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kinetic

Energy of motion is usually called "kinetic energy."

A simple example of the transformation of kinetic energy into potential energy, and vice versa, is afforded by the pendulum.

Available kinetic energy is possessed by a system of two or more bodies in virtue of the relative motion of its parts.

If a body whose mass is m grammes be moving with a velocity of v centimetres per second relative to the earth, the available kinetic energy possessed by the system is Zmv 2 ergs if m be small relative to the earth.

Thus the estimation of kinetic energy is intimately affected by the choice of our base of measurement.

These static and kinetic conditions succeed each other rapidly, and the result is to detach or throw off from the antenna semi-loops of electric force, which move outwards in all directions and are accompanied by expanding circular lines of magnetic force.

This energy is obtained especially by the chioroplastids, and part of it is at once devoted to the construction of carbohydrate material, being thus turned from the kinetic to the potential condition.

There is probably but little transformation of one form of kinetic energy into another in the plant.

Expenditure of Energy by Plants.The energy of the plant is, af we have seen, derived originally from the kinetic radiant energy 01 the sun.

This equation, which is mathematically deducible from the kinetic theory of gases, expresses the behaviour of gases, the phenomena of the critical state, and the behaviour of liquids; solids are not accounted for.

Now the unstable movements of the needles are of a mechanically irreversible character; the energy expended in dissociating the members of a combination and placing them in unstable positions assumes the kinetic form when the needles turn over, and is ultimately frittered down into heat.

Instead of following the motion of each individual part of a material system, he showed that, if we determine its configuration by a sufficient number of variables, whose number is that of the degrees of freedom to move (there being as many equations as the system has degrees of freedom), the kinetic and potential energies of the system can be expressed in terms of these, and the differential equations of motion thence deduced by simple differentiation.

Besides this most important contribution to the general fabric of dynamical science, we owe to Lagrange several minor theorems of great elegance, - among which may be mentioned his theorem that the kinetic energy imparted by given impulses to a material system under given constraints is a maximum.

As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of time considered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium.

b2' and this, by § 36, is also the ratio of the kinetic energy in the annular 4,1 interspace between the two cylinders to the kinetic energy of the liquid moving bodily inside r = b.

The kinetic energy of the liquid inside a surface S due to the velocity function 4' f i (s given by T=2p + (d) 2+ (t) dxdydz, pff f 75 4 dS (I) by Green's transformation, dv denoting an elementary step along the normal to the exterior of the surface; so that d4ldv = o over the surface makes T = o, and then (d4 2 d4) 2 'x) + (dy) + (= O, dd?

In plane motion the kinetic energy per unit length parallel to Oz T 2p J J [(d4)) 2+ (d dy (P)1dxdy=lpfl[ a) 2+ (=zp 4d ds=zp f, ydvds.

(to) Integrating over the base, to obtain one-third of the kinetic energy T, 3T = 2 pf '3 4R2(3x4-h4)dx/h 3 = pR2h4 / 1 35 V 3 (II) so that the effective k 2 of the liquid filling the trianglc is given by k 2 = T/Z p R 2 A = 2h2/45 = (radius of the inscribed circle) 2, (12) or two-fifths of the k 2 for the solid triangle.

But supposing them determined for the motion of a body through a liquid, the kinetic energy T of the system, liquid and body, is expressible as a quadratic function of the components U, V, W, P, Q, R.

Conversely, if the kinetic energy T is expressed as a quadratic function of x, x x3, y1, y2, y3, the components of momentum, the partial differential coefficient with respect to a momentum component will give the component of velocity to correspond.

These theorems, which hold for the motion of a single rigid body, are true generally for a flexible system, such as considered here for a liquid, with one or more rigid bodies swimming in it; and they express the statement that the work done by an impulse is the product of the impulse and the arithmetic mean of the initial and final velocity; so that the kinetic energy is the work done by the impulse in starting the motion from rest.

In the motion which can be solved by the elliptic function, the most general expression of the kinetic energy was shown by A.

ZI /t = - (a - s) M'Q 2 sine cos ° - EQ sin() =[ - (a - (3)M'U+E]V (8) Now suppose the cylinder is free; the additional forces acting on the body are the components of kinetic reaction of the liquid - aM' (Ç_vR), - (3M' (-- E -FUR), - EC' dR, (9) so that its equations of motion are M (Ç - vR) _ - aM' (_vR) - (a - $) M'VR, (io) M (Ç+uR) = - OM' (dV+U R) - (a - ()M'UR - R, '(II) C dR = dR + (a - Q)M'UV+0V; (12) and putting as before M+aM'=ci, M+13M' = c2, C+EC'=C3, ci dU - c2VR=o, dV +(c1U+E)R=o, c 3 dR - (c 1 U+ - c 2 U)V =o; showing the modification of the equations of plane motion, due to the component E of the circulation.

If we consider any short length of the stream bounded by two imaginary cross-sections A and B on either side of the plug, unit mass of the fluid in passing A has work, p'v', done on it by the fluid behind and carries its energy, E'+ U', with it into the space AB, where U' is the kinetic energy of flow.

