Fossil fuels & Alternate Sources of energy (SEC2_Renewable energy)

Fossil fuels

&

Alternate Sources of energy

• Fossil fuels:

               Fossil fuel is a term used to describe a group of energy sources that were formed from ancient plants and organisms during the Carboniferous Period, approximately 360 to 286 million years ago, prior to the age of dinosaurs.

              At that time, the land was covered with swamps filled with microorganisms, marine organisms, trees, ferns and other large leafy plants. As the organisms and plants died, they sank to the bottom of the swamps and oceans and formed layers of a spongy material called peat. Over millions of years, the peat was covered by sand, clay, and other minerals, which converted the peat into sedimentary rock. Over time, different types of fossil fuels formed, depending on the combination of organic matter present, how long it was buried, and what temperature and pressure conditions existed when they were decomposing

There are three major types of fossil fuels:

1. Coal is formed from ferns, plants and trees which hardened due to pressure and heat
2. Oil (Petroleum) is formed from smaller organisms, like zooplankton and algae. Intense amounts of pressure caused this complex organic matter to decompose into oil. 
3. Natural Gas undergoes the same process as oil; however the process is longer and subject to higher amounts of heat and pressure, causing further decomposition.

Note: Fossil fuels are the world’s dominant energy source, making up 82% of the global energy supply. Non-OECD countries hold the majority of proven reserves for all fossil fuels. These energy sources have powered, and continue to power, the industrialization of nations. They have a variety of applications, from electricity production to transport fuel.  Moreover, fossil fuels are necessary for the production of a variety of common products, such as paints, detergents, polymers (including plastics), cosmetics and some medicines.

Some fossil fuels, such as coal, are an abundant and cheap form of energy. Others, like oil, have a variable cost depending on geographic location. For this reason, geopolitical issues arise due to the geographic allocation of these highly valuable resources.

Fossil fuels are non-renewable resources, as they have taken millions of years to form. Once these resources are used, they will not be replenished. Moreover, fossil fuels are the largest source of carbon dioxide, a greenhouse gas which contributes to climate change, and their production causes both environmental and human health impacts. These concerns are triggering the world to look at alternate sources of energy that are both less harmful and renewable. Additionally, the gradual depletion of conventional fossil fuel reserves has led companies to develop more challenging reserves.  These unconventional resources usually have higher production costs and a greater risk of environmental impact.

Advantages of Fossil fuels

• Fossil fuels have several advantages over other sources of energy. This is the main reason why they are still the major energy supplier of the world. The advantages of fossil fuels are as follows:
• Fossil fuels have a very high calorific value. Thus, burning 1 gm of fossil fuel releases tremendous amount of energy. Thus, the energy produced by fossil fuels is greater than that produced by an equivalent amount of other energy resource.
• The reservoirs of fossil fuels are pretty easy to locate with the help of advanced equipment and technology.
• Coal is a fossil fuel that is found in abundance. It is used in most power plants because it reduces the production cost to a great extent.
• Transportation of fossil fuels that are in liquid or gaseous forms is very easy. They are simply transported through pipes.
• Construction of power plants that work on fossil fuels is also easy.
• Petroleum is the most predominantly used form of fossil fuels for all types of vehicles.
• Fossil fuels are easier to extract and process, hence are cheaper than the non-conventional forms of energy. 

Disadvantage of Fossil fuels

Although, fossil fuels were a preferred source of energy until recently, their over consumption and some undesirable properties have led to several issues of grave importance. The disadvantages of fossil fuels are as follows:

• Although, oil, natural gas and coal are found in abundance in nature, the alarming rate at which they are being consumed has resulted in substantial depletion of their reservoirs. Besides, it is impossible to replenish the resources as it takes millions of years for the hydrocarbon chains to form from organic remains.
• The hydrocarbons present in the fossil fuels, release greenhouse gases, such as methane, carbon dioxide etc., which are capable of damaging the ozone layer.
• Besides, other harmful gases such as carbon monoxide and sulfur dioxide are responsible for acid rain, which has spelled disaster for the ecology.
• Extraction of fossil fuels has endangered the environmental balance in some areas. Moreover, coal mining has jeopardized the lives of several mine workers.
• The depletion of reservoirs has made the extraction of fossil fuels an expensive affair. This is likely to affect the fuel prices in near future.
• Leakage of some fossil fuels, such as natural gas, crude oil can lead to severe hazards. Hence, transportation of these fuels is very risky.
• Fossil fuels have contributed in more than one way for global warming, the issue that is being combated all over the world.

