Sources of Energy in the World

Lessons

Senior 4 · Physics

Sources of Energy in the World

4 lessons

Lesson 4 of 4

Impacts of Energy Use, Conservation and the Future

25 min

The price of a kilowatt-hour

From 1 October 2025, a Rwandan household paid REG 89 Frw for each of its first 20 kWh in a month, 310 Frw for each of the next 30 kWh, and 369 Frw for every kWh above 50, before VAT (REG tariffs). So the more electricity a home uses, the more each extra unit costs. But the bill is not the whole cost of energy. Burning a fuel puts carbon dioxide into the air; smoke from cooking fires damages lungs; dams flood valleys; mines scar land. This lesson weighs those environmental and economic impacts, shows how the same service can be had with less energy, and looks at how Rwanda plans to supply the much larger demand of the coming decades.

Environmental impacts of energy sources

Every source has costs as well as benefits; a renewable source is not automatically harmless. Table 4.1 summarises the main impacts.

Source	Main environmental impacts
coal, oil, natural gas, peat, Lake Kivu methane	carbon dioxide from burning, a greenhouse gas (Unit 9); soot, sulfur dioxide and nitrogen oxides from coal, peat and oil; land dug up for mining; methane that leaks unburned
firewood and charcoal	smoke in kitchens; forests cut faster than they regrow; much of the wood's energy lost when charcoal is made
hydroelectric power	land and homes flooded by reservoirs; changed river flow and fish movement; sediment trapped behind dams
solar and wind	large areas of land per megawatt; mining of materials; disposal of old panels and batteries; no emissions while running
nuclear fission	long-lived radioactive waste; risk of serious accidents; very little carbon dioxide while running
geothermal	small releases of gases such as hydrogen sulfide and carbon dioxide from the wells

Table 4.1: The main environmental impacts of energy sources.

The carbon dioxide from a fuel can be worked out from its chemical equation. For methane,

\mathrm{CH_4} + 2\,\mathrm{O_2} \rightarrow \mathrm{CO_2} + 2\,\mathrm{H_2O}

One mole of methane (16 g) gives one mole of carbon dioxide (44 g), so each kilogram of methane burned releases $\frac{44}{16} = 2.75\,\mathrm{kg}$ of $\mathrm{CO_2}$ . With a specific energy of $50\,\mathrm{MJ\,kg^{-1}}$ (Lesson 2), that is $\frac{2.75}{50} = 0.055\,\mathrm{kg}$ of $\mathrm{CO_2}$ for every megajoule of heat.

Definition

The carbon intensity (or emission factor) of electricity is the mass of carbon dioxide released for each kilowatt-hour of electrical energy delivered, in $\mathrm{kg\,CO_2}$ per kWh. For a fuel-burning station of efficiency $\eta$ , each kWh needs $\frac{3.6\,\mathrm{MJ}}{\eta}$ of fuel energy. Example: a methane station of efficiency 40% needs $\frac{3.6}{0.40} = 9.0\,\mathrm{MJ}$ of fuel per kWh, which releases $9.0 \times 0.055 = 0.50\,\mathrm{kg}$ of $\mathrm{CO_2}$ .

Worked example 1: the carbon dioxide from a methane plant

In Lesson 2 you found that a plant like KivuWatt delivers about 209 GWh in a year. Assuming an efficiency of 40%, find the mass of carbon dioxide it releases in a year.

E_{\text{fuel}} = \frac{209 \times 10^{6}\,\mathrm{kWh} \times 3.6\,\mathrm{MJ\,kWh^{-1}}}{0.40} = 1.88 \times 10^{9}\,\mathrm{MJ}

m_{\mathrm{CO_2}} = 1.88 \times 10^{9}\,\mathrm{MJ} \times 0.055\,\mathrm{kg\,MJ^{-1}} = 1.03 \times 10^{8}\,\mathrm{kg} \approx 1.0 \times 10^{5}\ \text{tonnes}

About a hundred thousand tonnes a year, or half a kilogram for every kilowatt-hour. A hydroelectric or solar plant delivering the same energy releases almost none while it runs; its emissions come from building it.

