Option D- Energy and the environment

Question 1

What is the intensity of the radiation measured at the top of the atmosphere?

Answer 1

The solar constant is 1.37kW/m²

Question 1

How much of the total solar energy is reflected in the atmosphere, surface and clouds?

Answer 1

30% reflected in total

6% by atmosphere
20% by clouds
4% by surface

Question 2

Is the solar input from the sun constant?

Answer 2

No
It varies by around 0.1% due to changes in sun-Earth distance and sunspots.

Question 3

What is the greenhouse effect?

Answer 3

The raised temperature of the Earth due to the absorption and re-emission of IR radiations by the atmosphere.

Question 4

What are greenhouse gasses ands the 3 main types?

Answer 4

Gasses that contribute to the greenhouse effect.
CO₂ (Carbon dioxide)
CH₄ (Methane gas)
Water vapor

Question 4

What is the formula for the temperature on Earth (Without an atmosphere)

Answer 4

T⁴ = μI/4σ

Where:
μ = Faction of radiation absorbed by surface
I = Solar constant (1.37kW/m²)
σ = Stefan’s constant

This formula predicts the Earths temperature to be 255k but it’s actual temperature is 288k meaning the greenhouse effect accounts for 33K

Question 5

What are the two reasons for rising sea levels?

Answer 5

1) Thermal expansion of the sea
2) Melting land ice (but no sea ice due to Archimedes’ principle)

Question 6

What is Archimedes’ principle?

Answer 6

Any object, wholly or partially immersed in a fluid experiences a force equal to the weight of the fluid dispersed by the object

Question 7

If the volume of an iceberg is V’, what volume is submerged?

Answer 7

W = p₁Vg
Weight = Density of ice x Volume of berg x 9.81

Let the submerged volume = V’
therefore the upthrust, U is:
U = P₂V’g
where p₂ = density of water

To be floating, W = U
P₂V’g = p₁Vg
V’ = p₁V/p₂

As ice is less dense than water, the iceberg floats.

Question 8

Do melting icebergs have an impact on climate change?

Answer 8

Due to Archimedes principle, they don’t impact on rising sea levels
But the white ice bergs reflected a lot of solar radiation back into space so loosing them increases the energy the Earth absorbed and thus global temperatures.

Question 9

What are the two processes of Uranium enrichment?

Answer 9

Gaseous diffusion
Gas centrifugation

Question 10

What is the process of gaseous diffusion?

Answer 10

High pressured Uranium hexafluoride (UF₆) is forced into a chamber with semi-permeable membranes.
From kinetic theory:
1/2mc²=3/2kT
c ∝ 1/√m
hence the lighter UF₆ with Uranium-235 will be moving faster and be more likely to pass through the semi-permeable membrane so the uranium is enriched.
After doing this many times, the uranium becomes more an more enriched.

Question 11

What is the enrichment factor for gaseous diffusion?

Answer 11

Enrichment ratio = √m₂/m₁
Molar mass of Uranium 235 = 234g
Molar mass of Uranium 238 = 238g
Molar mass of Fluorine = 19g

UF₆ so their is 6 Fluorine for each Uranium isotope.
Mass of UF₆ with U-235 is 349g and mass of UF₆ with U-238 is 352g.
Therefore:
Enrichment ratio = √352/349
= 1.0043
This is very small but over many cycles, the fuel will be enriched to the required 3.5%

Question 12

What is the require percentage of Uranium 235 needed for nuclear fuel?

Answer 12

3.5%

Question 13

What happens in gas centrifugation?

Answer 13

A long cylindrical container filled with UF₆ gas is turns at very fast speeds with a heat source at the bottom.
The heavier U-238 moves to the outside of the cylinder while the lighter U-235 stays in the middle and tends to move to the top.
The UF₆ from the centre/top is then placed into another cylinder where the process is repeated again and again until the Uranium is properly enriched.

Question 14

What is breeding?

Answer 14

This is the process of neutrons being absorbed by U-238 in a ‘breeding reactor’ (which fissiles U-235) where is becomes Plutonium-239 which is widely used in nuclear power and nuclear weapons.

U-238 + 1n → β + Np-239 → β Pu-239

Question 15

What is the proton-proton chain process in the sun?

