Energy, Water & Material Resources — Problem set, Grade 12

The three fossil fuels are coal, oil, and natural gas. Nuclear fuel (uranium) is different because energy is released by splitting atomic nuclei (fission), not by burning, and it produces almost no CO2.

Coal, oil, and natural gas are all fossil fuels — carbon-rich fuels formed from ancient organisms, burned in combustion to release energy and CO2. Nuclear fuel is uranium, and a nuclear plant does not burn it; instead it splits uranium-235 nuclei through fission, releasing heat with almost no CO2 but producing long-lived radioactive waste.

3,900 lb less CO2.

Coal: 2.2 lb/kWh x 3,000 kWh = 6,600 lb. Natural gas: 0.9 lb/kWh x 3,000 kWh = 2,700 lb. The difference is 6,600 - 2,700 = 3,900 lb of CO2 avoided by choosing gas over coal.

Low direct operational CO₂ is one benefit, while fuel extraction, construction, radioactive waste, accident risk, costs, and reliability require separate assessment.

Separate operational from life-cycle boundaries; compare current local evidence rather than making an undated disposal-site or cost claim.

Geothermal — renewable; coal — nonrenewable; solar — renewable; uranium — nonrenewable.

Geothermal (Earth's internal heat) and solar (the Sun) are replenished continuously on a human timescale, so they are renewable. Coal is a fossil fuel that takes millions of years to form, and uranium is a finite mined element, so both are nonrenewable.

40%.

Capacity factor = average output / maximum capacity = 100 MW / 250 MW = 0.40 = 40%. This means the plant delivers about 40% of the electricity it theoretically could if it ran at full output every hour of the year.

Output varies with resource and conditions rather than automatically matching demand. Storage can shift delivery but has energy, power, and loss constraints; other sources, connections, and demand management can also contribute.

Solar output is absent without incident sunlight and generally reduced under clouds rather than universally zero. Wind output depends on wind and turbine operating limits. Compare generation and demand over time. Storage can shift surplus energy into later delivery with losses and capacity constraints; interconnection, complementary resources, and demand management can also help. None alone guarantees reliability without a complete timing and constraint account.

About 3% is freshwater, but most of that is frozen in ice and glaciers or stored deep underground, leaving less than 1% of all water as accessible surface freshwater.

Roughly 97% of Earth's water is salty ocean, so only about 3% is freshwater. Of that 3%, the large majority is locked in ice caps and glaciers or buried in deep groundwater, so less than 1% of all the water on Earth is the easily accessible liquid freshwater in lakes, rivers, and shallow aquifers that most human use depends on.

140 billion liters.

Agriculture's share is 70% of 200 billion liters: 0.70 x 200 = 140 billion liters. (Industry gets 0.19 x 200 = 38 billion, and homes get 0.11 x 200 = 22 billion, which all add back to 200 billion.)

Because all the rain and runoff from a watershed drains into its rivers and reservoirs, keeping the land clean and forested lets the soil and plants naturally filter the water, so pollution never enters the supply in the first place.

A watershed funnels all the water that falls on its land into a shared body of water, so any pollution, sewage, or eroded soil on the land ends up downstream in the reservoir. By keeping the watershed forested and limiting development, the vegetation and soil filter and slow the water, trapping sediment and absorbing pollutants before they reach the reservoir. Protecting the land therefore keeps the water clean naturally, which is how New York City delivers largely unfiltered water from its Catskill watershed.

From top to bottom: O horizon (surface litter), A horizon (topsoil, the fertile crop-growing layer), B horizon (subsoil), C horizon (weathered parent rock), then bedrock.

A soil profile stacks distinct horizons. At the surface is the O horizon of leaf litter and humus. Below it is the A horizon — the dark, fertile topsoil where most roots grow and crops are raised. Under that is the B horizon (subsoil, where clays and minerals accumulate), then the C horizon of weathered parent rock, all resting on solid bedrock. The A horizon (topsoil) is the fertile layer that feeds agriculture.

Recycling takes 150 units, saving 350 units of energy.

Recycled steel uses about 30% of the energy of new steel: 0.30 x 500 = 150 units. The energy saved compared to making it new is 500 - 150 = 350 units. This is why recycling metals conserves both energy and the ore itself.

Farmers plowed up the deep-rooted prairie grasses; when drought hit, the bare topsoil blew away in huge dust storms. Because soil forms over centuries but can erode in years, it must be conserved like a nonrenewable resource.