Smoke in the kitchen

The energy impact that harms the most people is not on the grid at all. The World Health Organization estimates that household air pollution from cooking with open fires and inefficient stoves caused about 2.9 million deaths in 2021, including over 309 000 children under five, and that around 2.1 billion people still cook this way (WHO, 2025). In Rwanda, firewood was the main cooking fuel of 92.5% of rural households in 2023–24 (NISR, EICV7).

Physics offers part of the answer. A three-stone fire lets most of its heat escape around the pot. An improved cookstove surrounds the fire with an insulating liner, draws air up through a grate so the fuel burns more completely, and channels the hot gases against the pot. It gives the same cooking with less wood and less smoke.

Worked example 2: wood for one pot of water

A family heats 5.0 kg of water from 20 °C to 100 °C. Take the specific heat capacity of water as $4200\,\mathrm{J\,kg^{-1}\,K^{-1}}$ , dry firewood as $16\,\mathrm{MJ\,kg^{-1}}$ , and assume efficiencies of 10% for a three-stone fire and 30% for an improved stove. Find the wood used by each, and the wood saved in a year at two such pots a day.

Q = mc\Delta T = 5.0 \times 4200 \times 80 = 1.68 \times 10^{6}\,\mathrm{J}

m_{\text{fire}} = \frac{1.68\,\mathrm{MJ}}{0.10 \times 16\,\mathrm{MJ\,kg^{-1}}} = 1.05\,\mathrm{kg}, \qquad m_{\text{stove}} = \frac{1.68}{0.30 \times 16} = 0.35\,\mathrm{kg}

Saving per year: $(1.05 - 0.35) \times 2 \times 365 = 511\,\mathrm{kg}$ , about half a tonne of wood, and the smoke that would have come from it.

Economic impacts

Energy decisions are also money decisions. Hydroelectric, solar and wind plants cost a lot to build but have no fuel bill; diesel generators are cheap to build but expensive to run, which is why REG uses its diesel units only for emergencies and peak hours (REG, 2025). Imported fuels, such as the petroleum used for transport, must be paid for in foreign currency. A reliable, affordable supply attracts factories and creates jobs, while power cuts force businesses to run their own generators.

For a household the cost appears in the bill. Block tariffs such as REG's charge each kilowatt-hour at the price of the block it falls in, so the bill must be built up block by block.

Worked example 3: a household electricity bill

Using REG's household tariff from 1 October 2025, find the bill before VAT and the average price per kWh for a month's use of (a) 45 kWh, (b) 80 kWh.

(a) $20 \times 89 + 25 \times 310 = 1780 + 7750 = 9530$ Frw; average $\frac{9530}{45} = 212$ Frw per kWh.

(b) $20 \times 89 + 30 \times 310 + 30 \times 369 = 1780 + 9300 + 11\,070 = 22\,150$ Frw; average $\frac{22\,150}{80} = 277$ Frw per kWh.

Each kilowatt-hour saved by the second household is worth 369 Frw, because savings come off the top block first.

Using less energy for the same service

"Energy conservation" has two meanings. In physics it is a law: energy is never created or destroyed. In daily life it means saving energy: getting the same service (light, a cooked meal, a cold drink, a journey) from less energy input. There are three ways to do it.

Better efficiency: an LED lamp gives about as much light as an old incandescent bulb for a sixth of the power; a well-sealed fridge, an improved stove and an efficient motor do the same job with less input.
Better habits: switching off lights and machines that are not in use, and keeping fridge doors shut.
Better timing: REG asks customers to avoid running large appliances during the peak hours of 6:00 to 9:00 in the morning and 6:00 to 9:00 in the evening (REG). Using the same energy at another time lowers the peak that the most expensive plants must cover.

Whether an efficient appliance is worth its higher price is judged by its payback time.

Definition

Saving energy (energy conservation, in everyday use) means meeting the same need with less energy input, by greater efficiency, better habits or better timing. The payback time of a saving measure is the time for the money it saves to equal its extra cost:

\text{payback time} = \frac{\text{extra cost of the measure}}{\text{money saved per unit time}}

Example: a stove that costs 12 000 Frw more and saves 1500 Frw of charcoal a week pays for itself in $\frac{12\,000}{1500} = 8$ weeks.