Nuclear Energy:

Nuclear energy is the energy held in the nucleus of an atom; it can be obtained through two types of reactions - fission and fusion.

Nuclear fission produces energy through the splitting of atoms, which releases heat energy that can generate steam and then be used to turn a turbine to produce electricity. All of today’s nuclear plants use fission to generate electricity. The fuel most commonly used for fission is uranium, although additional elements such as plutonium or thorium can be used.

Nuclear fusion is a nuclear reaction in which two or more atomic nuclei collide at very high speeds and join to form a new type of atomic nucleus. During this process, matter is not conserved because some of the matter of the fusing nuclei is converted into photons, which produces usable energy.  This process is what allows the sun and stars to give off energy. Fusion power offers the prospect of an almost inexhaustible source of energy for future generations; however, creating the conditions for nuclear fusion presents a potentially insurmountable scientific and engineering challenge. A recent experiment has shown that nuclear fusion can be achieved; however, it has not yet been successfully demonstrated on a commercial scale.

Note: 

• Today, nuclear power plants account for 11% of global electricity generation with about 80% of that installed capacity being in OECD countries. All of this capacity is nuclear fission.
• Nuclear energy, through fission, can release 1 million times more energy per atom than fossil fuels. It can also be integrated into electricity grids, which currently utilize fossil fuel generation, with few changes to existing infrastructure.
• Nuclear has large power-generating capacity and low operating costs, making it ideal for base load generation. However, upfront capital costs are intensive and present financial risk to investors given the extended time frames power plants must operate to recuperate their costs.
• Nuclear energy does not emit greenhouse gas emissions. For this reason, it is often seen as a substitute for fossil fuel energy generation and a solution for mitigating climate change.
• However, nuclear fission has a wide variety of environmental and health issues associated with electricity generation. The largest concern is the generation of radioactive wastes such as uranium mill tailings, spent (used) reactor fuel, and other radioactive wastes. Some of these materials can remain radioactive and hazardous to both human health and the environment for thousands of years. Several large nuclear meltdowns in history released radioactive waste that had lasting negative impacts on the environment and surrounding communities. This has made nuclear fission technologies controversial.

Advantages of Nuclear Energy

Despite potential drawbacks and the controversy that surrounds it, nuclear energy does have a few advantages over some other methods of energy production.

Expense

Less uranium is needed to produce the same amount of energy as coal or oil, which lowers the cost of producing the same amount of energy. Uranium is also less expensive to procure and transport, which further lowers the cost.

Reliability

When a nuclear power plant is functioning properly, it can run uninterrupted for up to 540 days. This results in fewer brownouts or other power interruptions. The running of the plant is also not contingent of weather or foreign suppliers, which makes it more stable than other forms of energy.

No Greenhouse Gases

While nuclear energy does have some emissions, the plant itself does not give off greenhouse gasses. Studies have shown that what life-cycle emissions that the plants do give off are on par with renewable energy sources such as wind power. This lack of greenhouse gases can be very attractive to some consumers.

Disadvantages of Nuclear Energy

One of the reasons that nuclear energy falls under fire so frequently is due to the many disadvantages it brings.

Raw Material

Uranium is used in the process of fission because it's a naturally unstable element. This means that special precautions must be taken during the mining, transporting and storing of the uranium, as well as the storing of any waste product to prevent it from giving off harmful levels of radiation.

Water Pollutant

• Nuclear fission chambers are cooled by water, in both the boiling water reactors (BWRs) and pressurized water reactors (PWRs). In PWRs, cold water enters through primary pipes and the secondary pipes remove the heated water away, so the coolant is not in contact with the reactor. In BWRs, water runs through the reactor core, so if there is any leakage of fuel, the water can get contaminated and is transported to the rest of system.
• Used nuclear rods are immersed in water in the spent fuel pool, to cool them before they can be transported for disposal. Radio-active water can leak out of doors in the pool when the seals that keep the doors airtight malfunction.
• Other pollutants released by nuclear plants are heavy metals and toxic pollutants that harm plant and animal life in aquatic bodies. Water is released into the atmosphere after being cooled but is still warm and damages the ecosystem of the sinks it flows into.