The energy is less than that of an ideal gas by the term npc. If we imagine that the defect of volume c is due to the formation of molecular aggregates consisting of two or more single molecules, and if the kinetic energy of translation of any one of these aggregates is equal to that of one of the single molecules, it is clear that some energy must be lost in co-aggregating, but that the proportion lost will be different for different types of molecules and also for different types of co-aggregation.

The loss of energy could not be greater than this on the simple kinetic theory, unless there were some evolution of latent heat of co-aggregation, due to the work done by the mutual attractions of the co-aggregating molecules.

If mechanical work or kinetic energy is directly converted into heat by friction, reversal of the motion does not restore the energy so converted.

In this case the work of expansion, pdv, is expended in the first instance in producing kinetic energy of motion of parts of the gas.

U, Kinetic energy of flow of fluid.

Tait and Dewar, as a consequence of the kinetic theory of the constitution of gaseous media.

The hypothesis that the state was steady, so that interchanges arising from convection and collisions of the molecules produced no aggregate result, enabled him to interpret the new constants involved in this law of distribution, in terms of the temperature and its spacial differential coefficients, and thence to express the components of the kinetic stress at each point in the medium in terms of these quantities.

In point of fact it is found that the properties which are most easily explained are those connected with the gaseous state; the explanation of these properties in terms of the molecular structure of matter is the aim of the " Kinetic Theory of Gases."

The best estimates which we now possess of the sizes of molecules are provided by calculations based upon the kinetic theory of gases.

In the following table are given the values of the diameters of the molecules of six substances with which it is easy to experiment in the gaseous state, these values being calculated in different ways from formulae supplied by the kinetic theory.

The agreement of the values obtained for the same quantity by different methods provides valuable confirmation of the truth of the molecular theory and of the validity of the methods of the kinetic theory of gases.

originally impinged on that at rest is now represented by the energy, kinetic and potential, of the small motions of the individual molecules.

The kinetic theory of gases attempts to give a mathematical account, in terms of the molecular structure of matter, of all the non-chemical and non-electrical properties of gases.

The remainder of this article is devoted to a brief statement of the methods and results of the kinetic theory.

The Kinetic Theory of Gases.

The determination of the series of configurations developing out of given initial conditions is not, however, the problem of the kinetic theory: the object of this theory is to explain the general properties of all gases in terms only of their molecular structure.

(21) The comparison of this formula with experiment provides a striking confirmation of the truth of the kinetic theory but at the same time discloses the most formidable difficulty which the theory has so far had to encounter.

The kinetic energy of the molecules of these gases must contain two terms in addition to those representing translational energy.

For a rigid body the kinetic energy will, in general, consist of three terms (AW1 2 +BW2 2 +CW3 2) in addition to the translational energy.

We shall show that if we sum these up for a whole wave the potential energy is equal to the kinetic energy.

The kinetic energy per cubic centimetre is 2 pu t, where is the density and u is the velocity of disturbance due to the passage of the wave.

If r is of the order of A, n is of the order of y; and the kinetic energy of the radial motion is of the same order as that of the longitudinal motion.

During the quarter swing ending with greatest nodal pressure, the kinetic energy is changed to potential energy manifested in the increase of pressure.

This becomes again kinetic in the second quarter swing, then in the third quarter it is changed to potential energy again, but now manifested in the decrease of pressure.

In the last quarter it is again turned to the kinetic form.

There will be more kinetic energy formed in the return journey and the vibration tends to grow.

But if the heat is given at the instant of greatest rarefaction, the increase of pressure lessens the difference from the undisturbed pressure, and lessens the potential energy, so that during the return less kinetic energy is formed and the vibration tends to die away.

Let E be the effective elasticity of the aether; then E = pc t, where p is its density, and c the velocity of light which is 3 X 10 10 cm./sec. If = A cos" (t - x/c) is the linear vibration, the stress is E dE/dx; and the total energy, which is twice the kinetic energy Zp(d/dt) 2 dx, is 2pn2A2 per cm., which is thus equal to 1.8 ergs as above.

If we rest on the synthesis here described, the energy of the matter, even the thermal part, appears largely as potential energy of strain in the aether which interacts with the kinetic energy associated with disturbances involving finite velocity of matter.

When the atoms are in motion these strain-forms produce straining and unstraining in the aether as they pass across it, which in its motional or kinetic aspect constitutes the resulting magnetic field; as the strains are slight the coefficient of ultimate inertia here involved must be great.

After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area Acpm, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e d2 I + p, a in which the factor 4(k 2 /d 2)tan 2 S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than I %.

The importance of a study of the changes of the vis viva depending on squares of velocities, or what is now called the "kinetic energy" of a system, was recognized in Newton's time, especially by Leibnitz; and it was perceived (at any rate for special cases) that an increase in this quantity in the course of any motion of the system was otherwise expressible by what we now call the "work" done by the forces.

The energy of a system is the measure of its capacity for doing work, on the assumption of suitable connexions with other systems. When the motion of a body is checked by a spring, its kinetic energy being destroyed, the spring, if perfectly elastic, is capable of restoring the motion; but if it is checked by friction no such restoration can be immediately effected.

On certain assumptions required for the extension of the methods of the kinetic theory of gases to liquids, L.

We can calculate, by the help of the kinetic theory and the theory of chances, the frequency with which the necessary conjunctions of ions will occur, and show that the general law will be that the coagulative powers should be in the ratios of 1: x: x 2.

