(b) Power lost = Input power — Useful power
P_waste = 60kW — 15kW = 45kW
The engine wastes 45kW as heat, sound, and other losses.

Light energy = 15% of input = 0.15 × 216kJ = 32.4kJ
Heat energy = 85% of input = 0.85 × 216kJ = 183.6kJ

Most of the electrical energy becomes unwanted heat rather than useful light.

Solar power chain efficiency:
η_solar = η_panel × η_LED = 0.20 × 0.90 = 0.18 = 18%

Analysis:
Despite lower solar panel efficiency, the direct solar system (18%) is much closer to the coal system (25.7%) than might be expected. However, this comparison reveals important considerations:

**Energy policy implications:**
1. **Coal advantages:** Higher overall efficiency, reliable 24/7 operation
2. **Solar advantages:** No fuel costs, no emissions during operation, distributed generation
3. **System complexity:** Coal requires mining, transport, plant operation, grid infrastructure

**Environmental impact:**
— **Coal:** High CO₂ emissions (≈1 kg CO₂/kWh), air pollution, mining damage
— **Solar:** Zero operational emissions, manufacturing impacts, recyclable panels

**Economic factors:**
— **Coal:** Fuel costs, plant maintenance, environmental regulations
— **Solar:** High initial cost, minimal operating costs, government incentives

**Future considerations:**
— Solar panel efficiency improving (>25% in lab)
— Coal plant efficiency limited by thermodynamics
— Battery storage addressing solar intermittency
— Grid-scale solar becoming cost-competitive

**Conclusion:** While coal currently shows higher efficiency, solar’s environmental benefits, decreasing costs, and improving technology make it increasingly attractive for sustainable energy policy.

Part (a): Useful energy output
Useful energy = Water heating + Motor work
E_useful = 0.4kWh + 0.3kWh = 0.7kWh

Part (b): Efficiency calculation
Efficiency = (Useful output / Total input) × 100%
η = (0.7kWh / 2.5kWh) × 100% = 28%

Part (c): Energy lost per cycle
Energy lost = Total input — Useful output
E_lost = 2.5kWh — 0.7kWh = 1.8kWh

Analysis:
The washing machine is only 28% efficient, with 72% of energy wasted as heat and sound. This shows why energy-efficient appliances are important for reducing electricity costs and environmental impact.

Part (a): Plant efficiency
Efficiency = (Electrical output / Fuel input) × 100%
η = (18 MW / 50 MW) × 100% = 36%

Part (b): Daily useful energy production
Daily electrical energy = Power × Time
E_useful = 18 MW × 12h = 216 MWh = 216,000 kWh

Part (c): Daily energy waste
Total fuel energy per day = 50 MW × 12h = 600 MWh
Energy waste = 600 MWh — 216 MWh = 384 MWh = 384,000 kWh
This represents 64% of the input energy lost as heat.

Part (d): Economic analysis
Daily revenue = 216,000 kWh × $0.12/kWh = $25,920
Economic value of waste = 384,000 kWh × $0.12/kWh = $46,080

Key insights:
1. **Efficiency impact:** 36% efficiency is typical for gas turbines but shows significant improvement potential
2. **Economic loss:** $46,080/day ($16.8M/year) in wasted energy value
3. **Environmental cost:** 384 MWh/day of waste heat requires cooling systems
4. **Improvement potential:** Combined cycle plants achieve 50-60% efficiency

Real-world applications:
— **Cogeneration:** Use waste heat for district heating or industrial processes
— **Combined cycle:** Use exhaust heat to drive steam turbines
— **Efficiency improvements:** Better turbine designs, advanced materials
— **Renewable alternatives:** Solar/wind with 35-45% system efficiency but no fuel costs