Answer 15

Step 1
¹H + ¹H → ²H + (e+) + Ve
Step 2
²H + ¹H → ³He + γ
Step 3
³He + ³He → ⁴He + 2¹H

In total
4¹H → ⁴He + 2(e+) + 2Ve

Question 16

Why can’t the sun’s proton-proton fusion process happen on Earth?

Answer 16

The first step:
¹H + ¹H → ²H + (e+) + Ve
Depends on the weak nuclear force which can be very slow- in the sun the lifetime of a proton is billions of years.

Question 17

What is the fusion process on Earth?

Answer 17

²H +³H → ⁴He + ¹n

Question 18

What are the requirements for fusion on Earth?

Answer 18

1) High temperatures (T) so the hydrogen nuclei have enough KE to overcome repulsion. 1 x 10⁸

2) High number density (n) of particles. Around 10²⁰ particles per m³ (which is less than normal air but is hard to achieve with higher temperatures )

3) A long confinement time, 𝜏, around 3 seconds

Question 19

What is the fusion triple product and the number needed to achieve fusion?

Answer 19

The product of all the requirements for fusion to occur
Temperature = T
Density of particles = n
Confinement time = 𝜏

Fusion triple product = nT𝜏

The number to achieve fusion is:
3 x 10²⁸ K s m^-3

Question 20

What is the hydrogen fuel cell process?

Answer 20

1) Hydrogen is drawn to the anode and ionised (electrons removed) by a platinum catalyst.
2) Protons then diffuse across the liquid electrolyte
3) Electrons from the ionised hydrogen travel around an external circuit where they do work and re-enter the fuel cell at the cathode
4) Here they combine with oxygen and the diffused protons to produce water. (This reaction also required a catalyst)

Question 20

What are the advantages of a hydrogen fuel cell?

Answer 20

• Hydrogen cell us approximately 85% efficient (burning hydrogen is only 40% efficient)
• Electricity is produced directly
• Waste product is water
• Overall no greenhouse gases are produced. Although water vapour is a greenhouse gas, no extra water is produced as hydrogen gas is produced from water.
• It doesn’t produce acid rain

Question 21

What is the equation for power of a photovoltaic cell?

Answer 21

P = IAμcosθ

I = solar constant (1367Wm^-2)
A = Area of solar panel
μ = Efficiency of cell
θ = Angle between normal of a cell and the direction of sunlight hitting the cell.

Question 22

What is the inverse square law?

Answer 22

I = P/4πR²

Question 23

What is the formula for power of a turbine and its derivation?

Answer 23

1) The volume of the fluid through the turbine in each unit time = Av
2) Mass of the fluid = pAv
3) The kinetic energy per unit time = 1/2mv² = 1/2(pAv)v²

So P = 1/2pAv³
p = density of air/ water
A = Area swept out by turbines
v = Wind/ water speed

Question 24

What is the maximum theoretical efficiency of a wind turbine and why?

Answer 24

60%
It’s impossible to gain all the energy from the wind as this would stop it and thus stop the spin of the blades.
So some air must move away from the turbine and the theoretical efficiency of a wind turbine is 60%

Question 25

What is the formula for rate of transfer of energy by heat conduction?

Answer 25

ΔQ/Δt = -AK(Δθ/Δx)

Where
ΔQ/Δt = Rate pf transfer of energy by heat
A = Area of conduction surface
K = coefficient of thermal conductivity of the material
Δθ = Difference in temperature across two sides of the conductor
Δx = Distance between two sides of the conductor

Question 26

What is the order of magnitude for coefficient of thermal conductivity for different materials?

Answer 26

Glasses (air/argon): 10^-2
Concrete/brick/ceramic: 1
Metals: 10²

Question 27

What is the formula for rate of transfer of energy by heat conduction using the U-value?

Answer 27

P = UAΔθ

Question 28

How do you calculate the U-value from the coefficient of thermal conductivity of the material?

Answer 28

U = k/Δx
U = Wm^−1K^−1

Question 29

Why is the U-value useful?

Answer 29

In the building industry, the thickness of many building materials is governed by building regulations meaning there is no point including this in the heat flow equation.
Also, a layer of insulating air usually covers insulating materials, changing its coefficient of thermal conductivity so the U- value can be more accurate as it takes this into account from testing

Question 30

What is the wavelength of infrared radiation and visible light?

Answer 30

Visible light:
400nm-700nm

Infrared:
750nm(or 0.75μm) to 1000μm
Usually 5μm - 20μm