4, which, according to the kinetic theory, is an indication that an important fraction of the energy absorbed is devoted to rotation or vibration.

It is much more probable that heat is really the kinetic energy of motion of the molecules, and is passed on from one to another by collisions.

The high conductivity of metals is then explained by the small mass and high velocity of diffusion of these electric atoms. Assuming the kinetic energy of an electric atom at any temperature to be equal to that of a gaseous molecule, its velocity, on Sir J.

On the kinetic theory the molecules of a gas are relatively far apart and there is nothing analogous to friction between two adjacent layers A and B moving with different velocities.

This potential energy becomes kinetic when the slag is brought into contact with lime in the presence of water, and causes the formation of a true hydraulic silicate of lime.

Thus The Direct Experimental Evidence Is Somewhat Meagre And Conflicting, But The Question Of The Relation Of The Specific Heats Of Gases Is One Of Great Interest In Connexion With The Kinetic Theory And The Constitution Of The Molecule.

According To The Elementary Kinetic Theory Of An Ideal Gas, The Molecules Of Which Are So Small And So Far Apart That Their Mutual Actions May Be Neglected, The Kinetic Energy Of Translation Of The Molecules Is Proportional To The Absolute Temperature, And Is Equal To 3/2 Of Pv, The Product Of The Pressure And The Volume, Per Unit Mass.

If The Molecules Are Supposed To Be Like Smooth, Hard, Elastic Spheres, Incapable Of Receiving Any Other Kind Of Energy Except That Of Translation, The Specific Heat At Constant Volume Would Be The Increase Per Degree Of The Kinetic Energy Namely 3Pv/20=3R/2, That At Constant Pressure Would Be 5R/2, And The Ratio Of The Specific Heats Would Be 5/3 Or 1.666.

In 1879 Maxwell Considered It One Of The Greatest Difficulties Which The Kinetic Theory Had Yet Encountered, That In Spite Of The Many Other Degrees Of Freedom Of Vibration Revealed By The Spectroscope, The Experimental Value Of The Ratio S/S Was 1.40 For So Many Gases, Instead Of Being Less Than 4/3.

When Bosanquet says that in " Heat is a mode of motion " there is no reference to individual objects, but " a pure hypothetical form which absolutely neglects the existence of objects," he falls far short of expressing the nature of this scientific judgment, for in his Theory of Heat Clerk Maxwell describes it as " believing heat as it exists in a hot body to be in the form of kinetic energy."

If steam or vapour is " wire-drawn " or expanded through a porous plug or throttling aperture without external loss or gain of heat, the total heat (E+pv) remains constant (Thermodynamics, § I I), provided that the experiment is arranged so that the kinetic energy of flow is the same on either side of the throttle.

The mass-system is then said to possess kinetic symmetry about 0.

Young in connection with the kinetic theory of the tides, where the same point arises.

The product 4muf is called the kinetic energy of the particle, and the equation.

(21) is therefore equivalent to the statement that the increment of the kinetic energy is equal to the work done on the particle.

which asserts that when no extraneous forces act the sum of the kinetic and potential energies is constant.

be to increase the sum of the kinetic and potential energies by an amount equal to the work done by them.

If we assume that there is no loss of apparent kinetic energy we have also miuii +miuf2 = miui2 +mfuzi.

It follows from the formula 15 (10) for the internal kinetic energy of a system of particles that as a result of the impact this energy is diminished by the amount i m1mi 2(1 _ei)m+m(ui_uf)1.

The unit of work on the same principles is ML2T2, and itis to be noticed that this is identical with the unit of kinetic energy.

Next consider the kinetic energy of the system.

the total kinetic energy is equal to the kinetic energy of the whole mass supposed concentrated at G and moving with this point, together with the kinetic energy of the motion relative to G.

The latter may be called the internal kinetic energy of the system.

which expresses the internal kinetic energy in terms of the relative velocities of the several pairs of particles.

Also by (10) the internal kinetic energy is - m,m~

mif-mi The increase of the kinetic energy of the system in any interval of time will of course be equal to the total work done by all the forces acting on the particles.

If T denote the kinetic energy, we may say then that the sum T + V is in any interval of time increased by an amount equal to the work done by the extraneous forces.

The increase of the kinetic energy of a rigid body in any interval of time is equal to the work done by the extraneous forces acting on the body.

(13) The left-hand side is the kinetic energy of the whole mass, supposed concentrated at G and moving with this point, together with the kinetic energy of the motion relative to G (15); and the right-hand member represents the integral work done by the extraneous forces in the successive infinitesimal displacements into which the motion may be resolved.

the kinetic energy is 3/4MK262+

If q be any variable co-ordinate defining the position or (in the case of a system of bodies) the configuration, the velocity of each particle at any instant will be proportional to 4, and the total kinetic energy may be expressed in the form 1/8A42, where A is in general a function of q The special case where both cones are right circular and a is constant is important ~n astronomy and also in mechanism (theory of bevel wheels).

If m be the mass of a particle at P, and PN the perpendicular to the instantaneous axis, the kinetic energy T is given by 2T=2~{m(w.

In this case the kinetic energy is given by 2T = M0 (u1 +v2+w1) +AP2 +Bq2 +Cr2 2Fqr 2Grp 2Hpq, (13) where M0 is the mass, and A, B, C, F, G, H are the moments and products of inertia with respect to the mass-centre; cf.

