MOT Seminar

8/2/2019 MOT Seminar

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ByHari Narayanan TRKarthik MachaniKeshav K RanganNarayan Srivastava


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All matter is inherently discontinuous, as it is comprised of distinct building blocks,

the molecules. Each molecule consists of a finite number of atoms, which in turn

consist of finite numbers of nuclei and electrons.

Many important physical phenomena involve matter in large length and time scales.

This is generally the case when matter is considered at length scales much larger

than the characteristic length of the atomic spacings and at time scales much larger

than the characteristic times of atomic bond vibrations. The preceding characteristic

lengths (A) and times (fs) can vary considerably depending on the state of the

matter (e.g., temperature, precise composition, deformation).


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As long as the physical problems of interest occur at length and time scales

of several orders of magnitude higher that those noted previously, it is

possible to consider matter as a continuous medium, namely to effectively

ignore its discrete nature without introducing any even remotely significant

errors.


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The behavior of individual molecules comprising a fluid determines the observed

properties of the fluid and for an absolutely complete analysis, the fluid should be

studied at the molecular scale. The behaviour of any one molecule is highly complex,

continuously varying and may indeed be very different from neighboring molecules at

any instant of time.

The problems normally encountered by engineers do not require knowledge and

prediction of behaviour at the molecular level but on the properties of the fluid mass

that may result. Thus the interest is more on the average rather than the individual

responses of the molecules comprising the fluid.

For our analysis weassume that the fluid is a continuum, that is a continuousdistribution of matter with no empty space.


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Materials, such as solids, liquids and gases, are composed of molecules separated by

empty space. On a macroscopic scale, materials have cracks and discontinuities.However, certain physical phenomena can be modelled assuming the materials exist as

a continuum, meaning the matter in the body is continuously distributed and fills the

entire region of space it occupies. A continuum is a body that can be continually sub-

divided into infinitesimal elements with properties being those of the bulk material.

CONTINUUMConsidered as


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Continuum mechanics deals with physical properties of solids and fluids

which are independent of any particular coordinate system in which they

are observed

Concept of continuum

applied to an F1 car.

Here air is considered to be

a medium as a whole andcomposition of air at any

instant is not considered


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Continuum mechanics deals with deformable bodies, as opposed to rigid bodies. A

solid is a deformable body that possesses shear strength. A solid can support shear

forces (forces parallel to the material surface on which they act). Fluids, on the

other hand, do not sustain shear forces. For the study of the mechanical behavior of

solids and fluids these are assumed to be continuous bodies, which means that the

matter fills the entire region of space it occupies, despite the fact that matter ismade of atoms, has voids, and is discrete. Therefore, when continuum mechanics

refers to a point or particle in a continuous body it does not describe a point in the

inter-atomic space or an atomic particle, rather an idealized part of the body

occupying that point.

Internal Forces

External Forces


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Surfaceforces or contactforces, expressed as force per unit area, can act either on

the bounding surface of the body, as a result of mechanical contact with other bodies,

or on imaginary internal surfaces that bound portions of the body, as a result of themechanical interaction between the parts of the body to either side of the surface

When a body is acted upon by external contact forces, internal contact forces are

then transmitted from point to point inside the body to balance their action,

according to Newton's second law of motion of conservation of linear momentum

and angular momentum

In continuum mechanics a body is considered stress-free if the only forces present

are those inter-atomic forces (ionic, metallic, and van der Waals forces) required to

hold the body together and to keep its shape in the absence of all external influences,

including gravitational attraction. Stresses generated during manufacture of the body

to a specific configuration are also excluded when considering stresses in a body.

Therefore, the stresses considered in continuum mechanics are only those producedby deformation of the body, sc. only relative changes in stress are considered, not the

absolute values of stress.


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Bodyforces are forces originating from sources outside of the body that act on the

volume (or mass) of the body

These forces arise from the presence of the body in force fields, e.g.gravitationalfield (gravitational forces) or electromagnetic field (electromagnetic forces), or from

inertial forces when bodies are in motion. As the mass of a continuous body is

assumed to be continuously distributed, any force originating from the mass is also

continuously distributed. Thus, body forces are specified by vector fields which are

assumed to be continuous over the entire volume of the body, i.e. acting on every

point in it.

Body forces and contact forces acting on the body lead to corresponding moments of

force (torques) relative to a given point. Thus, the total applied torque about the

origin is given by


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Gases are one of the classical states of matter (i.e solids, liquids and gases). They have

no definite volume and occupy the entire volume of the container they are stored in.

The molecules in gases have a large intermolecular distance and hence there is little or

no interference from the neighboring molecule. The gas molecules have high energywhen compared to liquids and solids and hence have a high value of mean free path.

Gases are classified into

Real Gas

Ideal Gas


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Boyles Law:Boyles law states that atconstanttemperature for a fixed mass, the absolute pressure and the

volume of a gas are inversely proportional.

Charless Law:

Charless Law states that the volume of an ideal gas at constant pressure is directly proportional

to the absolute temperature.


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Gay-Lussacs Law:Gay-Lussacs law states that an ideal gas, when at constant volume, the pressure is directly

proportional to its absolute temperature.