Worked example 4: changing to LED lamps

A household replaces five 60 W incandescent bulbs with five 9 W LED lamps that give similar light. The lamps are on for 5.0 hours a day. The household's use is above 50 kWh a month, so each kWh saved is worth 369 Frw. The LED lamps cost 2000 Frw each (an illustrative price). Find the energy and money saved in a 30-day month, and the payback time.

\Delta E = 5 \times (60 - 9)\,\mathrm{W} \times 5.0\,\mathrm{h} \times 30 = 38\,250\,\mathrm{Wh} = 38.3\,\mathrm{kWh}

\text{saving} = 38.25 \times 369 = 14\,100\ \text{Frw per month}, \qquad \text{payback} = \frac{5 \times 2000}{14\,100} = 0.71\ \text{month}

The lamps pay for themselves in about three weeks and then keep saving for years.

Sustainable use and the future of supply

Energy use is sustainable when it meets today's needs without reducing the ability of future generations to meet theirs: renewable stocks such as forests are used no faster than they regrow, pollution stays within what the environment can absorb, and supply keeps pace with a growing population. Several trends will shape how that is done.

Solar and wind power are the fastest-growing sources in the world (Lesson 1). Rwanda's sunshine is fairly even across the country, so solar can be built close to users.
Storage in batteries and in pumped water lets variable sources supply the evening peak.
Regional grids: Rwanda already imports electricity from Uganda and receives a 26.7 MW share of the regional Rusumo hydroelectric plant; Rusizi III, a 68 MW regional hydro plant, is planned for 2031 (REG, 2025).
Electric transport and electric cooking will move energy demand from imported petroleum and wood to electricity, so the grid must grow.

REG's least-cost plan (Figure 4.1) expects domestic production to rise from 1488.9 GWh in 2025 to 17 923.8 GWh in 2050, about twelve times as much. Hydro and solar grow, and new sources appear: natural gas, geothermal, hydrogen and, by 2045, nuclear power. Committed projects in the near term include the 43.5 MW Nyabarongo II hydro plant and two 100 MW solar parks, expected from 2027 and 2028 (REG, 2025, Table 6).

Figure 4.1: Planned electricity production by technology in 2025 and 2050. Data: REG, Rwanda Least Cost Power Development Plan, 2024 Review (September 2025), Table 9; chart drawn by Ganzaa.

Worked example 5: how much can a solar park give?

The map in this lesson shows that a solar plant in eastern Rwanda produces about 4.2 kWh per day for each kilowatt-peak (kWp) of panels; a kilowatt-peak is the panel output in full sunshine of $1000\,\mathrm{W\,m^{-2}}$ . Estimate the yearly output of a 100 MW ( $1.0 \times 10^{5}$ kWp) solar park there, and its capacity factor.

E = 4.2\,\frac{\mathrm{kWh}}{\mathrm{kWp\ day}} \times 1.0 \times 10^{5}\,\mathrm{kWp} \times 365\,\text{days} = 1.53 \times 10^{8}\,\mathrm{kWh} = 153\,\mathrm{GWh}

\text{capacity factor} = \frac{4.2\,\mathrm{kWh}}{1\,\mathrm{kW} \times 24\,\mathrm{h}} = 0.175

This agrees with the 17.08% that REG gives for the Gigawatt Global solar plant (Lesson 2). One 100 MW solar park would supply about a tenth of Rwanda's 2024 demand of 1.477 TWh, but only in daylight.

Warning

Common mistakes. (1) Saying a renewable source has no impact: dams flood land and solar farms cover it. (2) Saying "energy is used up": it is converted to less useful forms; what we save is fuel and money. (3) Pricing every kWh of a block tariff at one rate: build the bill block by block. (4) Forgetting that a CO₂ figure per kWh of electricity must divide by the station's efficiency.

Tip

Three questions for any energy choice: What does it do to the air, land and water? What does it cost to build, run and import? Could the same service be had with less energy, or at a better time of day?

Energy Efficiency 101 (Student Energy). Watch how efficiency is defined as useful output over input, and how improving it gives the same service, such as light or heat, for less energy, as in Worked example 4.

