(a) CO2 emissions C from a nation’s energy system can be expressed as:
C = Population x Energy consumption per person x CO2 emissions per unit of energy consumption.
Initially, total emissions are 600 million tonnes of CO2 per year. If, over a 50-year period, population doubles, energy consumption per person is reduced by 30% by means of energy efficiency and CO2 emissions per unit of energy consumption are reduced by 20% by renewable energy, what is C at the end of the 50-year period?
[Hint: If you try to guess the answer, you will be wrong. It may help to write out the equation in algebraic symbols.]
(b) (i) Jim and Jane’s house has a rooftop solar photovoltaic system with conversion efficiency 20% and surface area of collectors equal to 16 m2. It generates its rated power of 2 kW at noon on a clear day in summer. A neighbour decides to install a photovoltaic system with the same power generation. However, the neighbour chooses a cheaper system with conversion efficiency only 10%. Assuming that both roofs face the same direction, what surface area of collectors will the neighbour need?
(ii) Over a period of 12 months, Jim and Jane’s PV system generates 2.628 MWh of electricity. What is its capacity factor for the year?
a) Consider per person C consumption.
C=K (.7)(.8) so a .56 factor per person
But population doubles, so 1.12 increase, or a 12 percent increase in emissions.
b. Let I be the energy density coming in.
Jim has .2I to generate 2Kwatts
Neighbor gets .1I, to get 2Kw her will need 2*16m^2
(a) To find C at the end of the 50-year period, we need to calculate the new values for population, energy consumption per person, and CO2 emissions per unit of energy consumption.
Let's denote:
- P0 as the initial population
- E0 as the initial energy consumption per person
- C0 as the initial CO2 emissions per unit of energy consumption
- P1 as the population after 50 years (doubled from the initial population)
- E1 as the energy consumption per person after a 30% reduction
- C1 as the CO2 emissions per unit of energy consumption after a 20% reduction
Using the given equation, we have:
C0 = P0 * E0 * C0
After 50 years, the values change as follows:
P1 = 2 * P0 (population doubled)
E1 = (1 - 0.30) * E0 (30% reduction in energy consumption per person)
C1 = (1 - 0.20) * C0 (20% reduction in CO2 emissions per unit of energy consumption)
So, at the end of the 50-year period, the new CO2 emissions (C) can be calculated as:
C1 = P1 * E1 * C1
Substituting the values, we have:
C1 = (2 * P0) * ((1 - 0.30) * E0) * ((1 - 0.20) * C0)
(b) (i) To find the surface area of collectors the neighbor needs, we'll use the power generation and conversion efficiency of both systems.
Let's denote:
- A1 as the surface area of collectors for Jim and Jane's system (with 20% conversion efficiency)
- A2 as the surface area of collectors for the neighbor's system (with 10% conversion efficiency)
- P as the rated power (2 kW)
The power generated by a photovoltaic system is given by:
Power generated = Conversion efficiency * Solar energy * Collector surface area
For Jim and Jane's system:
P = 0.20 * Solar energy * A1
For the neighbor's system:
P = 0.10 * Solar energy * A2
Since the power generated should be the same for both systems (2 kW), we can equate the two equations:
0.20 * Solar energy * A1 = 0.10 * Solar energy * A2
Cancelling out the Solar energy term, we get:
A1 = (0.10 * A2) / 0.20
(ii) To calculate the capacity factor for Jim and Jane's PV system for the year, we need to consider the actual electricity generated and the maximum possible electricity generation.
Capacity factor = (Actual electricity generated / Maximum possible electricity generation) * 100
Given:
Actual electricity generated = 2.628 MWh
Maximum possible electricity generation can be obtained by multiplying the rated power (2 kW) by the number of hours in a year (8760 hours):
Maximum possible electricity generation = 2 kW * 8760 hours
Now we can calculate the capacity factor:
Capacity factor = (2.628 MWh / (2 kW * 8760 hours)) * 100
Simplifying the equation and converting MWh to kWh, we find the capacity factor for the year.