Hence the change of kinetic energy is TT=~.1/8(u+u) +n.1/8(v+v)+1.1/8(w+w),

We are thus led to the following statement: the change of kinetic energy due to any system of impulsive forces is equal to the sum of the products of the several forces into the semisum of the initial and final velocities of their respective points of application, resolved in the directions of the forces.

77 the kinetic energy generated is ~M (ic2H- Cq2)cuf, if C be the instantaneous centre; this is seen to be equal to ~F.

The kinetic energy T of the motion relative to 0 will be constant.

Motion of a Solid of Revolution.In the case of a solid of revolution, or (more generally) whenever there is kinetic syminetry about an asks through the mass-centre, or through a fixec point 0, a number of interesting problems can be treated almost directly from first principles.

If the direction of the axis of kinetic symmetry be specified by means of the angular co-ordinates 0, ~

kinetic energy is given by 2T=A(O2+sinO ~2)+Cnh.

The former is, in fact, equal to 2T, and the latter to ~2, where T is the kinetic energy an.d r the resultant angular momentum.

If OA, OB, OC be principal axes of inertia of a solid, and if A, B, C denote the corresponding moments of inertia, the kinetic energy is given by 2TA(~ sin 4,sin 0 cos 44~)2+B Ce cos 4,+sin0 sin$)i +C (~+cos0~)2.

This equation expresses that the kinetic energy is increasing at a rate equal to that at which work is being done by the forces.

To apply the equations (11) to the case of the top we start with the expression (15) of 22 for the kinetic energy, the simplified form (i) of 20 being for the present purpose inadmissible, since it is essential that the generalized co-ordinates employed should be competent to specify the position of every particle.

Connecting the experimental study of the physical and chemical properties is the immense theoretical edifice termed the kinetic theory of gases.

But no one can tell whether the study of physiological phenomena in general, and of nervous phenomena in particular, will not reveal to us, besides the vis viva or kinetic energy of which Leibnitz spoke, and the potential energy which was a later and necessary adjunct, some new kind of energy which may differ from the other two by rebelling against calculation" (Bergson, Time and Free Will, Eng.

203) show that chemical action is to be referred to the latter of these vectors, but whether Fresnel's or Neumann's hypothesis be correct is only to be decided when we know if it be the mean kinetic energy or the mean potential energy that determines chemical action.

Ann., 1875), who regarded electricity as consisting of atoms much smaller than those of matter, and supposed that heat was the kinetic energy of these electric atoms. If we suppose that an electric current in a metal is a flow of negative electric atoms in one direction, the positive electricity associated with the far heavier material atoms remaining practically stationary, and if the atomic heat of electricity is of the same order as that of an equivalent quantity of hydrogen or any other element, the heat carried per ampere-second at o C., namely P, would be of the order of 030 of a joule, which would be ample to account for all the observed effects on the convection theory.

Coulomb pointed out long ago that the resistance of a body to be set in motion was in many cases much greater than the resistance which it offered to continued motion; and since his time writers have always distinguished the "friction of rest," or static friction, from the "friction of motion," or kinetic friction.

These experiments distinctly point to the conclusion, although without absolutely proving it, that in such cases the coefficient of kinetic friction gradually increases as the velocity becomes extremely small, and passes without discontinuity into that of static friction.

accelerated from rest, also acquires kinetic energy and so its inertial mass must increase as speed increases.

G-actin was polymerized into F-actin in a similar kinetic process to rabbit muscle actin was polymerized into F-actin in a similar kinetic process to rabbit muscle actin.

Kinetic methods which measure the clearances (removal) of urea and creatinine are now the gold standard for the assessment of dialysis adequacy.

Bayesian inference for stochastic kinetic models using a diffusion approximation.

Research areas include bioenergetics, molecular biology, fermentation, protein biochemistry, kinetic and paramagnetic spectroscopy and X-ray crystallography.

Chen, O. Delumeau and M. Yudkin) we are measuring a variety of kinetic and equilibrium constants for RsbT and RsbU.

dispersion relation for the arbitrary velocity distribution in a fully kinetic limit is obtained.

Viscid silk also needs to absorb the kinetic energy of the fly, corresponding to a high value.

Hamiltonian matrix is then calculated using the discrete Fast Fourier Transform method to compute the kinetic energy part of the operator.

Hence one can generally safely neglect kinetic inductance for normal electronics.

inelastic collisions are those in which kinetic energy is not conserved.

instantaneous snapshot during the interaction of incoming wake with gas turbine blade showing dynamically adapted mesh & turbulence kinetic energy distribution.

The kinetic transport coeffs. are computed from explicit collision integrals and compared favorably with detailed simulations.

A constellation of space-based kinetic interceptors could not be deployed for many years, although small numbers of prototypes could possibly be deployed earlier.

Waves and instabilities in fully ionized (and magnetized) fluid and kinetic plasmas will also be addressed.

Kinetic Whitney falls in with some former jocks who have kryptonite tattoes that give them the power to walk through the walls.