Part (a): Energy at each stage

**Stage 1 — Engine output:**
E₁ = η₁ × E₀ = 0.35 × 100 MJ = 35 MJ
Loss₁ = 100 — 35 = 65 MJ (heat, exhaust)

**Stage 2 — Generator output:**
E₂ = η₂ × E₁ = 0.90 × 35 MJ = 31.5 MJ
Loss₂ = 35 — 31.5 = 3.5 MJ (heat, magnetic losses)

**Stage 3 — Battery stored energy:**
E₃ = η₃ × E₂ = 0.85 × 31.5 MJ = 26.8 MJ
Loss₃ = 31.5 — 26.8 = 4.7 MJ (heat, electrochemical losses)

**Stage 4 — Battery output:**
E₄ = η₄ × E₃ = 0.95 × 26.8 MJ = 25.4 MJ
Loss₄ = 26.8 — 25.4 = 1.4 MJ (internal resistance)

**Stage 5 — Motor mechanical output:**
E₅ = η₅ × E₄ = 0.92 × 25.4 MJ = 23.4 MJ
Loss₅ = 25.4 — 23.4 = 2.0 MJ (motor losses)

Part (b): Overall system efficiency
Overall efficiency = (Final output / Initial input) × 100%
η_total = (23.4 MJ / 100 MJ) × 100% = 23.4%

**Alternative calculation:**
η_total = η₁ × η₂ × η₃ × η₄ × η₅
η_total = 0.35 × 0.90 × 0.85 × 0.95 × 0.92 = 0.234 = 23.4% ✓

Part (c): Sankey diagram description
«`
Fuel (100 MJ) → [Engine 35%] → 35 MJ
↓ (65 MJ heat loss)
35 MJ → [Generator 90%] → 31.5 MJ
↓ (3.5 MJ loss)
31.5 MJ → [Charging 85%] → 26.8 MJ
↓ (4.7 MJ loss)
26.8 MJ → [Discharge 95%] → 25.4 MJ
↓ (1.4 MJ loss)
25.4 MJ → [Motor 92%] → 23.4 MJ (wheel output)
↓ (2.0 MJ loss)
«`

Total losses: 65 + 3.5 + 4.7 + 1.4 + 2.0 = 76.6 MJ

Part (d): Loss analysis and improvements

**Biggest loss:** Engine inefficiency (65 MJ, 65% of input)
**Ranking of losses:**
1. Engine: 65 MJ (85% of total losses)
2. Battery charging: 4.7 MJ (6% of total losses)
3. Generator: 3.5 MJ (5% of total losses)
4. Motor: 2.0 MJ (3% of total losses)
5. Battery discharge: 1.4 MJ (2% of total losses)

**Improvement strategies:**

**1. Engine improvements (highest priority):**
— Advanced engine designs (Atkinson cycle, variable compression)
— Better combustion control and timing
— Improved materials and manufacturing tolerances
— Target: 40-45% efficiency possible

**2. System optimization:**
— Reduce battery cycling (charge/discharge losses)
— Direct mechanical connection for highway driving
— Optimize power management algorithms
— Regenerative braking to recover energy

**3. Component upgrades:**
— Higher efficiency electric motors (>95%)
— Advanced battery chemistry (Li-ion → solid state)
— Better power electronics for charging/conversion

**4. Alternative approaches:**
— Fuel cell hybrid (50-60% electrical conversion efficiency)
— Plug-in hybrid with grid charging (avoid engine use)
— Full electric with high-efficiency charging

**Economic impact of improvements:**
If engine efficiency improved to 40%:
New overall efficiency = 0.40 × 0.90 × 0.85 × 0.95 × 0.92 = 26.8%
Improvement = (26.8 — 23.4)/23.4 = 14.5% better fuel economy

This analysis demonstrates why hybrid vehicle development focuses primarily on engine efficiency improvements, as the internal combustion engine remains the dominant source of energy loss in the system.

Part (a): Electrical energy input
E_input = P × t = 2000W × 240s = 480,000J = 480kJ

Part (b): Useful energy output
Mass of water: m = ρV = 1000 × 0.001 = 1kg
Energy to heat water: E_useful = mcΔT = 1 × 4200 × 80 = 336,000J = 336kJ

Part (c): Efficiency of kettle
Efficiency = (E_useful/E_input) × 100% = (336,000/480,000) × 100% = 70%

The kettle is 70% efficient; 30% of electrical energy is lost as heat to surroundings, sound, and other losses.

