Topic 1: Energy

Energy cannot be created or destroyed, only shifted between stores and transferred by different pathways. This topic shows you how to calculate the energy in moving, raised, and stretched objects, how heating relates to temperature, and how we judge useful energy through power and efficiency. It finishes by comparing the energy resources that power modern life.

Energy stores and transfers

Energy is held in stores and moved by transfers. The main stores you must know are kinetic (movement), gravitational potential (height), elastic potential (stretched or squashed objects), thermal (internal, linked to temperature), chemical (fuels, food, batteries), nuclear, electrostatic, and magnetic. Energy is transferred between stores by four pathways: mechanically (a force doing work), electrically (charge moving through a circuit), by heating, and by radiation such as light or sound. The key principle is conservation of energy: the total energy in a closed system stays the same. When a ball falls, energy shifts from the gravitational store to the kinetic store, and on impact much of it spreads to thermal and sound. Energy that ends up spread out into the surroundings is called dissipated energy and is no longer useful.

Kinetic energy

Any moving object has energy in its kinetic store. The amount depends on the object's mass and the square of its speed: Ek = 0.5 m v^2, where Ek is in joules (J), m is in kilograms (kg) and v is in metres per second (m/s). Because speed is squared, doubling the speed gives four times the kinetic energy. For example, a 1500 kg car travelling at 20 m/s has Ek = 0.5 x 1500 x 20^2 = 0.5 x 1500 x 400 = 300000 J, or 300 kJ. If the same car reaches 40 m/s, its kinetic energy becomes 1200 kJ, four times larger. This is why higher speeds make braking distances grow so sharply.

Gravitational potential energy

Lifting an object higher in a gravitational field stores energy in its gravitational potential store. The change is Ep = m g h, where m is mass in kg, g is the gravitational field strength (about 9.8 N/kg on Earth, often taken as 10 N/kg in calculations) and h is the change in height in metres. For example, raising a 2 kg book 1.5 m onto a shelf stores Ep = 2 x 9.8 x 1.5 = 29.4 J. If that book then falls and air resistance is ignored, all of this transfers to the kinetic store, so you can set m g h equal to 0.5 m v^2 to find the speed just before it lands.

Elastic potential energy

When a spring or elastic band is stretched or compressed without going past its limit of proportionality, it stores energy in its elastic potential store. The amount is Ee = 0.5 k e^2, where k is the spring constant in newtons per metre (N/m) and e is the extension in metres. A stiffer spring has a larger spring constant and stores more energy for the same extension. For example, a spring with k = 200 N/m stretched by 0.1 m stores Ee = 0.5 x 200 x 0.1^2 = 0.5 x 200 x 0.01 = 1 J. This equation only works while the spring obeys Hooke's law, meaning extension is still proportional to the force applied.

Specific heat capacity

Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 degree C. The energy transferred when heating is E = m c deltaT, where m is mass in kg, c is the specific heat capacity in J/kg degC and deltaT is the temperature change in degC. Materials with a high specific heat capacity, like water, need a lot of energy to warm up and cool down slowly, which is why water is used in central heating systems. Worked example: how much energy is needed to heat 0.5 kg of water from 20 degC to 80 degC, given c = 4200 J/kg degC? The temperature change is deltaT = 80 - 20 = 60 degC. So E = 0.5 x 4200 x 60 = 126000 J, or 126 kJ. You can rearrange the equation to find c from a practical: c = E / (m x deltaT).

Power and efficiency

Power is the rate of energy transfer, or the rate of doing work, measured in watts (W), where 1 W equals 1 joule per second. It can be calculated as P = E / t (energy transferred divided by time) or P = W / t (work done divided by time). A 60 W bulb transfers 60 J every second. Efficiency compares useful output energy to total input energy: efficiency = useful output energy transfer / total input energy transfer, and you can multiply by 100 to get a percentage. The same ratio works with power: efficiency = useful power output / total power input. For example, a motor supplied with 500 J that delivers 350 J of useful kinetic energy has an efficiency of 350 / 500 = 0.7, or 70 percent. No real device is ever 100 percent efficient because some energy is always dissipated, usually as thermal energy through friction.

Reducing unwanted energy transfers

Some energy transfers are wasteful, so we design systems to cut them down. Friction between moving parts dissipates energy as heat and sound; lubrication with oil or grease reduces this so machines run more efficiently. In buildings, thermal energy escapes through walls, roofs and windows. Insulation slows this loss: thicker walls and materials with low thermal conductivity reduce the rate of energy transfer, so heat leaves more slowly. Cavity wall insulation, loft insulation, and double glazing all trap air, which is a poor conductor. Streamlining vehicles reduces energy wasted against air resistance. The general aim is to keep useful energy in the intended store for longer and reduce how much is dissipated to the surroundings.

Energy resources

Energy resources are split into renewable and non-renewable. Non-renewable resources will run out and include the fossil fuels coal, oil and natural gas, plus nuclear fuel. Burning fossil fuels is reliable and produces large amounts of energy on demand, but releases carbon dioxide and other pollutants. Renewable resources are replenished as fast as they are used and include wind, solar, hydroelectric, tidal, wave, geothermal, and bio-fuel. Renewables produce little or no carbon dioxide during use but many depend on weather or location and can be less reliable. Choosing resources involves balancing reliability, cost, environmental impact, and how easily output can be matched to demand.