This means that you already have 108 thousand joules of kinetic energy for every kg.

kinetic energy of the air current, cooling the air which then descends.

kinetic sculpture given to the house by the artist George Rickey.

kinetic modeling.

kinetic theory of gases.

kinetic equations to the level of fluid mechanics.

kinetic parameters like K m.

A high temperature from a match or spark etc., gives the reactant molecules enough kinetic energy to overcome the activation energy * .

There is an incredibly kinetic dynamic to act for him.

If enough individuals turn kinetic, it starts accelerating into a collective form.

Tony comments that, " although the structure was fastened, as the viewer moved around the form it became kinetic.

kinetic energy of the fly, corresponding to a high value.

Viscid silk also needs to absorb the kinetic energy of the fly, corresponding to a high value.

Air from the atmosphere enters the eye of the first impeller it then acquires kinetic energy from the rotating impellers.

Mecca simply wanted what they eventually got - pure raw, kinetic energy dispersed under a geometric ceiling that resembled an inverted space station.

In both static and kinetic perimetry, the effective visual field enlarged during the training.

Kinetic studies on the nanosecond timescale are also possible using a laser flash photolysis instrument.

In both cases, we need extensive experimental studies seeking to identify all long-lived polymorphs in order to understand the kinetic factors involved.

This should ensure that the data-mining analysis could find the most effective correlation between the observed polymorphs and the predicted thermodynamic and kinetic properties.

Hence, we need to rationalize the kinetic factors that can lead to the observation of metastable polymorphs.

Kinetic an crystallographic analysis of the key active site acid/base arginine in a soluble fumarate reductase.

Identification of the active site acid/base catalyst in a bacterial fumarate reductase: a kinetic and crystallographic study.

The high kinetic energies are needed to overcome the repulsion of the two positive nuclei.

It slows down, losing kinetic energy as its potential energy, of electrical repulsion, increases in compensation.

kinetic sculptures by Jean Tinguely are on display to 24th September.

These kinetic differences were confirmed by short-term in vitro culture both in fetal calf serum and in AS.

viscid silk also needs to absorb the kinetic energy of the fly, corresponding to a high value.

instantaneous snapshot during the interaction of incoming wake with gas turbine blade showing dynamically adapted mesh & turbulence kinetic energy distribution.

Q: Is bug splat only for kinetic weapons?

He played a bouncy techno set from the hazy days of Kinetic alongside Storm.

Topics include: chemical thermodynamics, kinetic molecular theory, chemical kinetics, and statistical thermodynamics.

The increased kinetic motion of some receiving molecules should become vigorous enough to dislodge electrons.

For the best solution a prize was offered by the philosophical faculty of the University, and this he succeeded in winning with the paper which was published in 1880 on the "Kinetic Energy of Electricity in Motion."

Energy of motion is usually called "kinetic energy."

A simple example of the transformation of kinetic energy into potential energy, and vice versa, is afforded by the pendulum.

When passing through its position of equilibrium, since gravity can do no more work upon it without changing its fixed point of support, all the energy of oscillation is kinetic. At intermediate positions the energy is partly kinetic and partly potential.

Available kinetic energy is possessed by a system of two or more bodies in virtue of the relative motion of its parts.

If a body whose mass is m grammes be moving with a velocity of v centimetres per second relative to the earth, the available kinetic energy possessed by the system is Zmv 2 ergs if m be small relative to the earth.

Thus the estimation of kinetic energy is intimately affected by the choice of our base of measurement.

When the stresses acting between the parts of a system depend only on the relative positions of those parts, the sum of the kinetic energy and potential energy of the system is always the same, provided the system be not acted upon by anything outside it.

In some cases, as when heat is converted into the kinetic energy of moving machinery or the potential energy of raised weights, there is an ascent of energy from the less available form of heat to the more available form of mechanical energy, but in all cases this is accompanied by the transfer of other heat from a body at a high temperature to one at a lower temperature, thus losing availability to an extent that more than compensates for the rise.

These static and kinetic conditions succeed each other rapidly, and the result is to detach or throw off from the antenna semi-loops of electric force, which move outwards in all directions and are accompanied by expanding circular lines of magnetic force.

This energy is obtained especially by the chioroplastids, and part of it is at once devoted to the construction of carbohydrate material, being thus turned from the kinetic to the potential condition.

Thus even ir these constructive processes there occurs a constant pas,age of energy backwards and forwards from the kinetic to the potential condition and vice versa.

There is probably but little transformation of one form of kinetic energy into another in the plant.

Expenditure of Energy by Plants.The energy of the plant is, af we have seen, derived originally from the kinetic radiant energy 01 the sun.

These expressions indicate what frequent changes in the power are required as the train pursues its journey up and down gradients, against wind resistance, j ournal friction and perhaps the resistance of a badly laid track; and show how both the potential energy and kinetic energy of the train are continually changing: the first from a change in vertical position due to the gradients, the second from changes in speed.

One of his greatest investigations bore on the " Kinetic Theory of Gases."

Between 1886 and 1892 he published a series of papers on the foundations of the kinetic theory of gases, the fourth of which contained what was, according to Lord Kelvin, the first proof ever given of the Waterstdn-Maxwell theorem of the average equal partition of energy in a mixture of two different gases; and about the same time he carried out investigations into impact and its duration.

This equation, which is mathematically deducible from the kinetic theory of gases, expresses the behaviour of gases, the phenomena of the critical state, and the behaviour of liquids; solids are not accounted for.