**Energy breakdown:**
— Motors: 40% × 1000 = 400 MWh, efficiency 85%
— Lighting: 30% × 1000 = 300 MWh, efficiency 60%
— Heating: 20% × 1000 = 200 MWh, efficiency 70%
— Other: 10% × 1000 = 100 MWh, efficiency 90%

**Current useful energy and waste:**
— Motors: Useful = 400 × 0.85 = 340 MWh, Waste = 60 MWh
— Lighting: Useful = 300 × 0.60 = 180 MWh, Waste = 120 MWh
— Heating: Useful = 200 × 0.70 = 140 MWh, Waste = 60 MWh
— Other: Useful = 100 × 0.90 = 90 MWh, Waste = 10 MWh

Total useful: 750 MWh, Total waste: 250 MWh
**Current overall efficiency: 75%**

Option (a): Upgrade motors to 95% efficiency
New motor energy needed for same useful output: 340/0.95 = 358 MWh
Energy saving: 400 — 358 = 42 MWh/month
Cost saving: 42 × $80 = $3,360/month = $40,320/year

Option (b): LED lighting at 90% efficiency
New lighting energy needed: 180/0.90 = 200 MWh
Energy saving: 300 — 200 = 100 MWh/month
Cost saving: 100 × $80 = $8,000/month = $96,000/year

Option (c): Improve heating to 85% efficiency
New heating energy needed: 140/0.85 = 165 MWh
Energy saving: 200 — 165 = 35 MWh/month
Cost saving: 35 × $80 = $2,800/month = $33,600/year

ROI Analysis (assuming typical upgrade costs):
— **Motor upgrade:** ~$200,000 cost, payback = $200,000/$40,320 = 5.0 years
— **LED lighting:** ~$150,000 cost, payback = $150,000/$96,000 = 1.6 years
— **Heating system:** ~$100,000 cost, payback = $100,000/$33,600 = 3.0 years

**Recommendation:** LED lighting upgrade provides best ROI with shortest payback period and highest annual savings. Should be implemented first, followed by heating improvements, then motor upgrades.

Part (a): Heat generated by servers
Heat generated = Waste energy from servers
Q_servers = 0.80 × 10 MW = 8 MW thermal

Part (b): Cooling power required
Using COP = Heat removed / Electrical power input
3.5 = 8 MW / P_cooling
P_cooling = 8 MW / 3.5 = 2.29 MW

Part (c): Total facility power consumption
P_total = P_servers + P_cooling = 10 MW + 2.29 MW = 12.29 MW

Part (d): Overall facility efficiency
Useful computing work = 20% of server power = 0.20 × 10 MW = 2 MW
Overall efficiency = (2 MW / 12.29 MW) × 100% = 16.3%

Only 16.3% of total electrical input performs useful computing work.

Part (e): Efficiency improvement strategies

**1. Waste heat recovery applications:**
— **District heating:** Use 8 MW thermal for nearby buildings
— **Absorption cooling:** Use waste heat to drive cooling systems
— **Industrial processes:** Supply heat to manufacturing facilities
— **Greenhouse heating:** Agricultural applications
— **Swimming pool heating:** Recreational facilities

**2. Cooling efficiency improvements:**
— **Higher COP chillers:** Modern systems achieve COP 4-6
— **Free cooling:** Use outside air when ambient temperature allows
— **Liquid cooling:** Direct chip cooling reduces cooling power by 30-50%
— **Hot aisle containment:** Improves cooling system efficiency

**3. Server efficiency improvements:**
— **Better processors:** Modern CPUs achieve 25-30% efficiency
— **Optimized workloads:** Virtualization and load balancing
— **Dynamic power management:** Scale power with computing demand
— **Specialized hardware:** GPUs and TPUs for specific tasks

**4. System integration:**
— **Combined heat and power (CHP):** Generate electricity on-site using waste heat
— **Thermal energy storage:** Store cooling capacity during low-demand periods
— **Smart grid integration:** Shift computing loads to optimize grid efficiency

