Second law of thermodyamics
In a power station, a tonne of coal has a certain calorific value or energy content, measured in BTU, or Joules. When it is burned, all of that energy content is conserved, but only some of it turns into the mechanical energy that turns the electric turbine, and only some of that turns into electricity. Energy is ‘lost’ as heat at each stage in the process. Temperature differences between different stages in the process are part of what drive the turbine, so thermal power stations need to actively get rid of heat as part of the process, either using cooling towers or water from rivers or the sea. The energy balance – conserving the total amount of energy as per the first law of thermodynamics, is as follows:
Calorific value of coal burned (J) = waste heat (J) + electricity produced (J)
Primary energy and conversion examples
| Primary | Stored or carried in primary form? | Converted by | Vector/carrier | Storage |
| Oil | Yes | Oil refinery | Petrol or Diesel | Petrol or diesel |
| Coal or natural gas | Yes | Fossil fuel power station | Electricity | Batteries, compressed air, hydroelectric and much more. |
| Coal or natural gas | Yes | Stove or boiler | Heat | Hot water tank, fabric of building and more |
| Uranium | Somewhat | Nuclear power plant | Electricity | Batteries, compressed air, hydroelectric and much more. |
| Wind | No | Wind turbine | Electricity | Batteries, compressed air, hydroelectric and much more. |
| Solar energy | No | Solar photovoltaic, or solar thermal | Electricity | Batteries, compressed air, hydroelectric and much more. |
| Falling and flowing water, water moved by the tides | (if using a dam) | Hydropower, tidal power station | Electricity | Batteries, compressed air, hydroelectric and much more. |
| Biomass (wood, straw etc) | Yes | Biomass power plant | Electricity | Batteries, compressed air, hydroelectric and much more. |
| Biomass (wood, straw etc) | Yes | Boiler | Heat | Hot water tank, fabric of building and more |
| Geothermal energy | Maybe as heat | Geothermal power station | Electricity | Batteries, compressed air, hydroelectric and much more. |
| Geothermal energy | Maybe as heat | Heat pump | Heat | Hot water tank, fabric of building and more |
Energy Efficiency
In general, energy efficiency can be measured as follows:
Energy efficiency = useful energy out / total energy in
And remembering the law of conservation of energy, there is an ‘energy balance’:
total energy in = useful energy out + non-useful energy out
When we burn coal in a power station, the useful energy out is the electricity produced, and the energy in is the calorific value of the coal. The overall efficiency of the power station is therefore defined as follows:
Efficiency of power station = electricity produced (J) / calorific value of coal burned (J)
Where the energy balance is:
Calorific value of coal burned = Electricity produced + waste heat
Efficiency is a ratio of one thing relative to another, which can be expressed as a percentage. The two things must have the same unit – both electricity and calorific value of coal are measured in Joules.
Similarly when we switch on an electric light bulb, electricity is converted into useful light, and waste heat.
Efficiency of light bulb = light produced (J) / electricity consumed (J)
There are physical limits to how much electricity can be obtained from a thermal power station. However, we can increase the ‘efficiency’ beyond this point by making use of some of the waste heat produced, e.g. for heating houses or for industrial processes in a combined heat and power plants. The energy balance then changes:
Calorific value of coal (J) = electricity (J) + useful heat (J) + waste heat (J)
The overall efficiency could then be measured as:
Overall efficiency = (electricity (J) + useful heat (J) ) / calorific value of coal (J)
Often, it is useful to break this down into two different efficiencies:
Thermal efficiency = useful heat (J) / calorific value of coal (J)
Electrical efficiency = electricity (J) / calorific value of coal (J)
There may be trade-offs between the thermal efficiency and the electrical efficiency, and designing the combined heat and power plant to produce more heat, or to produce more electricity, may affect the overall efficiency.
Electricity storage
Storage of electricity or heat involves the conversion of energy from one form to another, and leads to losses. Some efficiencies for energy transformation processes and energy storage are listed in the table below.