Avogadros Law:Avogadro's law states that the volume occupied by an ideal gas is proportional to the amountof moles (or molecules) present in the container. This gives rise to the molar volume of a

gas, which at STP is 22.4 dm3 (or liters).

Taking STP to be 101.325 kPa and 273.15 K, we can find the volume of one mole of a gas:


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Ideal Gas Law:The equation of state of an ideal gas which is a good approximation to real gases at

sufficiently high temperatures and low pressures; that is, PV=RT, where P is the pressure, V

is the volume per mole of gas, Tis the temperature, andR is the gas constant.

Where the constant, now named R, is the gas constant with a value of .08206 (atmL)/(molK)

Daltons Law:

Daltons Law is a law stating that the pressure exerted by a mixture of gases equals the sum ofthe partial pressures of the gases in the mixture; the pressure of a gas in a mixture equals the

pressure it would exert if it occupied the same volume alone at the same temperature

OR


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BOYLES LAW

One of the most common and popular applications of Boyles Law is breathing

Pulmonary ventilation, or breathing, is the exchange of air between the atmosphere

and the lungs. As air moves into and out of the lungs, it travels from regions of

high air pressure to regions of low air pressure.

Boyles law is also important in scuba diving


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Pulmonary Ventilation - Explanation

When air is to be sucked in into the lung, the diaphragm and the external intercostal

muscles slightly contract thus enlarging the thoracic/lung cavity. This results in anincreased volume.

From Boyles law, pressure in inversely proportional to volume. Hence, due to

increase in volume of the lung cavity, the pressure drops to a value lesser than the

external pressure. This causes air to be sucked in so that the pressures are equal.

Once the oxygen is absorbed by the blood vessels, the remaining air is to be pushedout of the lungs. To facilitate this the diaphragm and the external intercostal muscles

expand in order to reduce the volume of the lung cavity.

Due to reduction in volume there in an increase in pressure in the lungs. Hence the

air in the lungs rushes out.


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SCUBA DIVINGEXPLANATIONBends or Decompression Illness is caused when a diver ascends too quickly after diving. This

happens when there are nitrogen bubbles formed in the blood stream due to the sudden

expansion of the gas. Expansion of the gas takes as the pressure drops considerably over a short

period of time.

Also

What Boyle's Law Means On A Dive

In volumetric terms, this means that for a diver:

At the surface, or 0 feet seawater (fsw), the air in a divers lungs--is under one atmosphere of

pressure (1 ata), which equals 14.7 pounds per square inch (psi) pressure. Likewise for the airin their buoyancy compensator (BC).

At a depth of 33 fsw, the weight of the water column is equal to another atmosphere, so now

the pressure on the divers body is two atmospheres absolute (2 ata, or 29.4 psi). The divers

lungs are now compressed to one-half their surface volume. In addition, their BC has lost

volume and therefore buoyancy ; they may need to add air to to control their descent.

At a depth of 66 fsw, the pressure is 3 atmospheres absolute (3 ata, or 44.1 psi), and the

divers lungs are one-third their surface volume. Again, it may be necessary to to add air to theBC.

At a depth of 99 fsw, the pressure is 4 atmospheres absolute (4 ata, or 58.8 psi), and the lung

volume of the diver is one-quarter their surface volume. At this depth, the amount of air that

must be added to a BC to maintain control begins to be significant.


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VAPOUR COMPRESSION REFRIGERATION

The vapour compression refrigeration cycle is an important and very commonly

used application of the gas laws.


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WORKING:

The refrigerant is in the form of vapour at low pressure and low temperature

before it enters the compressor. In the compressor the vapour is compressedisentropically. As the vapour is compressed, its pressure is increased

substantially. Hence the volume decreases (Boyles Law) and the temperature

increases(Gay-Lussacs Law).

Due to the increase in temperature, the refrigerant is in the form of a hot vapour.

This hot vapour then enters the condenser where it loses its heat to an external

medium like air or water. Due to the loss in heat the refrigerant condenses intoliquid.

This liquid vapour passes into an expansion value. Here the pressure is dropped

to a very low value due to sudden expansion of the refrigerant(Boyles Law)

and due to this the temperature of the refrigerant also falls to a very low

value(Charles Law).

This low temperature liquid refrigerant is then passed in to the evaporator whereis gains heat from the surrounding medium, therefore cooling it.


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Expansion Valve Compressor

RELEVANT COMPONENTS OF REFRIGERATOR


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OTHER APPLICATIONS

Aerosol Cans

When you discard a used aerosol can into a fire and it explodes. First off, P

increases as T increases, until the can ruptures. The propellant in aerosol cans

these days is butane. Consequently the can explodes. This is an illustration of Gay-

Lussacs Law


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In the filling of tyres with air, air from a compressor is pumped into the tyre at

very high pressure. Once it is completely filled the tyre forms a closed system.

At any instant the air inside the tyre will have only a certain number of molecules

present in it. This is in accordance with Avogadros Law.

Domestic Gas cylinders and Air brakes

also work on gas law principles

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