**Potential improvements with waste heat recovery:**
If 80% of waste heat (6.4 MW thermal) is recovered for heating:
— Displaced natural gas heating: ~6.4 MW / 0.85 efficiency = 7.5 MW equivalent
— Overall system value: 2 MW computing + 6.4 MW heating = 8.4 MW useful output
— Effective efficiency: (8.4 / 12.29) × 100% = 68.4%

**Economic impact:**
— Annual electricity cost: 12.29 MW × 8760 h × $0.08/kWh = $8.6M
— With heat recovery value: 6.4 MW × 8760 h × $0.04/kWh thermal = $2.2M revenue
— Net operating cost reduction: 26%

This analysis demonstrates how waste heat recovery can dramatically improve the economic and environmental performance of energy-intensive facilities, transforming «waste» into valuable resources.

Daily energy demand:
— Electricity: 5 MWh
— Heating: 3 MWh
— Transportation: 2 MWh
— **Total: 10 MWh/day**

Resource assessment:
— Solar: 22% panel efficiency
— Wind: 35% system efficiency
— Battery: 90% round-trip efficiency
— Diesel backup: 35% efficiency
— Available land/sea area for renewable installation

Part 1: Renewable energy sizing

**Solar system design:**
— Peak sun hours: ~5 hours/day (typical island location)
— Required solar capacity for electricity: 5 MWh / 5h = 1 MW peak
— Accounting for losses and variability: 1.5 MW solar installation
— Panel area needed: 1.5 MW / 0.22 efficiency / 1 kW/m² = 6,818 m²

**Wind system design:**
— Average wind capacity factor: ~30% (island location)
— Required wind capacity: 5 MWh / (24h × 0.30) = 0.69 MW average
— Wind turbine installation: 2 MW capacity (multiple smaller turbines for reliability)

**Part 2: Energy storage system**

**Battery sizing for reliability:**
— Storage for 3 days backup: 15 MWh total demand
— Accounting for battery efficiency: 15 MWh / 0.90 = 16.7 MWh battery capacity
— Daily cycling depth: 50% maximum for battery life
— **Required battery bank: 33.4 MWh capacity**

**Part 3: Integrated system efficiency analysis**

**Energy flow optimization:**

**Direct renewable usage (highest efficiency):**
— Solar/wind → immediate electricity use: 90% efficiency (inverter losses)
— Direct heating via heat pumps: COP 3.0 using renewable electricity
— EV charging during peak renewable generation: 85% efficiency

**Battery-mediated usage:**
— Renewable → battery → load: 90% × 90% = 81% efficiency
— Critical for evening/night electricity demand

**Backup diesel system:**
— Generator efficiency: 35%
— Only for extended periods of low renewable generation
— Target: <5% annual energy from diesel

**Part 4: System integration strategies**

**Demand management:**
— **Smart EV charging:** Prioritize charging during peak renewable generation
— **Thermal storage:** Heat water/buildings during excess renewable periods
— **Load shifting:** Schedule energy-intensive activities for optimal times

**Efficiency optimization:**
— **Waste heat recovery:** Use EV charger and inverter waste heat for building heating
— **Seasonal storage:** Larger battery bank provides seasonal energy balance
— **Grid integration:** Smart inverters provide voltage/frequency support

**Part 5: Complete system design**

**Generation capacity:**
— Solar: 1.5 MW (provides ~7.5 MWh/day average)
— Wind: 2.0 MW (provides ~14.4 MWh/day average)
— **Total renewable generation: ~22 MWh/day average**

**Storage and backup:**
— Battery storage: 33.4 MWh
— Diesel backup: 2 MW (for emergency periods)

**System efficiency analysis:**

**Annual energy balance:**
— Renewable generation: 22 MWh/day × 365 = 8,030 MWh/year
— Community demand: 10 MWh/day × 365 = 3,650 MWh/year
— Excess generation: 4,380 MWh/year (120% oversupply for reliability)

**Overall system efficiency:**
— Direct renewable use (60% of demand): 90% efficiency
— Battery-mediated use (35% of demand): 81% efficiency
— Diesel backup (5% of demand): 35% efficiency