Waste

When the uranium has finished splitting, the resulting radioactive byproducts need to be removed. While recycling efforts of this waste product have been undertaken in recent years, the storage of the by-product could lead to contamination through leaks or containment failures.

Leaks

Nuclear reactors are built with several safety systems designed to contain the radiation given off in the fission process. When these safety systems are properly installed and maintained, they function adequately. When they are not maintained, have structural flaws or were improperly installed, a nuclear reactor could release harmful amounts of radiation into the environment during the process of regular use. If a containment field were to rupture suddenly, the resulting leak of radiation could be catastrophic.

Shutdown Reactors

There have been several nuclear reactors that have failed and been shutdown that are still in existence. These abandoned reactors are taking up valuable land space, could be contaminating the areas surrounding them, yet are often too unstable to be removed.

Why Do We Need Renewable Energy?

• For thousands of years we have relied on burning fossil fuels to generate
• energy, but in today’s world using oil, gas and coal for our energy needs is becoming a problem. Climate change is one of the greatest environmental challenges that we have ever faced, and the main cause behind it is our dependence on fossil fuels. Burning coal, petroleum and other fossil fuels is the primary means by which we produce electricity, but it also leads to heavy concentrations of pollutants in our air and water.
• Another problem with using fossil fuels to generate energy is that there is not a limitless amount available. For the past couple of centuries, we have come to rely more and more on the world’s supply of fossil fuels, and that supply is fast running out. As the demand for fossil fuels has increased, the cost of using them has also increased and each year we find ourselves with larger and larger energy bills.
• The answer to all of these problems? Renewable energy. Energy such as solar energy, wind energy and water power is generated from natural energy sources and unlike fossil fuels, these sources of energy never run out. With a much lower impact on the environment, using renewable energy helps to protect our planet by significantly reducing the amount of carbon emissions that we produce. By using renewable energy sources, we also reduce our dependence on fossil fuel gas and oil reserves, which means that we can avoid the rising cost of energy bills and improve our energy security.
• In order to preserve our planet, our wallets and our energy sources we all need to be involved in switching to renewable energy sources and making or homes more energy efficient
• Many people probably wonder: if renewable energy is so beneficial, why don’t we consume more of it? The answer to the question is that many of the renewable energy sources are more expensive and more difficult to retrieve. Thus, because of these limitations, the consumption of fossil fuels has grown to an exorbitant rate.

Biomass:

Biomass is fuel that is developed from organic materials, a renewable and sustainable source of energy used to create electricity or other forms of power.

Some examples of materials that make up biomass fuels are:

• Scrap lumber
• Forest debris
• Certain crops
• Manure
• Some types of waste residues.

With a constant supply of waste – from construction and demolition activities, to wood not used in papermaking, to municipal solid waste – green energy production can continue indefinitely. 

Biomass is a renewable source of fuel to produce energy because:

Waste residues will always exist – in terms of scrap wood, mill residuals and forest resources; and

Properly managed forests will always have more trees, and we will always have crops and the residual biological matter from those crops.

What is biomass power?

Biomass power is carbon neutral electricity generated from renewable organic waste that would otherwise be dumped in landfills, openly burned, or left as fodder for forest fires.
When burned, the energy in biomass is released as heat. If you have a fireplace, you already are participating in the use of biomass as the wood you burn in it is a biomass fuel.
In biomass power plants, wood waste or other waste is burned to produce steam that runs a turbine to make electricity, or that provides heat to industries and homes. Fortunately, new technologies — including pollution controls and combustion engineering — have advanced to the point that any emissions from burning biomass in industrial facilities are generally less than emissions produced when using fossil fuels (coal, natural gas, oil). 

Biochemical Conversion of Biomass

Biochemical conversion of biomass involves use of bacteria, microorganisms and enzymes to breakdown biomass into gaseous or liquid fuels, such as biogas or bioethanol. The most popular biochemical technologies are anaerobic digestion (or biomethanation) and fermentation. Anaerobic digestion is a series of chemical reactions during which organic material is decomposed through the metabolic pathways of naturally occurring microorganisms in an oxygen depleted environment. Biomass wastes can also yield liquid fuels, such as cellulosic ethanol, which can be used to replace petroleum-based fuels.

