Compare the kinetic energy of 1,000 kg of air at 5 m/s with that of 1,000 kg of air at 10 m/s.

Air of 1,000 kg moving at 5 m/s carries 12,500 J, a quarter of the 50,000 J it has at 10 m/s. Kinetic energy depends on v², so halving the speed leaves one quarter of the energy.

How much kinetic energy does one cubic metre of air moving at 8 m/s carry, taking air density as 1.2 kg/m³?

One cubic metre of air carries about 38 J at 8 m/s. The mass is 1.2 kg, and ½ × 1.2 × 8² = 38.4 J.

Why is the power in the wind proportional to the cube of wind speed rather than the square?

Kinetic energy per kilogram rises with v², and the mass of air passing the rotor each second also rises with v. The two effects multiply, giving power proportional to v³.

State the equation for the power available in the wind passing through a turbine rotor.

The power available is P = ½ρAv³, where ρ is air density, A is swept area and v is wind speed. Air density is usually taken as 1.2 kg/m³.

CCEA A-Level Environmental Technology 3930

Fossil Fuels

Topic overview Coal, oil and gas in modern society Reserves, lifespan and accessibility Fossil fuel combustion and the IPCC evidence Carbon trading schemes Fossil fuel demand, emerging economies and fuel security Environmental impacts of fossil fuel use

Global Action on Energy Conservation and Climate Change

Topic overview Sustainable development and climate agreements Emissions and energy efficiency targets for 2020 Renewable energy and demand reduction in policy Nuclear power as an alternative

Macrogeneration

Topic overview Conservation of energy and the simple generator Thermal power stations and steam turbines Direct and indirect renewable electricity Electricity transmission through the National Grid Smart grids and interconnectors Combined heat and power

Microgeneration

Topic overview Microgeneration technologies Benefits of home and community microgeneration The heat pump cycle and coefficient of performance Air source and ground source heat pumps

Energy From Wind

Topic overview Horizontal and vertical axis wind turbines Kinetic energy, wind power and the Betz limit Power curves, rated output and energy losses Swept area, blade length and turbine mass Air density, hub height and turbine siting Power control, yawing and survival speed Choosing a location for a commercial wind farm

Energy From the Sun

Topic overview Solar radiation, tracking and concentrating solar power Flat plate and evacuated tube collectors Sizing a domestic solar thermal system Photovoltaic cells and semiconductor wafers Types of photovoltaic module compared Planning regulations and solar incentives Passive solar design in new and existing buildings

Energy From Biomass

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Energy Storage

Topic overview Intermittency and reliability of renewable supply Why renewable energy needs storing Pumped hydro and compressed air energy storage Where energy storage is most beneficial

Plastics for the Future

Topic overview Crude oil as a fuel and a feedstock Refinery gases and the making of polymers Persistent plastic waste and the Great Pacific Garbage Patch Toxic gases from incinerating plastics Biodegradable, photodegradable and compostable plastics Testing photodegradable plastic against polythene Bio-derived polyethylene and a sustainable plastics future

Renewable Energy Investigations

Topic overview Desktop research on renewable energy technologies Choosing an investigation and its variables Apparatus and risk assessment for energy practicals Accuracy and reliability of energy measurements Presenting and analysing energy data Evaluating a method and site-based recommendations

Sustainable Development

Topic overview Population growth and demand for resources The I = PAT equation and the role of technology Ecological footprints, carbon footprints and One Planet Living

Waste Management

Topic overview Landfill dependence and the landfill tax Waste types, priority waste streams and EU directives The waste management hierarchy Recycling at a Materials Recovery Facility Landfill decomposition, methane and leachate Engineered landfill: dry tomb and bioreactor designs

Waste to Energy Technologies

Topic overview Embodied energy Incineration with energy recovery Digester design: solids content, residence time and staging Stages of anaerobic digestion and biogas CHP Composting and catering waste

