Energy is a number, not a substance. You can calculate how much a system holds before a change and after it, and in a closed system the two totals match. This topic uses equations to calculate changes in energy stores, and applies conservation of energy to real processes in which some energy is dissipated.
A system is simply the object or group of objects you have decided to think about. When something happens to the system, energy is shifted between stores, and describing a change means saying which stores increased and which decreased.
The stores are kinetic, gravitational potential, elastic potential, thermal, chemical, magnetic, electrostatic and nuclear. Energy is shifted between them mechanically (by a force doing work), electrically (by a current), by heating, or by radiation.
A ball thrown upwards shows this: the kinetic store decreases as the gravitational store increases, and on the way down the reverse happens. If the system is closed and there is no air resistance, the total is unchanged throughout.
A moving object holds energy in its kinetic store, and the amount is \(E_k = \tfrac12 m v^2\), with mass in kilograms and speed in metres per second.
The square matters. Doubling the mass doubles the kinetic energy, but doubling the speed multiplies it by four. That single fact explains why stopping distances grow so sharply with speed.
Raising an object increases its gravitational potential store by \(E_p = mgh\), where g is the gravitational field strength, which is about 9.8 N/kg on Earth and is often taken as 10 N/kg.
Only the vertical height counts. Carrying a box up a ramp and lifting it straight up to the same height increase the gravitational potential energy store by the same amount. The ramp changes the force needed, not the energy stored.
Stretching or compressing a spring stores energy elastically: \(E_e = \tfrac12 k e^2\), where k is the spring constant in N/m and e is the extension in metres.
The equation only holds while the spring has not been stretched past its limit of proportionality. As with kinetic energy, the square means doubling the extension quadruples the stored energy.
Heating a material raises its temperature by an amount that depends on how much there is, what it is made of, and how much energy was supplied: \(\Delta E = mc\Delta\theta\).
Specific heat capacity c is the energy needed to raise the temperature of one kilogram of a substance by one degree Celsius. Water’s is unusually high, at about 4200 J/kg°C, so water is used in heating systems, and coastal climates are milder than inland ones.
Power is the rate of energy transfer, measured in watts: \(P = \frac{E}{t}\), and equivalently \(P = \frac{W}{t}\) where W is work done. One watt is one joule per second.
Two motors that raise the same load to the same height transfer the same energy; the more powerful one does it faster. Energy transferred and power are therefore different quantities.
Energy is always conserved, but it is not always useful. In real processes some energy is usually dissipated to the surroundings, often by heating, and is then spread out so thinly that it is no longer useful. This is dissipation.
Common causes of dissipation are friction between moving surfaces, air resistance, and the heating of wires by a current. Calling the energy ‘lost’ is loose language: it is dissipated, not destroyed.
Unwanted transfers can be reduced but never eliminated. Lubrication reduces friction between surfaces that move against each other. Thermal insulation reduces the rate at which energy leaves a building.
Two important properties of the walls are their thickness and their thermal conductivity. Thicker walls of lower conductivity give a slower rate of cooling. Cavity wall insulation, loft insulation and double glazing all work by trapping air, which conducts poorly and cannot circulate.
Efficiency is the fraction of the energy supplied that ends up in the useful store: \(\text{efficiency} = \frac{\text{useful output}}{\text{total input}}\), either as a decimal or multiplied by 100 for a percentage. The same ratio works with power instead of energy.
Efficiency can never exceed 1, or 100%. If a calculation gives more, the useful and total figures have been swapped. Efficiency can be increased by reducing wasteful transfers, for example through better lubrication, better insulation or lower-resistance wiring.
Renewable resources are naturally replenished on a human timescale: wind, solar, hydroelectric, tidal, wave, geothermal and biofuel. Non-renewable resources are not: coal, oil, gas and nuclear fuel.
Each resource involves trade-offs. Fossil fuels are reliable and can be increased on demand, but they are finite and release carbon dioxide, and coal and oil also release sulfur dioxide, which causes acid rain. Nuclear is reliable and releases no carbon dioxide in use, but produces waste that stays hazardous for a very long time.
Most renewables release no carbon dioxide in use, but wind and solar are variable: their output follows the conditions rather than the demand. Hydroelectric, geothermal and biofuel can be turned up and down far more readily. Hydroelectric and tidal are more predictable but need particular geography and disrupt habitats. Pumped storage is one way of meeting a sudden surge in demand, because water can be released within seconds.