Source: Wikipedia
| Conversion process | Conversion type | Energy efficiency |
| Electricity generation | ||
| Gas turbine | Chemical to electrical | up to 40% |
| Gas turbine plus steam turbine (combined cycle) | Chemical/thermal to electrical | up to 60% |
| Water turbine | Gravitational to electrical | up to 90% (practically achieved) |
| Wind turbine | Kinetic to electrical | up to 59% (theoretical limit) |
| Solar cell | Radiative to electrical | 6–40% (technology-dependent, 15-20% most often, 85–90% theoretical limit) |
| Fuel cell | Chemical to electrical | up to 85% |
| World Electricity generation 2008 | Gross output 39% | Net output 33%[8] |
| Electricity storage | ||
| Lithium-ion battery | Chemical to electrical/reversible | 80–90% [9] |
| Nickel-metal hydride battery | Chemical to electrical/reversible | 66% [10] |
| Lead-acid battery | Chemical to electrical/reversible | 50–95% [11] |
| Engine/motor | ||
| Combustion engine | Chemical to kinetic | 10–50%[12] |
| Electric motor | Electrical to kinetic | 70–99.99% (> 200 W); 50–90% (10–200 W); 30–60% (< 10 W) |
| Turbofan | Chemical to kinetic | 20-40%[13] |
| Natural process | ||
| Photosynthesis | Radiative to chemical | up to 6%[14] |
| Muscle | Chemical to kinetic | 14–27% |
| Appliance | ||
| Household refrigerator | Electrical to thermal | low-end systems ~ 20%; high-end systems ~ 40–50% |
| Incandescent light bulb | Electrical to radiative | 0.7–5.1%,[15] 5–10%[citation needed] |
| Light-emitting diode (LED) | Electrical to radiative | 4.2–53% [16] |
| Fluorescent lamp | Electrical to radiative | 8.0–15.6%,[15] 28%[17] |
| Low-pressure sodium lamp | Electrical to radiative | 15.0–29.0%,[15] 40.5%[17] |
| Metal-halide lamp | Electrical to radiative | 9.5–17.0%,[15] 24%[17] |
| Switched-mode power supply | Electrical to electrical | currently up to 96% practically |
| Electric shower | Electrical to thermal | 90–95% (multiply with the energy efficiency of electricity generation for comparison with other water-heating systems) |
| Electric heater | Electrical to thermal | ~100% (essentially all energy is converted into heat, multiply with the energy efficiency of electricity generation for comparison with other heating systems) |
| Others | ||
| Firearm | Chemical to kinetic | ~30% (.300 Hawk ammunition) |
| Electrolysis of water | Electrical to chemical | 50–70% (80–94% theoretical maximum) |
Power – energy used over time
Power = energy transferred/time
Watts = Joules / second;
W = J / s
One watt is not very much power – a typical kettle uses around 2000-3000 W, which we can abbreviate as 2-3kW. Prefixes kilo (k), mega (M), and giga (G) are often used to represent thousands, millions or billions of something. These and other prefixes are shown below (Table from Sustainable Energy Without the Hot Air – David MacKay – p328):
| Prefix | Kilo | Mega | Giga | Tera | Peta | Exa |
|---|---|---|---|---|---|---|
| Factor | 103 | 106 | 109 | 1012 | 1015 | 1018 |
| Symbol | c | m | μ | n | p | f |
| Factor | 10-2 | 10-3 | 10-6 | 10-9 | 10-12 | 10-15 |
Power is often used to express the size of an engine, a power station or an electricity using device.
Here are a few examples:
- Typical engine of a small car such as a Nissan Micra: 109 horsepower, or 81kW
- One of the UK’s smallest coal fired power stations (Wilton) is 227MW ( 227,000kW), and the largest (Drax) is 3906MW (3,906,000 kW).
- A typical electric kettle uses 2kW
- Largest offshore wind turbines – 6-8MW – 6,000-8,000kW
- The London Array offshore wind farm is 630MW, or 630,000kW, with 175 turbines each at 3.6MW.
- Typical household solar PV array: 2kW peak (this is the maximum output at midday on a sunny summer day)
Units of energy
The two origins of the definition of energy, as moving objects (‘work’) and burning fuels, have given rise to different units.
Work done = force x distance
In standard scientific units, the force needed to accelerate a mass of one kilogram by one metre-per-second is one Newton. A force of one Newton moving one metre uses one Joule (J) of energy.
The standard unit of energy considered as the ability to heat a defined mass of water a known amount is the calorie. This is the energy needed to heat one gram of water by one degree Celsius.
And we need a conversion factor between the units of work and the units of heat energy:
1 calorie = 4.184 Joules or 1 c = 4.184 J
Food labels often include the number of kilocalories (kcal, or 1000 calories), often referred to by the misnomer ‘calorie’. The term ‘calorific value’ is sometimes used to mean the energy content of a fuel that is to be burned.
(We can also convert calories, or Joules, into other commonly used units of energy, such as kilowatt hours, or British Thermal Units.)
The kWh – our main unit of energy
Energy / time = power J/s = W or 1000 J/s = 1 kW (remember, k means x 1000)
Energy = power x time 1000 W x 60s = kWh
One kWh is 1000 times one Watt times 1 hour. This is a bit like saying that a distance of 60 miles is the same as one hour times 60 mph. Of course, that assumes that we are driving consistently at 60mph. In practice, maybe the car stops at traffic lights, slows down for a roundabout, goes on a dual carriageway at 70 for a while. If we want to know how far we’ve travelled in an hour, we need to know the average speed. Many electrical appliances have a ‘rated’ power, or maximum power, but on average use much less. Fridges, for example, cycle on and off throughout the day (you may have heard the fridge get loud for a few minutes, then quieten).
The amount of energy used by some example appliances, and their peak (maximum) and average power consumption, is shown below:
| Appliance | power consumption | hours per week | energy use in in one year |
| EV saloon car charging | 7000W | 21hrs | 7600 kWh |
| Immersion heater | 3000W | 28hrs | 4400 kWh |
| Electric shower | 9000W | 3.5hrs | 1600 kWh |
| LED bulb | 10W | 30hrs | 16 kWh |
| Incandescent bulb | 100W | 30hrs | 156 kWh |
| Fridge-freezer | 300W | 30hrs | 450 kWh |
| LCD TV | 200W | 21hrs | 220 kWh |
| Microwave oven | 1000W | 2hrsd | 100 kWh |
| Steam iron | 2000W | 1.5hrs | 150 kWh |
| Tumble dryer | 2500W | 7hrs | 900 kWh |
| Smartphone charger | 5W | 28hrs | 7 kWh |
| W-fi router | 7W | 168hrs | 9 kWh |