Lesson 22: Energy Conservation & Efficiency

Warm-Up

The cheapest, cleanest kilowatt-hour is the one you never use. Before we build a single new power plant, we can slash demand simply by wasting less — better insulation, LED bulbs, efficient engines, capturing waste heat. Energy efficiency and conservation are the least glamorous and most powerful tools in the whole unit, and they're where APES concentrates its math: given a power rating and hours of use, calculate energy, cost, and CO₂; given input and useful output, calculate efficiency. This lesson closes Unit 6 by drilling those calculations with clean dimensional analysis — the single most reliable way to earn FRQ 3 points — and by cataloging the efficiency measures the exam expects.

Core Concept

Conservation vs. efficiency

• Energy conservation = using less energy by changing behavior (turning off lights, driving less, lowering the thermostat, carpooling).
• Energy efficiency = using technology to get the same service with less energy (LED bulbs, efficient appliances, better insulation, hybrid engines).

Both reduce demand, emissions, and cost. Most systems are far from perfectly efficient: a typical incandescent bulb converts only ~5–10% of energy to light (the rest is waste heat); an internal-combustion car engine is only ~20–25% efficient; a coal plant is ~33–40% efficient. Efficiency improvements have huge leverage.

Energy efficiency is quantified as: efficiency (%) = (useful energy output ÷ energy input) × 100

[DIAGRAM: Energy-flow (Sankey-style) diagram for an incandescent bulb — 100 units energy in; ~10 units out as light (useful), ~90 units lost as heat. Compare to an LED — 100 in, ~90 out as light, ~10 lost as heat. Efficiency = useful out ÷ in.]

Passive and active solar design

• Passive solar — designing a building to capture, store, and distribute solar heat without mechanical systems: south-facing windows (in the NH), thermal mass (concrete/stone/water that absorbs heat by day and releases it at night), overhangs that block high summer sun but admit low winter sun, and good insulation.
• Active solar — uses mechanical equipment (pumps, fans, solar collectors) to move captured solar heat, e.g., solar water heaters.

Efficiency measures across sectors

• Buildings: insulation, double/triple-pane windows, LED lighting, Energy Star appliances, smart thermostats, green roofs, passive solar design.
• Transportation: fuel-efficient/hybrid/electric vehicles, public transit, higher CAFE fuel-economy standards, better urban planning (smart growth, Lesson 17).
• Industry: cogeneration/CHP (Lesson 20) captures waste heat, raising overall efficiency from ~33% to ~80%; efficient motors and process heat recovery.
• Grid: reducing transmission losses, smart grids, demand management.

Energy math and dimensional analysis

The exam's guaranteed calculations. Core relationships: - Energy = Power × Time → kWh = kW × h - Cost = Energy × price → $ = kWh × ($/kWh) - Convert units carefully: 1 kW = 1,000 W. - CO₂ or fuel: multiply energy by an emission factor (e.g., kg CO₂ per kWh) or divide by an energy-content factor.

The method: write each quantity with its units, arrange conversion factors so units cancel, leaving the target unit. This is the same dimensional analysis you used for aquifers (Lesson 15) and half-lives (Lesson 20).

Why this matters

Efficiency/conservation is the top "reduce energy impact" FRQ answer, and the math (energy → cost → CO₂) is the backbone of FRQ 3. Mastering clean dimensional analysis here pays off across the entire exam.

Worked Examples

Example 1 (easy): Conservation vs. efficiency

Classify each as conservation or efficiency: (i) replacing incandescent bulbs with LEDs, (ii) turning off lights when leaving a room.

Solution: (i) Efficiency — technology delivering the same light with less energy. (ii) Conservation — a behavior change that uses less energy.

Interpretation: Technology = efficiency; behavior = conservation.

Example 2 (medium): Efficiency calculation

A power plant takes in 1,000 MW of energy from fuel and produces 380 MW of electricity. Calculate its efficiency.

Strategy: efficiency = useful output ÷ input × 100.

Solution:

efficiency = (380 / 1,000) × 100 = 38%

Answer: 38% (typical of a coal plant; the other 62% is lost mostly as waste heat).

Interpretation: Most fuel energy in a thermal plant is lost as heat — hence the value of cogeneration.

Example 3 (AP-style): Energy cost calculation

A household uses 900 kWh per month. Electricity costs $0.12 per kWh. (a) Monthly cost? (b) If LED upgrades cut use by 20%, monthly savings?

Strategy: cost = kWh × $/kWh; savings = 20% of cost.

Solution:

(a) 900 kWh × $0.12/kWh = $108/month
(b) 20% × 900 = 180 kWh saved → 180 × $0.12 = $21.60/month saved

Answer: $108/month; save $21.60/month.

Interpretation: Track units ($/kWh × kWh = $). Percentage savings apply to energy, then convert to dollars.

Example 4 (AP-style): Energy → CO₂ (full dimensional analysis)

A home uses 12,000 kWh/year. The grid emits 0.5 kg CO₂ per kWh. (a) Annual CO₂? (b) If efficiency cuts use to 9,000 kWh, how much CO₂ is avoided?

Strategy: multiply energy by the emission factor; units cancel.

Solution:

(a) 12,000 kWh/yr × 0.5 kg CO₂/kWh = 6,000 kg CO₂/yr
(b) new: 9,000 kWh × 0.5 = 4,500 kg CO₂/yr
    avoided: 6,000 − 4,500 = 1,500 kg CO₂/yr

Answer: 6,000 kg/yr; avoids 1,500 kg CO₂/yr.

Interpretation: kWh × (kg CO₂/kWh) = kg CO₂ — the kWh cancels. This is the archetypal FRQ 3 chain.

Common Mistakes

• Confusing conservation and efficiency. Conservation = behavior (use less); efficiency = technology (same service, less energy).
• Dropping or mismatching units in dimensional analysis. Always write units and cancel; if the leftover unit isn't what's asked, the setup is wrong.
• Forgetting to convert W↔kW. 1 kW = 1,000 W; kWh = kW × h, not W × h (unless you then divide by 1,000).
• Computing efficiency upside-down. It's useful output ÷ input, always ≤ 100%. If you get >100%, you flipped it.
• Ignoring waste heat. Most thermal-plant and engine energy is lost as heat — cogeneration recaptures it.

Practice Problems

11. (FRQ-style) Distinguish conservation from efficiency with one example each, and explain why reducing demand is often cheaper and cleaner than building new power plants.

12. (Math) A 60-W bulb runs 6 h/day. (a) Daily kWh? (b) At $0.10/kWh, annual (365-day) cost? (c) If replaced by a 10-W LED, annual cost savings?

FRQ Practice — Analyze an Environmental Problem and Propose a Solution with Calculations (10 pts)

A town wants to cut electricity use and CO₂ emissions. An average home uses 10,000 kWh/year; the grid emits 0.6 kg CO₂ per kWh; electricity costs $0.13/kWh.

(a) Calculate one home's annual electricity cost. Show work. (2 pts) (b) Calculate one home's annual CO₂ emissions. Show work. (2 pts) (c) An efficiency program cuts each home's use by 25%. Calculate the new annual kWh and the CO₂ avoided per home. Show work. (3 pts) (d) Propose one efficiency measure and one conservation measure the town could promote, and justify each. (3 pts)