Energy, Work and Power

Energy stores and transfers

Energy stores are kinetic, gravitational potential, chemical, elastic, nuclear, electrostatic, and internal (thermal). Energy is transferred between stores by:

• mechanical work;
• electrical work;
• heating;
• waves, including light and sound.

Energy is conserved: it is not created or destroyed. Use a flow diagram to show the starting store, useful output, and wasted transfers. A Sankey diagram shows the relative sizes of useful and wasted energy transfers.

Kinetic and Gravitational Potential Energy formulae:

$$ E_k=\frac12mv^2,\qquad \Delta E_p=mg\Delta h $$

Worked examples:
A 2.0 kg object falls through 5.0 m.
Its gravitational potential energy decrease is $2.0\times9.8\times5.0=98\text{ J}$.
If 80 J becomes kinetic energy, the remaining 18 J is transferred to internal energy and sound.
A 4.0 kg object moving at 5.0 m/s has $E_k=\frac12\times4.0\times5.0^2=50\text{ J}$.

Work

Mechanical or electrical work done is energy transferred. For a force acting through a distance in its direction:

$$ W=Fd=\Delta E $$

Worked example: A 5.0 kg bag is lifted 2.0 m. Its weight is $5.0\times9.8=49\text{ N}$, so work done is $49\times2.0=98\text{ J}$. This transfers energy to the bag’s gravitational potential store.

Energy resources

Solar radiation is the main source of energy, except for geothermal, nuclear, and tidal resources. Nuclear fusion in the Sun releases the radiation. Research aims to use fusion as a large-scale energy source on Earth.

Resource	Main advantages	Main disadvantages
Fossil fuels	Reliable, controllable, high energy output	Finite; carbon dioxide and other pollution
Biofuels	Renewable if replanted; can use organic waste	Land and food competition; pollution when burned
Waves	Renewable; no fuel during operation	Intermittent and limited to suitable coasts
Tides	Renewable and predictable	Few suitable sites; environmental effects
Hydroelectric	Renewable, controllable, reliable	Floods land and changes river ecosystems
Geothermal	Renewable and reliable	Limited suitable locations
Nuclear fission	Reliable, large-scale output; low carbon dioxide during operation	Finite fuel, radioactive waste, accident risk
Solar cells/panels	Renewable; no fuel or direct pollution during operation	Intermittent; depends on sunlight and area
Wind	Renewable; no fuel during operation	Intermittent; needs suitable sites

Compare resources using renewability, availability, reliability, scale, and environmental effects. Enrichment: exact efficiencies and energy-density figures depend on technology and are not required here.

In a conventional power station:

1. A boiler transfers energy to water, producing steam.
2. A turbine changes the steam’s energy into rotation.
3. A generator changes rotation into electrical energy.

For hydroelectricity, falling water turns the turbine. Wind turns turbine blades. Solar cells transfer radiation directly to electrical energy; solar panels contain many solar cells.

Efficiency and power

Efficiency compares useful output with total input:

$$ \text{efficiency}=\frac{\text{useful energy output}}{\text{total energy input}}\times100% $$

It can also be calculated using power:

$$ \text{efficiency}=\frac{\text{useful power output}}{\text{total power input}}\times100% $$

Worked example: A device receives 500 J and gives 125 J of useful output. Its efficiency is $125/500\times100=25%$. If its input power is 800 W and useful output power is 200 W, efficiency is $200/800\times100=25%$.

Power is the rate of energy transfer or work done:

$$ P=\frac{W}{t}=\frac{\Delta E}{t} $$

The unit is the watt, $1\text{ W}=1\text{ J/s}$.

Worked example: A motor transfers 3600 J in 12 s. Its power is $3600/12=300\text{ W}$.

Energy input equals useful stored energy plus wasted transfers. Wasted energy is often transferred to the surroundings by heating or sound; it is not destroyed.