Land Contamination and Remediation

Topic overview Contaminated land, risk and traditional remediation Bioremediation principles and bioreactor systems Micro-organisms that degrade named pollutants Bioremediation benefits and genetically engineered microbes Phytoremediation of metals and other elements Phytoextraction with Indian mustard and alpine pennycress Biohydrometallurgy and phytomining of ores

Hydrogen Fuel Cells

Topic overview Hydrogen as a fuel: properties and storage Hydrogen production: steam reforming, electrolysis and photocatalysis How a fuel cell works and the PEM cell Alkaline, phosphoric acid, molten carbonate and solid oxide fuel cells Fuel cell applications and the challenges of hydrogen

Transport System Challenges

Topic overview Four key challenges for future transport New vehicle technologies and their infrastructure Bioethanol production and the heat energy of ethanol Biodiesel and the biofuel debate Strategies to reduce transport demand

Energy Performance of Buildings

Topic overview Energy conservation and residents' behaviour Insulation, air tightness and glazing U-values and the heat flow equation The zero carbon homes hierarchy BREEAM, the Code and upgrading existing homes

Emerging Technologies

Topic overview Tidal stream and tidal barrage power Wave energy converters Environmental impacts of wave and tidal energy Smart materials and smart systems Carbon capture and storage Geo-engineering, direct air capture and bio-photovoltaics

Sustainable Urban and Rural Communities

Topic overview Energy and buildings in sustainable urban developments Transport, waste and brownfield sites Water, drainage and urban green space Energy, water and waste for isolated rural dwellings Local food and communication technology in rural areas

The Code for Sustainable Homes

Topic overview Purpose, levels and assessment of the Code Energy, carbon dioxide and water categories Materials, surface water run-off and waste categories Pollution, health and wellbeing, management and ecology categories Measuring the performance of an existing building Performance profiles, improvements and evaluation

Energy From Wind

Kinetic energy, wind power and the Betz limit

3 things to know
AS 1

Overview

The kinetic energy of moving air, the power equation P = ½ρAv³ and why power rises with the cube of wind speed, worked rotor calculations, the Betz limit and the power coefficient of real turbines.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Numbers

Calculate the power in the wind passing through an 80 m diameter rotor at 10 m/s, taking air density as 1.2 kg/m³.

Key term

State the equation for the kinetic energy of a moving mass of air.

Numbers

Calculate the kinetic energy of 1,000 kg of air moving at 10 m/s.

Questions from this subtopic

Each one with the model answer underneath.

1
State the equation for the kinetic energy of a moving mass of air.
Model answer
Kinetic energy equals half the mass multiplied by the speed squared, Eₖ = ½mv². Energy is in joules when mass is in kilograms and speed in metres per second.
2
Calculate the kinetic energy of 1,000 kg of air moving at 10 m/s.
Model answer
The kinetic energy is 50,000 J, or 50 kJ. The working is ½ × 1,000 kg × (10 m/s)² = 50,000 J.
3
Compare the kinetic energy of 1,000 kg of air at 5 m/s with that of 1,000 kg of air at 10 m/s.
Model answer
Air of 1,000 kg moving at 5 m/s carries 12,500 J, a quarter of the 50,000 J it has at 10 m/s. Kinetic energy depends on v², so halving the speed leaves one quarter of the energy.
4
How much kinetic energy does one cubic metre of air moving at 8 m/s carry, taking air density as 1.2 kg/m³?
Model answer
One cubic metre of air carries about 38 J at 8 m/s. The mass is 1.2 kg, and ½ × 1.2 × 8² = 38.4 J.
5
Why is the power in the wind proportional to the cube of wind speed rather than the square?
Model answer
Kinetic energy per kilogram rises with v², and the mass of air passing the rotor each second also rises with v. The two effects multiply, giving power proportional to v³.
6
State the equation for the power available in the wind passing through a turbine rotor.
Model answer
The power available is P = ½ρAv³, where ρ is air density, A is swept area and v is wind speed. Air density is usually taken as 1.2 kg/m³.

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