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Practice

Show that burning 1.0 kg of methane releases 2.75 kg of carbon dioxide. How much is released by burning 1.0 kg of pure carbon ( $\mathrm{C} + \mathrm{O_2} \rightarrow \mathrm{CO_2}$ )?
A peat-fired station has an efficiency of 33%. Its peat releases 15 MJ per kg and 1.5 kg of carbon dioxide per kg burned (assumed values). Find the mass of peat burned, and the carbon dioxide released, for each kWh of electricity.
Using REG's household tariff from 1 October 2025, find the bill before VAT, and the average price per kWh, for a month's use of 30 kWh.
An old fridge uses 1.2 kWh a day and a new one 0.45 kWh a day. Find the energy saved in a year, its value at 369 Frw per kWh, and the payback time if the new fridge costs 150 000 Frw more (an illustrative price).
A family burns 3.0 kg of charcoal a day in a stove of efficiency 25%. How much would it burn in a stove of efficiency 35% for the same cooking, and how much would it save in a year?
A school in Nyanza installs 5.0 kWp of solar panels. Use the map's value of about 4.2 kWh per kWp per day to estimate the energy it produces in a year, and its capacity factor.
Explain why moving the use of a large appliance from 7 pm to 2 pm helps REG, even though the energy used is the same.
"Rwanda should replace all firewood with electric cooking at once." Evaluate this statement using data from this unit.

Show answersHide answers

16 g of $\mathrm{CH_4}$ gives 44 g of $\mathrm{CO_2}$ : $\frac{44}{16} = 2.75$ . For carbon, 12 g gives 44 g: $\frac{44}{12} = 3.67\,\mathrm{kg}$ .
Fuel energy per kWh $= \frac{3.6}{0.33} = 10.9\,\mathrm{MJ}$ ; peat $= \frac{10.9}{15} = 0.73\,\mathrm{kg}$ ; $\mathrm{CO_2} = 0.73 \times 1.5 = 1.1\,\mathrm{kg}$ per kWh, about twice the figure for a methane station.
$20 \times 89 + 10 \times 310 = 1780 + 3100 = 4880$ Frw; average $\frac{4880}{30} = 163$ Frw per kWh.
$(1.2 - 0.45) \times 365 = 274\,\mathrm{kWh}$ ; worth $274 \times 369 = 101\,000$ Frw a year; payback $\frac{150\,000}{101\,000} = 1.5$ years.
Same useful heat: $m \times 0.35 = 3.0 \times 0.25$ , so $m = 2.1\,\mathrm{kg}$ a day; saving $0.86 \times 365 = 310\,\mathrm{kg}$ a year (313 kg unrounded).
$5.0 \times 4.2 \times 365 = 7.7 \times 10^{3}\,\mathrm{kWh}$ ; capacity factor $\frac{4.2}{24} = 0.175$ .
7 pm is in the evening peak, which REG must meet with its most expensive plants (diesel units) and which sets how much capacity the grid needs. At 2 pm demand is lower and solar plants are producing, so the same energy is cheaper to supply and no extra peak capacity is needed.
Electric cooking would remove kitchen smoke and save forests, but the grid is not yet large enough: Rwanda's 2024 demand was 1.477 TWh with a peak of 242 MW, while firewood is the main cooking fuel of 92.5% of rural households, so a sudden switch would multiply the evening peak. Not every home is connected, and at up to 369 Frw per kWh electric cooking may cost more than wood for poor households. A gradual change, with improved stoves now and more generation, storage and connections over time, is more realistic.

Quick check

Methane burns as CH₄ + 2O₂ → CO₂ + 2H₂O. About how much carbon dioxide is released by burning 1 kg of methane? (C = 12, H = 1, O = 16)

Key points

Every source has impacts: $\mathrm{CO_2}$ and smoke from burning, flooded land from dams, land use from solar. Burning 1 kg of methane releases 2.75 kg of $\mathrm{CO_2}$ ; per kWh of electricity, divide the fuel energy by the efficiency.
Household smoke caused about 2.9 million deaths in 2021 (WHO); improved stoves cut wood use and smoke.
Block tariffs are summed block by block; savings come off the top block. Payback time = extra cost ÷ saving per unit time.
Save energy by efficiency, habits and timing (avoid 6–9 am and 6–9 pm). REG plans about twelve times today's production by 2050, with more solar, hydro, regional trade and new sources.

1The price of a kilowatt-hour

2Environmental impacts of energy sources

3Smoke in the kitchen

4Economic impacts

5Using less energy for the same service

6Sustainable use and the future of supply