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# Energy system essentials / foundations

In the previous video, we have introduced you to the technology of coal-fired power plants – an example of a thermal power plant, where fuel is converted to heat, which is then converted to electric power. But as you now probably realise, this is not the whole story. This power plant also generates heat that is rejected to the environment. Why does this loss of waste-heat to the environment occur? Is this avoidable? What are the wider implications for our energy systems?

Read on to get into the foundations of energy systems performance and, more importantly, performance losses. Obtain some underlying knowledge of the thermodynamic limits to energy systems performance and options to improve energy efficiency.

### Efficiency

The performance of energy conversion systems is a combination of output and energy efficiency. The system should provide useful, wanted outputs. Energy efficiency now refers to the ratio between the useful output of an energy conversion process and the input. For example, a car with an internal combustion engine usually runs on gasoline or diesel. Yet, the output of the engine, which is mechanical energy that provides traction (motion) ranges from 20-35% of the energy in the fuel consumed. Much energy is inevitably lost to the surroundings in the form of heat – via the car’s radiator and exhaust.

### The First Law of Thermodynamics

An efficiency lower than 100% implies something is lost. But where do the losses in energy systems go? The First Law of Thermodynamics states that “Energy can neither be formed nor created” – all processes occurring in energy systems are transformations of energy from one form to another – from the chemical energy contained in a fuel, to heat; from electricity to kinetic energy or heat. Only by labeling some of the products of the transformation as useful, we can define a ‘First Law Efficiency’.

A First Law efficiency lower than 100% implies some outputs are not useful, they are lost. The losses from energy systems are absorbed as heat in the environment.

### The Second Law of Thermodynamics

Entropy is the thermodynamic property for “disorder”. The Second Law of thermodynamics states that for every process running, total Entropy must increase – total Entropy being the Entropy within the system combined with the Entropy of the environment. Thus the Second Law formalises that total disorder of the Universe can only increase; within a system, Entropy can decrease, but only at the expense of an Entropy increase in the environment.

The Second Law of Thermodynamics implies that whenever an energy transformation proceeds, total Entropy must increase. This implies that some of the energy transformed must be lost, dissipated, as heat into the environment. Consider a car, for example. To keep on driving, we need to supply power to compensate for the friction between the car’s body and the air, and between the tires and the road. Friction causes heat dissipated into the environment. We can reduce the friction, but never entirely eliminate it.

The Second Law implies that we cannot realise energy transformations that have a 100% First Law efficiency. An exception appears to be the case where the useful output is heat. This obeys the Second Law, however, as in the conversion from electric power to heat Entropy increases. Indeed, a kettle or electric boiler approximates 100% conversion of electricity to heat for making hot water. As perfect insulation cannot be achieved, however, some heat is lost from the kettle and boiler. With time, all of the heat will be dissipated into the environment, as heat naturally flows from a high temperature to a low temperature. This is well-known. In industry and households, many energy systems therefore supply heat (as hot water or steam) for immediate use.

Insulation acts as a resistance to heat loss – putting in insulation slows-down the inevitable process of heat loss. Whenever hot water or steam is stored, the storage vessels will have insulation. In district-heating networks, where heat maybe transported over a considerable distance, insulation of the distribution pipelines is required to maintain hot water temperature. Buildings should be properly insulated to reduce their rate of heat loss, which directly translates into heating requirements. Realising insulation always carries a cost – for materials, installation etc. Deciding on insulation and on the proper amount of insulation thus always involves a trade-off – between the cost incurred and the reduction of heating cost achieved. Obviously, insulation payback correlates with energy price.

Conversion of heat into power

The Second Law also places restrictions on the transformation of heat into power. This transformation is core to our internal combustion engines and thermal power plants – both first combust fuels to liberate heat, which is then converted to mechanical energy, which can be used to deliver Work (power). In thermodynamics, a device that converts heat into power is known as a heat engine.

In a heat engine, heat flows from a heat source at high temperature to a heat sink at low temperature (the cold sink); in the process, part of the heat Qin is converted to mechanical energy to do Work W; an amount of heat Qout is rejected from the system to the cold sink.

Of course, the First Law holds and a First Law Efficiency can be formulated:

Qin = Qout + W

η = W / Qin

Where η is the 1st Law Efficiency of the Heat Engine (Useful Work divided by Heat Input).

The Second Law implies that it is not possible to construct a heat engine that converts all the heat into Work. The theoretically best achievable apparatus to convert heat into power is known as a Carnot heat engine, named after the French military engineer and physicist Nicolas Carnot (1796-1832) who proposed the idea in the year 1824. The maximum efficiency ηmax of this Carnot heat engine only depends on the temperature difference between Qin and Qout

ηmax= 1 – (Tout / Tin) *note that T is expressed in Kelvin

Wmax = ηmax* Qin

The equation for ηmax shows the larger the difference between inlet and outlet temperature of a heat engine, the higher the maximum theoretical efficiency for the conversion of heat to Work. This has become known as the Carnot efficiency.

The efficiency of real power plants is always lower than the Carnot efficiency – real technology is never ‘ideal’, it has irreversible energy losses. We can only build systems that approximate the ideal Carnot cycle as best as possible. The improvement of efficiency between the two power plants in the previous video is due to (1) achieve a plant efficiency that is closer to the Carnot efficiency. This involves reducing losses by advancement of technology. (2) to achieve a higher maximum theoretical Carnot efficiency. This involves operating at higher steam temperature and pressure, which is made possible by employing advanced design and materials in the plant’s steam cycle and furnace.

As the Carnot efficiency is an implication of the Second Law, it applies to all processes in which heat is transformed into mechanical energy to deliver Work (power) – internal combustion engines, gas turbines and thermal power plants. In each of these, to achieve maximum efficiency one tries to realise and operate at the highest temperatures feasible.

Implications of the First and Second Law

If 45% of the fuel input is transformed to electricity in a coal fired power plant, the other 55% is rejected to the environment as (unutilised) waste heat at ambient temperature, say 15°C. This can be done via direct cooling (using cooling water), using evaporative cooling (using a cooling tower) or via air cooling (using air fans).

However, neither the First nor the Second Law prevents us from modifying the design of the plant and to let this heat be rejected to a district-heating system, say at 100°C. While, due to the reduced temperature difference, the Carnot efficiency and thus the electric power output will go down, the First Law efficiency may increase dramatically – to 85-90%, as now a large part of previously rejected heat finds a useful purpose.

Depending on where you live in the world, providing comfortable warmth is an important end-use of our fuel consumption. Transporting heat from a power plant to nearby households via a district-heating system can replace much of your home fuel consumption. A similar principle is used in cogeneration plants, built around gas turbines which have waste heat temperatures around 500°C, which is high enough to facilitate making medium and low pressure steam to supply heat to industrial processes. We can connect the waste heat from our power plants to other utilities as much as possible, which drastically improves First Law efficiencies. Both applications are limited by spatial and safety constraints, but as mentioned, even small improvements make a large impact on a global scale.