongly reduced when steam bubbles form).
What are the features of a Boiling Water Reactor (BWR)?
- Less numerous than PWRs.
- Water boils inside reactor at high pressure (75 bar), corresponding to 285C.
- Negative void coefficient.
- Similar fuel composition to PWRs.
- Control rods are raised into place.
What are the features of a CANDU reactor?
- Also known as a Pressurised Heavy Water Reactor (PHWR).
- Advantages: can use natural uranium, online refuelling (a “calandria” containing individual pressure tubes with fuel & coolant rather than one large pressure vessel).
- Disadvantages : costly D2O, positive void coefficient (due to coolant slowing neutrons into the resonance capture region), large volume of high-level nuclear waste without reprocessing.
What is heavy water?
It is water formed with deuterium rather than regular hydrogen. Written as D20 rather than H20.
What is the formula for power available to a wind turbine?
P = 1/2 rho * A * v3 * Cp
Where rho = air density, A = area swept out by turbines, v = wind speed, and C_p = power coefficient (Max coefficient is Betz Limit, 16/27). Very similar to drag formula.
What is the Betz Limit?
According to Betz’s law, no turbine can capture more than 16/27 (59.3%) of the kinetic energy in wind. The factor 16/27 (0.593) is known as Betz’s coefficient. Practical utility-scale wind turbines achieve at peak 75% to 80% of the Betz limit.
How do slowly-rotating turbines create high-frequency AC current?
- Usually by a Doubly-Fed Electrical generator, to account for variations in turbine frequency.
How does one avoid capacitive losses over long distances from off-shore wind farms?
Off-shore substations convert AC to high-voltage direct current (HVDC), which is reconverted once on shore.
What is the formula for power P from a resevoir dam of height h running down to an outlet?
P = µ rho g h Q
Where µ = efficiency, rho = water density, g = gravitational acceleration (9.81 ms^-2), h = height of resevoir, and Q = volume of water through turbines per second.
In wave power, what is the formula for incident power per unit width of wave-front?
P = 1/4 rho * g * a2 * sqrt( g*lambda / 2π)
What are some methods of storing energy?
- Potential energy stored in water in reservoirs.
- Compressed air storage in caverns
- Interconnectors to neighbouring countries to share surpluses of renewable power or to alleviate shortcomings.
What are some methods of artificially tackling climate change (Climate engineering)?
- Carbon capture and storage in the earth
- Ocean fertilisation, to remove CO2 via photosynthesis
- Cloud seeding, in order to increase Earth’s albedo.
What is the atomic weight of carbon, hydrogen, and oxygen?
12, 1, and 16 respectively.
What is absolute zero in celsius?
-273C
In terms of the Solar Constant, S, what is the equation for solar flux, F? What is the equation to find S?
F = S/4 * (1-A)
Where A is earth’s albedo.
S = σ Ts (Rs / Rse)2
Where σ is Stefan’s constant, Ts is the temperature of the sun, Rs is the radius of the sun, and Rse is the average distance between the Sun and the Earth.
What are some problems in climate modelling?
- Not easy to represent the physics and chemistry correctly
- Data is often missing or noisy
- Anthropogenic effect is a small perturbation to the dynamics of a large complex system.
What is the T-s diagram for the Rankine cycle?
What is the P-V diagram for a Carnot cycle?
What are the p-V and T-s diagrams for the Brayton cycle?
What is the formula for Brayton efficiency?
Efficiency µ = 1 - r-(y-1)/y
Where r = pb / pa = pc / pd, and y = Cp / Cv.
Know how to derive.
Why do nuclei with an odd neutron number tend to be more fissile?
Due to the pairing term in the SEMF, binding energy for odd-neutron nuclei tend to be lower than their isotopes.
What is the formula for average number of fission neutrons produced per thermal neutron absorbed in fuel, eta?
What about for a fuel enriched to fraction x of fissile 235U and (1-x) non-fissile 238U?
eta = v σf / (σf + σc)
Where v = average number of fast neutrons per fission, σf = fission neutron cross-section, and σc = capture neutron cross-section.
For an enriched fuel:
eta = v xσf235 / [x(σf235 + σc235) + (1-x)σc238]
What is the equation for the total fraction of nuclei consumed in a fuel, in terms of fuel convertion ratio, C?
In the burn-up of N fissile nuclei, CN further fissile nuclei are created. If they are completely consumed, then C2N more nuclei are created, and so on.
Total fraction of nuclei consumed in a fuel:
y(%) = (xinitial (%) - xfinal (%)) / ( 1 - C)
Where x is the ratio of fissile nuclei to non-fissile nuclei (e.g 235 U to 238 U)
C = Cra + Crth
Where Cra arises from resonance absorbtion and Crth arises from thermal neutron flux.
What is the purpose of moderators in reactors?
A moderator is a substance that is used to slow neutrons, to make them capable of inducing fission in fissile nuclei.
This is because neutron cross-section decreases with velocity.
What is the diagram for wind turbine blade design?
W = width of blade
u1 = wind velocity, v = blade velocity, a = angle of attack
D = Drag vector, L = Lift vector
tan(phi) = u1/v
What are the equations for the ideal twist and width, W, of a wind turbine blade?
twist = phi - a = tan-1 (2R / (3r*lambda)) - a
Where tan(phi) = wind velocity / blade velocity, a = angle of attack, and lamda = tip speed ratio = vtip / u0
W = 8π* R * sin (phi) / (3 lambda * n * CL)
What are the effects on a turbine if tip speed ratio, lamda, is not optimal?
- If too slow, the Betz limit cannot be reached.
- If too fast, there is extra drag and turbulence.
- Larger optimal lambda implies narrower (therefore cheaper) blades.
What is the empirical formula for average wind turbine power, in terms of average wind speed uavg?
Pavg~= 0.2D2 * uavg3
Where D is turbine diameter.
What are the features of a Francis water turbine?
- They are reaction rather than impulse turbines.
- They are immersed in water.
- Can be used at much higher flow rates.
- Can (sometimes) be driven in reverse as pumps.
What is Tidal Range?
The difference in height between low and high tide.
Small over most open ocean ( <1 metre), but can be larger near shores or estuaries.
What is the resonance condtion for waves (wavelength lamda) in a pool of length L?
lamda = 4L
What is the formula for current due to photocell illumination?
Ic = IL - IS (eV/VT - 1)
What are the formulae for potential energy, E, and extractable power, P, in a pump-turbine system?
E = rho * g h V
P = eta * rho * g h Q
Where can captured CO2 be stored?
- Underground, trapped in rock
- Bottom of the ocean, where pressure keeps CO2 in liquid form
- Mineral carboration, converting CO2 to other forms of carbon (e.g constuction material).
What are 3 methods of converting solar energy to power?
- Solar hot water heating: partial or complete heating of domestic water via rooftop solar arrays.
- Photovoltaics: semiconductors use light from the sun to generate a current.
- Concentrated solar power: arrays of mirrors (curved or otherwise) concentrate sunlight onto pipes containing fluid, that is used to drive turbines.
What is the formula for Gibbs free energy, G?
G (p,T) = U + pV - TS
G (p,T) = H - TS
What is the diagram for a Combined Cycle Gas Turbine?