In the 1930 s, farmers on the Great Plains plowed up the native prairie grasses whose roots had held the soil together for millennia. When a severe drought arrived, there was nothing to anchor the exposed topsoil, and strong winds carried it away in enormous 'black blizzards.' Although soil does slowly regenerate from weathering and decay — technically making it renewable — it forms far too slowly (centuries per inch) to replace what erosion can remove in a few years. That mismatch is why environmental scientists manage soil as if it were nonrenewable, using conservation practices to keep it in place.

Both commonly make heat to drive a turbine; fossil fuels oxidize carbon compounds, while nuclear fission changes nuclei.

Response criteria

• State a scientifically accurate conclusion.
• Show the calculation or mechanism that supports it.
• Include units, conditions, or limits where relevant.

A:8000/40=200 g/MJ delivered. B:7000/50=140 g/MJ. Upstream leakage, transport or construction is omitted; this direct comparison is not a complete life-cycle ranking.

A:8000/40=200 g/MJ delivered.

B:7000/50=140 g/MJ.

Upstream leakage, transport or construction is omitted; this direct comparison is not a complete life-cycle ranking.

Response criteria

• Use the stated measurements or conditions, with correct units.
• Connect the result to the physical or environmental mechanism or evidence relationship.
• Identify the assumption, model limit or further evidence requested.

12/(2×24)=.25=25%; it is not conversion efficiency.

Response criteria

• State a scientifically accurate conclusion.
• Show the calculation or mechanism that supports it.
• Include units, conditions, or limits where relevant.

Generation=5×0.30×2000=3000 kWh. The allocated storage input returns400 kWh and loses/transfers100 kWh under the stated boundary; do not apply the storage loss to energy that bypasses it.

Generation=5×0.30×2000=3000 kWh.

The allocated storage input returns400 kWh and loses/transfers100 kWh under the stated boundary; do not apply the storage loss to energy that bypasses it.

Response criteria

• Use the stated measurements or conditions, with correct units.
• Connect the result to the physical or environmental mechanism or evidence relationship.
• Identify the assumption, model limit or further evidence requested.

10% for the remaining category in that stated model. Do not treat these shares as universal current observations.

Response criteria

• State a scientifically accurate conclusion.
• Show the calculation or mechanism that supports it.
• Include units, conditions, or limits where relevant.

Δstorage=8−2−9=−3 million m³/year. Exact water-level change also needs aquifer geometry, storage properties and spatial pumping/flow patterns.

Δstorage=8−2−9=−3 million m³/year.

Exact water-level change also needs aquifer geometry, storage properties and spatial pumping/flow patterns.

Response criteria

• Use the stated measurements or conditions, with correct units.
• Connect the result to the physical or environmental mechanism or evidence relationship.
• Identify the assumption, model limit or further evidence requested.

It may form much more slowly than it erodes; erosion can remove essential productive layers within the planning period.

Response criteria

• State a scientifically accurate conclusion.
• Show the calculation or mechanism that supports it.
• Include units, conditions, or limits where relevant.

Contained=60 kg; recovered=45 kg; unrecovered target=15 kg. Infiltration, organic matter, pore structure or measured erosion can characterize soil quality separately from mineral yield.

Contained=60 kg; recovered=45 kg; unrecovered target=15 kg.

Infiltration, organic matter, pore structure or measured erosion can characterize soil quality separately from mineral yield.

Response criteria

• Use the stated measurements or conditions, with correct units.
• Connect the result to the physical or environmental mechanism or evidence relationship.
• Identify the assumption, model limit or further evidence requested.

Write the relationship first; substitute with consistent units.

50 %

30/(5×12)×100=50.

Capacity factor compares output with rated output over time; efficiency compares useful output energy with input energy.

Response criteria

• State a scientifically accurate conclusion.
• Show the calculation or mechanism that supports it.
• Include units, conditions, or limits where relevant.

180+3n=9n gives n=30 uses. At50, reusable=330 and disposable=450, a120-unit advantage in this hypothetical energy category; other impacts need separate accounts.

180+3n=9n gives n=30 uses.

At50, reusable=330 and disposable=450, a120-unit advantage in this hypothetical energy category; other impacts need separate accounts.

Response criteria

• Use the stated measurements or conditions, with correct units.
• Connect the result to the physical or environmental mechanism or evidence relationship.
• Identify the assumption, model limit or further evidence requested.