By considerations based on the kinetic theory of gases (see Molecule) it may be shown that when no energy is utilized in separating the atoms of a molecule, this ratio is 5/3= 1.67.

Now the unstable movements of the needles are of a mechanically irreversible character; the energy expended in dissociating the members of a combination and placing them in unstable positions assumes the kinetic form when the needles turn over, and is ultimately frittered down into heat.

Instead of following the motion of each individual part of a material system, he showed that, if we determine its configuration by a sufficient number of variables, whose number is that of the degrees of freedom to move (there being as many equations as the system has degrees of freedom), the kinetic and potential energies of the system can be expressed in terms of these, and the differential equations of motion thence deduced by simple differentiation.

Besides this most important contribution to the general fabric of dynamical science, we owe to Lagrange several minor theorems of great elegance, - among which may be mentioned his theorem that the kinetic energy imparted by given impulses to a material system under given constraints is a maximum.

As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of time considered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium.

b2' and this, by § 36, is also the ratio of the kinetic energy in the annular 4,1 interspace between the two cylinders to the kinetic energy of the liquid moving bodily inside r = b.

With liquid of density p, this gives rise to a kinetic reaction to acceleration dU/dt, given by 7rp b 2 a 2 b l b d J = a 2 +b2 M' dU, if M' denotes the mass of liquid displaced by unit length of the cylinder r =b.

Round the cylinder r=a held fixed in the U current the liquid streams past with velocity q' =2U sin 0+m/a; (2) and the loss of head due to this increase of velocity from U to q' is q' 2 -U 2 - (2U sin e to space filled with liquid, and at rest at infinity, the cylinder will experience components of force per unit length (i.) -27rpmV, 27rpmU, due to the vortex motion; 2 dU 2dV (ii.) -71-pa 2 w,, -7rpa dt, due to the kinetic reaction of the liquid; (iii.) o, -7r(a-p)a 2 g, due to gravity, taking Oy vertically upward, and denoting the density of the cylinder by a; so that the equations of motion are 71-0-a 2 - di r = - 7pa2- -- 22rpmV, (4) aa 2 - = -7rpa 2 dV +27rpmV - 7r(cr - p) a2g, (5) 7r or, putting m = a 2 w, so that the vortex velocity is due to an angular velocity w at a radius a, (o+p)dU/dt+2pwV =o, (6) (a+ p) dV /dt - 2 pwU + (v - p)g = o.

The kinetic energy of the liquid inside a surface S due to the velocity function 4' f i (s given by T=2p + (d) 2+ (t) dxdydz, pff f 75 4 dS (I) by Green's transformation, dv denoting an elementary step along the normal to the exterior of the surface; so that d4ldv = o over the surface makes T = o, and then (d4 2 d4) 2 'x) + (dy) + (= O, dd?

To find the kinetic energy of such motion in a multiply connected space, the channels must be supposed barred, and the space made acyclic by a membrane, moving with the velocity of the liquid; and then if k denotes the cyclic constant of 0 in any circuit, or the value by which 4) has increased in completing the circuit, the values of 0 on the two sides of the membrane are taken as differing by k, so that the integral over the membrane dS= k f ?

d ddS, and this term is to be added to the terms in (I) to obtain the additional part in the kinetic energy; the continuity shows that the integral is independent of the shape of the barrier membrane, and its position.

In plane motion the kinetic energy per unit length parallel to Oz T 2p J J [(d4)) 2+ (d dy (P)1dxdy=lpfl[ a) 2+ (=zp 4d ds=zp f, ydvds.

(to) Integrating over the base, to obtain one-third of the kinetic energy T, 3T = 2 pf '3 4R2(3x4-h4)dx/h 3 = pR2h4 / 1 35 V 3 (II) so that the effective k 2 of the liquid filling the trianglc is given by k 2 = T/Z p R 2 A = 2h2/45 = (radius of the inscribed circle) 2, (12) or two-fifths of the k 2 for the solid triangle.

But supposing them determined for the motion of a body through a liquid, the kinetic energy T of the system, liquid and body, is expressible as a quadratic function of the components U, V, W, P, Q, R.

Conversely, if the kinetic energy T is expressed as a quadratic function of x, x x3, y1, y2, y3, the components of momentum, the partial differential coefficient with respect to a momentum component will give the component of velocity to correspond.

These theorems, which hold for the motion of a single rigid body, are true generally for a flexible system, such as considered here for a liquid, with one or more rigid bodies swimming in it; and they express the statement that the work done by an impulse is the product of the impulse and the arithmetic mean of the initial and final velocity; so that the kinetic energy is the work done by the impulse in starting the motion from rest.

In the motion which can be solved by the elliptic function, the most general expression of the kinetic energy was shown by A.

ZI /t = - (a - s) M'Q 2 sine cos Ã‚° - EQ sin() =[ - (a - (3)M'U+E]V (8) Now suppose the cylinder is free; the additional forces acting on the body are the components of kinetic reaction of the liquid - aM' (Ã‡_vR), - (3M' (-- E -FUR), - EC' dR, (9) so that its equations of motion are M (Ã‡ - vR) _ - aM' (_vR) - (a - $) M'VR, (io) M (Ã‡+uR) = - OM' (dV+U R) - (a - ()M'UR - R, '(II) C dR = dR + (a - Q)M'UV+0V; (12) and putting as before M+aM'=ci, M+13M' = c2, C+EC'=C3, ci dU - c2VR=o, dV +(c1U+E)R=o, c 3 dR - (c 1 U+ - c 2 U)V =o; showing the modification of the equations of plane motion, due to the component E of the circulation.