**Weighted average efficiency:**
η_total = 0.60 × 0.90 + 0.35 × 0.81 + 0.05 × 0.35 = 0.54 + 0.28 + 0.02 = 84%

**Part 6: Advanced optimization features**

**Smart grid technologies:**
— **Predictive control:** Weather forecasting for generation planning
— **Demand response:** Automatic load control during low generation periods
— **Vehicle-to-grid:** EV batteries provide grid storage when parked

**Waste heat recovery:**
— **Heat pump optimization:** Use waste heat from power electronics
— **Thermal mass:** Building thermal storage reduces heating demand
— **Industrial integration:** Coordinate with any local industry for waste heat utilization

**Reliability measures:**
— **Redundancy:** Multiple smaller wind turbines vs single large unit
— **Maintenance scheduling:** Coordinate renewable maintenance with high generation periods
— **Emergency protocols:** Automatic load shedding priorities

**Economic and environmental benefits:**
— **Fuel independence:** 95% renewable energy reduces diesel imports
— **Economic stability:** Predictable electricity costs vs volatile diesel prices
— **Environmental impact:** Minimal emissions, sustainable energy system
— **Energy security:** Reduced dependence on external fuel supplies

**Implementation timeline:**
1. **Phase 1:** Install core renewable generation and basic battery storage
2. **Phase 2:** Expand storage capacity and implement smart grid features
3. **Phase 3:** Add advanced optimization and vehicle-to-grid integration

**Performance metrics:**
— Overall efficiency: 84% (excellent for isolated grid)
— Renewable fraction: 95% (highly sustainable)
— System reliability: >99.9% (with proper sizing)
— Economic payback: 8-12 years vs continued diesel generation

This integrated design demonstrates how multiple energy technologies can be combined to achieve high efficiency while ensuring reliability in challenging environments, providing a model for sustainable island energy systems worldwide.

Part (a): When maximum efficiency isn’t optimal

**Economic limitations:**
— **Diminishing returns:** Going from 80% to 90% efficiency often costs more than the energy savings justify
— **Example:** Super-efficient windows may cost $10,000 more but save only $200/year in energy
— **Optimal efficiency:** Usually 70-85% efficiency provides best economic return

**Practical constraints:**
— **System complexity:** Higher efficiency often requires more complex control systems
— **Maintenance requirements:** Efficient systems may need more frequent, specialized maintenance
— **Reliability trade-offs:** Simple, robust systems may be preferable despite lower efficiency

**Performance characteristics:**
— **Load matching:** Systems optimized for peak efficiency may perform poorly at partial loads
— **Example:** High-efficiency heat pumps lose effectiveness in very cold climates

Part (b): Trade-offs analysis

**Efficiency vs Cost:**
**Case study — LED lighting:**
— **Standard LED:** 90% efficient, $5 per bulb, 25,000-hour life
— **Premium LED:** 95% efficient, $25 per bulb, 50,000-hour life
— **Analysis:** Premium LED saves 5% energy but costs 5× more
— **Conclusion:** Standard LED provides better cost-effectiveness for most applications

**Efficiency vs Environmental Impact:**
**Manufacturing intensity:**
— **High-efficiency products:** Often require rare materials, complex manufacturing
— **Example:** High-efficiency solar panels use more silver, specialized semiconductors
— **Lifecycle assessment:** Must consider manufacturing emissions vs operational savings

**Transportation and installation:**
— **Weight and size:** Efficient systems may be heavier, requiring more transportation energy
— **Installation complexity:** May require specialized equipment, skilled labor

**Efficiency vs Reliability:**
**System robustness:**
— **Simple systems:** Lower efficiency but proven reliability over decades
— **Complex systems:** High efficiency but potential failure points
— **Example:** Traditional incandescent vs CFL vs LED progression

Part (c): Efficiency and sustainability relationship

**Positive correlations:**
— **Resource conservation:** Higher efficiency reduces raw material consumption
— **Emission reduction:** Less energy use typically means lower emissions
— **Economic sustainability:** Lower operating costs improve long-term viability