Anaerobic Digestion

Anaerobic digestion is the natural biological process which stabilizes organic waste in the absence of air and transforms it into biofertilizer and biogas. Anaerobic digestion is a reliable technology for the treatment of wet, organic waste.  Organic waste from various sources is biochemically degraded in highly controlled, oxygen-free conditions circumstances resulting in the production of biogas which can be used to produce both electricity and heat. Almost any organic material can be processed with anaerobic digestion. This includes biodegradable waste materials such as municipal solid waste, animal manure, poultry litter, food wastes, sewage and industrial wastes.
An anaerobic digestion plant produces two outputs, biogas and digestate, both can be further processed or utilized to produce secondary outputs. Biogas can be used for producing electricity and heat, as a natural gas substitute and also a transportation fuel. A combined heat and power plant system (CHP) not only generates power but also produces heat for in-house requirements to maintain desired temperature level in the digester during cold season. In Sweden, the compressed biogas is used as a transportation fuel for cars and buses. Biogas can also be upgraded and used in gas supply networks.

Digestate can be further processed to produce liquor and a fibrous material. The fiber, which can be processed into compost, is a bulky material with low levels of nutrients and can be used as a soil conditioner or a low level fertilizer. A high proportion of the nutrients remain in the liquor, which can be used as a liquid fertilizer.

Biogas Generation:

Biogas is produced through the processing of various types of organic waste. It is a renewable and environmentally friendly fuel made from 100% local feedstocks that is suitable for a diversity of uses including road vehicle fuel and industrial uses. The circular-economy impact of biogas production is further enhanced by the organic nutrients recovered in the production process.Biogas can be produced from a vast variety of raw materials (feedstocks). The biggest role in the biogas production process is played by microbes feeding on the biomass.Digestion carried out by these microorganisms creates methane, which can be used as it is locally or upgraded to biogas equivalent to natural gas quality, enabling the transport of the biogas over longer distances. Material containing organic nutrients is also produced in the process, and this can be utilized for purposes such as agriculture.

Stages in biogas production

Biogas is produced using well-established technology in a process involving several stages:

1. Biowaste is crushed into smaller pieces and slurrified to prepare it for the anaerobic digestion process. Slurrifying means adding liquid to the biowaste to make it easier to process.
2. Microbes need warm conditions, so the biowaste is heated to around 37 °C.
3. The actual biogas production takes place through anaerobic digestion in large tanks for about three weeks.
4. In the final stage, the gas is purified (upgraded) by removing impurities and carbon dioxide.
5. After this, the biogas is ready for use by enterprises and consumers, for example in a liquefied form or following injection into the gas pipeline network.

Turning diverse range of materials into gas

Biogas production starts from the arrival of feedstocks at the biogas plant. A diverse range of solid as well as sludge-like feedstocks can be used.

Materials suitable for biogas production include:

• Biodegradable waste from enterprises and industrial facilities, such as surplus lactose from the production of lactose-free dairy products
• Spoiled food from shops
• Biowaste generated by consumers
• Sludge from wastewater treatment plants
• Manure and field biomass from agriculture

The material is typically delivered to the biogas plant's reception pit by lorry or waste management vehicle.

A delivery of solid matter such as biowaste will next undergo crushing to make its consistency as even as possible. At this point, water containing nutrients obtained from a further stage in the production process is also mixed with the feedstock to take the rate of solid matter down to only around one-tenth of the total volume.

This is also when any unwanted non-biodegradable waste, such as packaging plastic of out-of-date food waste from shops, is separated from the mixture. This waste is taken to a waste treatment facility where it is used to generate heat and electricity. Biomass that has passed through slurrification is combined with biomass delivered in the form of slurry to the biogas plant and pumped into the pre-digester tank where enzymes secreted by bacteria break down the biomass into an even finer consistency.

Next, the biomass is sanitized before entering the actual biogas reactor (digester). In sanitization, any harmful bacteria found in the material are eliminated by heating the mixture to above 70 °C for one hour. Once sanitized, the mass is pumped into the main reactor where biogas production takes place. Sanitization makes it possible to use the fertilizer product in agriculture.

Biomass is turned into gas by microbes

In the biogas reactor, microbial action begins and the biomass enters a gradual process of fermentation.

In practice this means that microbes feed on the organic matter, such as proteins, carbohydrates and lipids, and their digestion turns these into methane and carbon dioxide.