If we consider any short length of the stream bounded by two imaginary cross-sections A and B on either side of the plug, unit mass of the fluid in passing A has work, p'v', done on it by the fluid behind and carries its energy, E'+ U', with it into the space AB, where U' is the kinetic energy of flow.

The assumption usually made is that the total kinetic energy of the molecules, including possible energy of rotation or vibration if the molecules consist of more than one atom, is proportional to the energy of translation in the case of an ideal gas.

The energy is less than that of an ideal gas by the term npc. If we imagine that the defect of volume c is due to the formation of molecular aggregates consisting of two or more single molecules, and if the kinetic energy of translation of any one of these aggregates is equal to that of one of the single molecules, it is clear that some energy must be lost in co-aggregating, but that the proportion lost will be different for different types of molecules and also for different types of co-aggregation.

The loss of energy could not be greater than this on the simple kinetic theory, unless there were some evolution of latent heat of co-aggregation, due to the work done by the mutual attractions of the co-aggregating molecules.

If mechanical work or kinetic energy is directly converted into heat by friction, reversal of the motion does not restore the energy so converted.

In this case the work of expansion, pdv, is expended in the first instance in producing kinetic energy of motion of parts of the gas.

If this could be co-ordinated and utilized without dissipation, the gas might conceivably be restored to its initial state; but in practice violent local differences of pressure and temperature are produced, the kinetic energy is rapidly converted into heat by viscous eddy friction, and residual differences of temperature are equalized by diffusion throughout the mass.

As the section of the tube varies, the change of kinetic energy of flow, dU, is represented by The flow in this case is reversible, and the state of the fluid is the same at points where the section of the tube is the same.

U, Kinetic energy of flow of fluid.

Tait and Dewar, as a consequence of the kinetic theory of the constitution of gaseous media.

The hypothesis that the state was steady, so that interchanges arising from convection and collisions of the molecules produced no aggregate result, enabled him to interpret the new constants involved in this law of distribution, in terms of the temperature and its spacial differential coefficients, and thence to express the components of the kinetic stress at each point in the medium in terms of these quantities.

In point of fact it is found that the properties which are most easily explained are those connected with the gaseous state; the explanation of these properties in terms of the molecular structure of matter is the aim of the " Kinetic Theory of Gases."

The best estimates which we now possess of the sizes of molecules are provided by calculations based upon the kinetic theory of gases.

In the following table are given the values of the diameters of the molecules of six substances with which it is easy to experiment in the gaseous state, these values being calculated in different ways from formulae supplied by the kinetic theory.

The agreement of the values obtained for the same quantity by different methods provides valuable confirmation of the truth of the molecular theory and of the validity of the methods of the kinetic theory of gases.

The kinetic energy with which the moving mass.

originally impinged on that at rest is now represented by the energy, kinetic and potential, of the small motions of the individual molecules.

It is known, however, that when two bodies impinge, the kinetic energy which appears to be lost from the mass-motion of the bodies is in reality transformed into heat-energy.

The kinetic theory of gases attempts to give a mathematical account, in terms of the molecular structure of matter, of all the non-chemical and non-electrical properties of gases.

The remainder of this article is devoted to a brief statement of the methods and results of the kinetic theory.

The Kinetic Theory of Gases.

The determination of the series of configurations developing out of given initial conditions is not, however, the problem of the kinetic theory: the object of this theory is to explain the general properties of all gases in terms only of their molecular structure.

In this expression the first line may be supposed to represent the energy (or part of the energy) of s similar molecules of a kind which we shall call the first kind, the terms 2 (mu 2 +mv 2 +mw 2) being the kinetic energy of translation, and the remaining terms arising from energy of rotation or of internal motion, or from the energy, kinetic and potential, of small vibrations.

For instance, if the system is composed of a gas and a solid boundary, some of the terms in expression (2) may be supposed to represent the kinetic energy of the molecules of the boundary, so that equations (7) show that in the normal state the gas has the same temperature as the boundary.

It will at once be apparent that the kinetic theory of matter enables us to place the second law of thermodynamics upon a purely dynamical basis.

Thus the " Brownian movements " provide visual demonstration of the reality of the heat-motion postulated by the kinetic theory.

(21) The comparison of this formula with experiment provides a striking confirmation of the truth of the kinetic theory but at the same time discloses the most formidable difficulty which the theory has so far had to encounter.

The kinetic energy of the molecules of these gases must contain two terms in addition to those representing translational energy.

For a rigid body the kinetic energy will, in general, consist of three terms (AW1 2 +BW2 2 +CW3 2) in addition to the translational energy.

The energy in a train of waves carried forward with the waves is partly strain or potential energy due to change of volume of the air, partly kinetic energy due to the motion of the air as the waves pass.

We shall show that if we sum these up for a whole wave the potential energy is equal to the kinetic energy.