**Potential contradictions:**
— **Rebound effects:** Efficiency improvements may lead to increased usage
— **Example:** More efficient cars leading to more driving
— **Jevons paradox:** Historical tendency for efficiency gains to increase total resource consumption

**Lifecycle considerations:**
— **Embodied energy:** Manufacturing energy for efficient equipment
— **End-of-life impact:** Disposal/recycling of complex efficient systems
— **Durability:** Simple, maintainable systems may last longer

Part (d): Examples favoring lower efficiency systems

**Renewable energy systems:**
**Solar thermal vs photovoltaic:**
— **Solar thermal:** 60-70% efficiency for heating applications
— **PV + heat pump:** 20% × 300% COP = 60% overall efficiency
— **Advantage of solar thermal:** Simpler, more reliable, lower cost per BTU

**Heating systems:**
**Direct combustion vs heat pumps:**
— **Gas furnace:** 85-95% efficiency, simple, reliable
— **Heat pump:** 300-400% efficiency but expensive, complex
— **Climate dependency:** Heat pumps lose efficiency in cold weather
— **Infrastructure:** Gas systems use existing distribution networks

**Transportation:**
**Bicycles vs electric vehicles:**
— **Bicycle:** «Low» mechanical efficiency (~25%) but zero energy input
— **Electric vehicle:** High efficiency (85%) but requires electrical infrastructure
— **Overall impact:** Bicycle superior for short trips despite «lower efficiency»

**Industrial processes:**
**Batch vs continuous processing:**
— **Continuous:** Higher thermal efficiency, complex control systems
— **Batch:** Lower efficiency but flexible, easier maintenance
— **Optimal choice:** Depends on production volume, product variety

Advanced considerations:**

**System-level optimization:**
— **Component efficiency:** Optimizing individual components may suboptimize the system
— **Example:** Oversized efficient motors running at low load vs properly sized standard motors
— **System thinking:** Focus on overall performance, not component metrics

**Economic efficiency vs energy efficiency:**
— **Different metrics:** $/kWh saved vs kWh saved
— **Investment optimization:** Limited capital should maximize economic return
— **Policy implications:** Subsidies should target cost-effective efficiency improvements

**Temporal factors:**
— **Technology evolution:** Today’s efficient technology may be obsolete tomorrow
— **Example:** Investing heavily in efficient fossil fuel systems vs waiting for renewable alternatives
— **Timing optimization:** Balance current efficiency vs future technology adoption

**Regional variations:**
— **Climate dependency:** Efficiency technologies perform differently in various climates
— **Infrastructure:** Efficiency solutions must match local capabilities
— **Economic development:** Appropriate technology for economic conditions

Conclusion and recommendations:**

**The journalist’s statement fails because:**
1. **Economic optimization:** Maximum efficiency rarely equals minimum cost
2. **Practical constraints:** Real-world factors limit achievable efficiency
3. **System complexity:** Higher efficiency often reduces reliability
4. **Lifecycle impacts:** Manufacturing and disposal costs matter
5. **Context dependency:** Optimal solutions vary by application

**Better approach:**
1. **Cost-effectiveness analysis:** Optimize $/kWh saved, not just efficiency
2. **Lifecycle assessment:** Consider full environmental impact
3. **System perspective:** Optimize overall performance, not components
4. **Context sensitivity:** Match solutions to specific conditions
5. **Multiple objectives:** Balance efficiency, cost, reliability, and environmental impact

**Policy implications:**
— **Efficiency standards:** Should target cost-effective levels, not maximum possible
— **Incentive programs:** Should reward cost-effective improvements
— **Research priorities:** Focus on breakthrough technologies, not incremental gains
— **Building codes:** Balance efficiency requirements with affordability

The goal should be **optimal efficiency** (balancing multiple factors) rather than **maximum efficiency** (single-factor optimization). This requires sophisticated analysis considering economics, environmental impact, reliability, and practical constraints — demonstrating why simplistic statements about efficiency can be misleading in complex energy systems.