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3rd Year Undergraduate Physics > Climate and Energy > Flashcards

Climate and Energy Flashcards

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1
Q

What gases are the main contributors to the greenhouse effect?

A

Water vapour, CO2 and methane.

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2
Q

What is the equation for Black Body Radiation?

A

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.

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3
Q

What is the Stefan-Boltzmann law?

A

Total power F: F = σT4

Where σ is Stefan’s constant.

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4
Q

Around what wavelengths of light does CO2 absorb?

A

Around the Infrared spectrum, not visible light.

Similar for water vapour and other atmospheric gases, but not nitrogen.

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5
Q

What is the structure of the lower atmosphere?

A

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.

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6
Q

How does an increase in CO2 affect the tropopause (i.e. the top of the troposphere)?

A

It increases the height of the tropopause, which by dT/dH therefore increases temperature at the surface.

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7
Q

What is radiative forcing?

A

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.

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8
Q

What methods are there of tracking CO2 levels over periods of time?

A
  • 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)
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9
Q

What is solar variation?

A

The effective strength of the sun changes over time, due to sunspots (short term) and orbital cycles (long term).

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10
Q

What effect do clouds and aerosols have on the greenhouse effect?

A

Sub-visible particles (e.g. organics and black carbon) and cloud cover increase the albedo of the Earth, leading to negative radiative forcing.

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11
Q

What is the indirect aerosol (Twomey) effect?

A

Cloud droplets form on aerosol seeds, leading to ‘whiter’, more long lived clouds, which increase Earth albedo.

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12
Q

What are some approaches to fixing climate change?

A
  • Carbon pricing and trading
  • Energy efficiency
  • Investment in new technologies
  • Education
  • Climate engineering
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13
Q

How is a kilowatt-hour defined?

A

It is the energy equivalent of using a kilowatt of power for an hour.

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14
Q

What is the equation for heat capacity?

A

ΔQ = cΔT or c = dQ/dT

Where c is heat capacity.

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15
Q

What is the ideal gas equation?

A

pV = nRT

Where R is the gas constant, for n moles of gas.

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16
Q

What is the first law of thermodynamics?

A

Q = ΔU + W

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17
Q

What is the efficiency of a Carnot engine working between 2 temperatures, Tc and Th?

A

Efficiency µ = W/Q = 1 - Tc/Th

Where W = work done by the system, and Q = heat put into the system.

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18
Q

What is the equation for entropy, s?

A

Δs =ΔQreversible / T

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19
Q

What are the sources of energy loss in cars?

A
  • Kinetic energy required to speed up
  • Air resistance
  • Rolling resistance
  • Engine efficiency
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20
Q

What is the drag equation?

A

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.

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21
Q

What is binding energy?

A

The energy required to break up a nucleus into respective nucleons.

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22
Q

In the semi-empirical mass formula, what are the meanings of the coefficients av, as, ac, aa, and ap?

A
  • 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.
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23
Q

What is the most stable element? Why?

A

Iron, as it has the highest binding energy per nucleon.

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24
Q

What is the process behind fission?

A

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).

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25
Q

What is the 4-factor foumula for an infinite reactor?

Explain each term in the formula

A

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)

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26
Q

How is reactivity rho defined in terms of k?

A

rho = k - 1 / k

27
Q

What are delayed neutrons and what role to they play in reactivity?

A

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.

28
Q

What are the features of a Pressurised Water Reactor (PWR)?

A
  • 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).
29
Q

What are the features of a Boiling Water Reactor (BWR)?

A
  • 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.
30
Q

What are the features of a CANDU reactor?

A
  • 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.
31
Q

What is heavy water?

A

It is water formed with deuterium rather than regular hydrogen. Written as D20 rather than H20.

32
Q

What is the formula for power available to a wind turbine?

A

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.

33
Q

What is the Betz Limit?

A

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.

34
Q

How do slowly-rotating turbines create high-frequency AC current?

A
  • Usually by a Doubly-Fed Electrical generator, to account for variations in turbine frequency.
35
Q

How does one avoid capacitive losses over long distances from off-shore wind farms?

A

Off-shore substations convert AC to high-voltage direct current (HVDC), which is reconverted once on shore.

36
Q

What is the formula for power P from a resevoir dam of height h running down to an outlet?

A

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.

37
Q

In wave power, what is the formula for incident power per unit width of wave-front?

A

P = 1/4 rho * g * a2 * sqrt( g*lambda / 2π)

38
Q

What are some methods of storing energy?

A
  • 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.
39
Q

What are some methods of artificially tackling climate change (Climate engineering)?

A
  • Carbon capture and storage in the earth
  • Ocean fertilisation, to remove CO2 via photosynthesis
  • Cloud seeding, in order to increase Earth’s albedo.
40
Q

What is the atomic weight of carbon, hydrogen, and oxygen?

A

12, 1, and 16 respectively.

41
Q

What is absolute zero in celsius?

A

-273C

42
Q

In terms of the Solar Constant, S, what is the equation for solar flux, F? What is the equation to find S?

A

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.

43
Q

What are some problems in climate modelling?

A
  • 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.
44
Q

What is the T-s diagram for the Rankine cycle?

A
45
Q

What is the P-V diagram for a Carnot cycle?

A
46
Q

What are the p-V and T-s diagrams for the Brayton cycle?

What is the formula for Brayton efficiency?

A

Efficiency µ = 1 - r-(y-1)/y

Where r = pb / pa = pc / pd, and y = Cp / Cv.

Know how to derive.

47
Q

Why do nuclei with an odd neutron number tend to be more fissile?

A

Due to the pairing term in the SEMF, binding energy for odd-neutron nuclei tend to be lower than their isotopes.

48
Q

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?

A

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]

49
Q

What is the equation for the total fraction of nuclei consumed in a fuel, in terms of fuel convertion ratio, C?

A

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.

50
Q

What is the purpose of moderators in reactors?

A

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.

51
Q

What is the diagram for wind turbine blade design?

A

W = width of blade

u1 = wind velocity, v = blade velocity, a = angle of attack

D = Drag vector, L = Lift vector

tan(phi) = u1/v

52
Q

What are the equations for the ideal twist and width, W, of a wind turbine blade?

A

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)

53
Q

What are the effects on a turbine if tip speed ratio, lamda, is not optimal?

A
  • 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.
54
Q

What is the empirical formula for average wind turbine power, in terms of average wind speed uavg?

A

Pavg~= 0.2D2 * uavg3

Where D is turbine diameter.

55
Q

What are the features of a Francis water turbine?

A
  • 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.
56
Q

What is Tidal Range?

A

The difference in height between low and high tide.

Small over most open ocean ( <1 metre), but can be larger near shores or estuaries.

57
Q

What is the resonance condtion for waves (wavelength lamda) in a pool of length L?

A

lamda = 4L

58
Q

What is the formula for current due to photocell illumination?

A

Ic = IL - IS (eV/VT - 1)

59
Q

What are the formulae for potential energy, E, and extractable power, P, in a pump-turbine system?

A

E = rho * g h V

P = eta * rho * g h Q

60
Q

Where can captured CO2 be stored?

A
  • 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).
61
Q

What are 3 methods of converting solar energy to power?

A
  • 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.
62
Q

What is the formula for Gibbs free energy, G?

A

G (p,T) = U + pV - TS

G (p,T) = H - TS

63
Q

What is the diagram for a Combined Cycle Gas Turbine?

A

3rd Year Undergraduate Physics (3 decks)

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