The kinetic energy per cubic centimetre is 2 pu t, where is the density and u is the velocity of disturbance due to the passage of the wave.

But v/V =u/U from equation (2) and w =Eu/U from equation (3) Then 2wv/V = ZEu 2 /U 2 = 2 pu t from equation (6) Then in the whole wave the potential energy equals the kinetic energy and the total energy in a complete wave in a column 1 sq.

If r is of the order of A, n is of the order of y; and the kinetic energy of the radial motion is of the same order as that of the longitudinal motion.

During the quarter swing ending with greatest nodal pressure, the kinetic energy is changed to potential energy manifested in the increase of pressure.

This becomes again kinetic in the second quarter swing, then in the third quarter it is changed to potential energy again, but now manifested in the decrease of pressure.

In the last quarter it is again turned to the kinetic form.

There will be more kinetic energy formed in the return journey and the vibration tends to grow.

But if the heat is given at the instant of greatest rarefaction, the increase of pressure lessens the difference from the undisturbed pressure, and lessens the potential energy, so that during the return less kinetic energy is formed and the vibration tends to die away.

Let E be the effective elasticity of the aether; then E = pc t, where p is its density, and c the velocity of light which is 3 X 10 10 cm./sec. If = A cos" (t - x/c) is the linear vibration, the stress is E dE/dx; and the total energy, which is twice the kinetic energy Zp(d/dt) 2 dx, is 2pn2A2 per cm., which is thus equal to 1.8 ergs as above.

If we rest on the synthesis here described, the energy of the matter, even the thermal part, appears largely as potential energy of strain in the aether which interacts with the kinetic energy associated with disturbances involving finite velocity of matter.

It may, however, be maintained that an ultimate analysis would go deeper, and resolve all phenomena of elastic resilience into consequences of the kinetic stability of steady motional states, so that only motions, but not strains, would remain.

When the atoms are in motion these strain-forms produce straining and unstraining in the aether as they pass across it, which in its motional or kinetic aspect constitutes the resulting magnetic field; as the strains are slight the coefficient of ultimate inertia here involved must be great.

in the time At, during which the velocity falls from v+2Av to v-2Av, we have (12) RAs = loss of kinetic energy in foot-pounds =w(v+ZOv) 2 /g - w(v - ZOv) 2 /g=wvAv/g, so that (13) As =wvAv/nd 2 pg =CAS, where (14) AS = vAv/g p = vAT, and AS is the advance in feet of a shot for which C =1, while the velocity falls Av in passing through the average velocity v.

After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area Acpm, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e d2 I + p, a in which the factor 4(k 2 /d 2)tan 2 S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than I %.

The importance of a study of the changes of the vis viva depending on squares of velocities, or what is now called the "kinetic energy" of a system, was recognized in Newton's time, especially by Leibnitz; and it was perceived (at any rate for special cases) that an increase in this quantity in the course of any motion of the system was otherwise expressible by what we now call the "work" done by the forces.

The energy of a system is the measure of its capacity for doing work, on the assumption of suitable connexions with other systems. When the motion of a body is checked by a spring, its kinetic energy being destroyed, the spring, if perfectly elastic, is capable of restoring the motion; but if it is checked by friction no such restoration can be immediately effected.

On certain assumptions required for the extension of the methods of the kinetic theory of gases to liquids, L.

We can calculate, by the help of the kinetic theory and the theory of chances, the frequency with which the necessary conjunctions of ions will occur, and show that the general law will be that the coagulative powers should be in the ratios of 1: x: x 2.

4, which, according to the kinetic theory, is an indication that an important fraction of the energy absorbed is devoted to rotation or vibration.

It is much more probable that heat is really the kinetic energy of motion of the molecules, and is passed on from one to another by collisions.

The high conductivity of metals is then explained by the small mass and high velocity of diffusion of these electric atoms. Assuming the kinetic energy of an electric atom at any temperature to be equal to that of a gaseous molecule, its velocity, on Sir J.

On the kinetic theory the molecules of a gas are relatively far apart and there is nothing analogous to friction between two adjacent layers A and B moving with different velocities.

This potential energy becomes kinetic when the slag is brought into contact with lime in the presence of water, and causes the formation of a true hydraulic silicate of lime.

Thus The Direct Experimental Evidence Is Somewhat Meagre And Conflicting, But The Question Of The Relation Of The Specific Heats Of Gases Is One Of Great Interest In Connexion With The Kinetic Theory And The Constitution Of The Molecule.

According To The Elementary Kinetic Theory Of An Ideal Gas, The Molecules Of Which Are So Small And So Far Apart That Their Mutual Actions May Be Neglected, The Kinetic Energy Of Translation Of The Molecules Is Proportional To The Absolute Temperature, And Is Equal To 3/2 Of Pv, The Product Of The Pressure And The Volume, Per Unit Mass.

If The Molecules Are Supposed To Be Like Smooth, Hard, Elastic Spheres, Incapable Of Receiving Any Other Kind Of Energy Except That Of Translation, The Specific Heat At Constant Volume Would Be The Increase Per Degree Of The Kinetic Energy Namely 3Pv/20=3R/2, That At Constant Pressure Would Be 5R/2, And The Ratio Of The Specific Heats Would Be 5/3 Or 1.666.

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