Most of the organic matter is broken down into biogas – a mixture of methane and carbon dioxide – in approximately three weeks. The biogas is collected in a spherical gas holder from the top of the biogas reactors.

Measurements

Measurements

• Accuracy:

The accuracy of a measurement is how close a result comes to the true value.
For example, let’s say you know your true height is exactly 5’9″.You measure yourself with a yardstick and get 5’0″. Your measurement is not accurate.
You measure yourself again with a laser yardstick and get 5’9″. Your measurement is accurate.

Systematic error or Inaccuracy is quantified by the average difference (bias) between a set of measurements obtained with the test method with a reference value or values obtained with a reference method.

• Precision:

Precision is how close two or more measurements are to each other or in other words it refers to how well measurements agree with each other in multiple tests.
If you consistently measure your height as 5’0″ with a yardstick, your measurements are precise.

Random error or Imprecision is usually quantified by calculating the coefficient of variation from the results of a set of duplicate measurements

 

• Significant figures & Rounding:

Significant figures: The significant figures (also known as the significant digits and decimal places) of a number are digits that carry meaning contributing to its measurement resolution. The reliable digits and the first unreliable digit of a measurement are known as significant figure.

Rules for significant figures:

1. All non-zero numbers are significant. The number 33.2 has three significant figures because all of the digits present are non-zero.
2. All zeros between two non-zero digits are significant. 2051 has four significant figures. The zero is between a 2 and a 5.
3. Leading zeros are not significant. They're nothing more than "place holders." the number 0.54 has only two significant figures. 0.0032 also has two significant figures. All of the zeros are leading.
4. In a number with or without a decimal point, Trailing zeros to the right of the decimal are significant. There are four significant figures in 92.00.
5. Trailing zeros in a whole number with the decimal shown are significant. Placing a decimal at the end of a number is usually not done. By convention, however, this decimal indicates a significant zero. For example, "540." indicates that the trailing zero is significant; there are three significant figures in this value.
6. Trailing zeros in a whole number with no decimal shown are not significant. Writing just "540" indicates that the zero is not significant, and there are only two significant figures in this value.
7. Any zero to the right of non-zero digit is significant. All zeros between decimal point and first non-zero digits are not significant. 0.0074 has only two significant digits & 0.06020 has four significant digits.
8. For a number in scientific notation: N x 10^x, all digits comprising N ARE significant by the first 6 rules; "10" and "x" are NOT significant. 5.02 x 10⁴, has THREE significant figures: "5.02." "10 and "4" are not significant.
9. Exact numbers have an INFINITE number of significant figures. This rule applies to numbers that are definitions. For example, 1 meter = 1.00 meters = 1.0000 meters, etc.

Rounding: The basic concept of significant figures is often used in connection with rounding. Rounding to significant figures is a more general-purpose technique than rounding to n decimal places, since it handles numbers of different scales in a uniform way

Process of Rounding off:

1. Decide which is the last digit to keep.
2. In rounding off numbers, the last figure kept should be unchanged if the first figure dropped is less than 5. Example: 6.422 become 6.4.
3. In rounding off numbers, the last figure kept should be increased by 1 if the first figure dropped is greater than 5. Example: 6.997 become 7.00.
4. In rounding off numbers, if the first figure dropped is 5, and there are any figures following the five that are not zero, then the last figure kept should be increased by 1. Example: 6.6501 become 6.7.
5. In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero or if there are no figures after the 5, then the last figure kept should be unchanged if that last figure is even. Example: 6.6500 ≈ 6.6.
6. In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero or if there are no figures after the 5, then the last figure kept should be increased by 1 if that last figure is odd. Example: 6.755000 ≈ 6.76.

• Errors:

An error may be defined as the difference between the true or actual value and the measured value. Errors in measurements may happen from the various sources which are generally categorized into the following type. 

• Gross Errors:

The gross error occurs because of the human mistakes. Gross errors can be defined as physical errors in analysis apparatus or calculating and recording measurement outcomes. In general, these types of errors will happen throughout the experiments, wherever the researcher might study or record a worth different from the real one, possibly due to a reduced view. With human concern, types of errors will predictable, although they can be estimated and corrected.

Such type of error is very common in the measurement. The complete elimination of such type of error is not possible. Some of the gross errors easily detected by the experimenter but some of them are difficult to find. Two methods can remove the gross error.

These types of errors can be prohibited by the following couple of actions:

• Careful reading as well as a recording of information.
•  Taking numerous readings of the instrument by different operators. Secure contracts between different understandings guarantee the elimination of every gross error.

• Random Errors:

This type of error is constantly there in a measurement, which is occurred by essentially random oscillations in the apparatus measurement analysis, sudden change in the atmospheric condition or in the experimenter’s understanding of the apparatus reading. These types of errors show up as dissimilar outcomes for apparently the similar frequent measurement, which can be expected by contrasting numerous measurements, with condensed by averaging numerous measurements. These types of error remain even after the removal of the systematic error. Hence such type of error is also called residual error.

• Systematic Errors:

The systematic errors are mainly classified into three categories.

1. Observational Errors
2. Environmental Errors
3. Instrumental Errors

• Observational Errors: The observational errors may occur due to the fault study of the instrument reading, and the sources of these errors are many. For instance, the indicator of a voltmeter retunes a little over the surface of the scale. As a result, a fault happens except the line of the image of the witness is accurately above the indicator. To reduce the parallax error extremely precise meters are offered with reflected scales.
• Environmental Errors: Environmental errors will happen due to the outside situation of the measuring instruments. These types of errors mostly happen due to the temperature result, force, moisture, dirt, vibration otherwise because of the electrostatic field or magnetic. The remedial measures used to remove these unwanted effects include the following.

1. The preparation should be finished to remain the situations as stable as achievable.
2. By the instrument which is at no cost from these results.
3. With these methods which remove the result of these troubles.
4. By applying the computed modifications.

• Instrumental Errors: Instrumental errors will happen due to some of the following reasons.

• An inherent limitation of Devices:-

These errors are integral in devices due to their features namely mechanical arrangement. These may happen due to the instrument operation as well as the operation or computation of the instrument. These types of errors will make the mistake to study very low otherwise very high.
For instance – If the apparatus uses the delicate spring then it offers the high-value of determining measure. These will happen in the apparatus due to the loss of hysteresis or friction. 

• Abuse of Apparatus:-The error in the instrument happens due to the machinist’s fault. A superior device used in an unintelligent method may provide a vast result. For instance – the abuse of the apparatus may cause the breakdown to change the zero of tools, poor early modification, with lead to very high resistance. Improper observes of these may not reason for lasting harm to the device, except all the similar, they cause faults.

• Effect of Loading:- The most frequent type of this error will occur due to the measurement work in the device. For instance, as the voltmeter is associated to the high-resistance circuit which will give a false reading, as well as after it is allied to the low-resistance circuit, this circuit will give the reliable reading, and then the voltmeter will have the effect of loading on the circuit.

 Calculation of Error 

• Error:

Error in i-th observation,

  

Where x_i is the measured value in i-th observation & 

• Absolute Error:

• Relative Error:

• Percentage Error: Percentage error = Relative error × 100% = 
  

                                                              

• Rules of error calculation in different mathematical operation:

·

• Uncertainty analysis: Uncertainty analysis aims at quantifying the variability of the output that is due to the variability of the input. The quantification is most often performed by estimating statistical quantities of interest such as mean, median, and population quarantines. The estimation relies on uncertainty propagation techniques. Because of the limited sample size, these estimated quantities must be provided with the associated confidence intervals.

The main steps of the uncertainty propagation are summarized below:

1. Identify the model input parameters subject to uncertainty
2. Describe the knowledge about the variables by means of probability density functions and, if relevant, account for correlations between the variables by using multivariate Probability Density Functions (PDFs) or by providing a correlation matrix
3. Generate a sample from the original distribution
4. Execute the computer code for this set of sampled values
5. Apply statistical methods to compute the values of the quantities of interest

Statistical Analysis of Data:

• Arithmetic Mean:

• Mean Deviation: The mean deviation (also called the mean absolute deviation or Average Deviation) is the mean of the absolute deviations of a set of data about the data's mean. For a sample size, the mean deviation is defined by

• Standard Deviation: In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that Cumulative probability of a normal distribution with expected value 0 and standard deviation 1 the values are spread out over a wider range. So The Standard Deviation is a measure of how spreads out numbers are.

So the Standard deviation,

Note: Variance = Square of the standard deviation

Guassian Distribution:

In probability theory, a normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is,