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Kinetic Energy and Temperature

Changes in the moisture and temperature of air mass produce high and low pressure systems which move across the continent which finally effects our weather patterns. In any object, the particles whether at a higher temperature system or low temperature, the particles are always on the move. If they are moving at a high speed within a closed system then that leads to high pressure. The particles, atoms or molecules, moving at a varying speeds possess kinetic energy. 

More the temperature, the faster they move. When we get to see a transfer of energy from a hotter particle to a cooler one, the colder particle gains kinetic energy while the hot particle loses both heat and kinetic energy. The transfer of energy continue to take place till both the particles reach the same temperature and have same average kinetic energy. The energy of the particle and its dependency upon temperature confirms the relationship existing between kinetic energy and temperature. 

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Kinetic Energy and Temperature Relation

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Temperature is not as heat and this has to be understood very clearly. The particles like atoms and molecules in solids and liquids along with gas have kinetic energy because they are moving. These also have potential energy because their motion keeps these particles apart and oppose the bonds which try to pull them together. 

The gaseous particles have the maximum potential as they are the furthest apart. The total kinetic energy and potential energy of these atoms and molecules in a material is called its internal energy. The hotter a material feels like, the faster its particles move around and the more internal energy it will have.

The energy transferred from a material at higher temperature to another with a lower temperature is known as heat. To understand the basic framework of gas behaviour and the aspect of pressure, we need to understand the phenomenon related to for a confined gas, known as kinetic molecular theory. This theory focuses on.
  • Gaseous mass contains randomly moving minute particles which move either individually or in molecular forms.
  • As compared to the total volume of the gas occupied, the total volume of these gaseous particles is quite large and we put the total volume of particles close to zero.
  • These gaseous particles are independent of each other and neither there is any repulsion or attraction observed.
  • The inter particle as well as collision against the container wall are found to be elastic and hence could be attributed for constant kinetic energy of these gas particles under constant temperature.
  • The gaseous particles average kinetic energy is found to be directly proportional to the absolute temperature of the gas matter.

These laws aptly work for all ideal or perfect gas. Any gas which conforms to kinetic molecular theory, have volume and exert forces each other. Under normal pressure and temperature conditions are categorised as ideal. Only in case the gases are under very low temperature and extremely high pressure that these gases behave otherwise. 

Temperature can be considered as a measure of the random motion of the particles which constitute the matter. More specifically, the temperature is a measure of the kinetic energy of the material’s particles. A body derive kinetic form of energy by virtue of its movement or motion. The formula for kinetic energy is given out as:

Kinetic energy (KE): ½ *(m) (v2)

The kinetic form completely depends upon the mass and velocity of the object. Hence, the higher and lower velocities of the particle could give varying forms of higher and lower magnitude of kinetic energy. So the change in temperature at molecular level can varying amount of kinetic energy. An increase in temperature can imply for greater energetic forms of the particles and a decrease shoots down the energy of the particles and we get to see lesser kinetic forms of the particles.

The absolute zero and kinetic theory has another interesting phenomenon. The collision rate against each other and against the container wall also reduces drastically under low temperature conditions and eventually might stop completely causing no pressure on the wall of the container. This is observed when the temperature is brought down to lowest possible value of absolute zero or -273 C.

Kinetic Energy and Temperature Equation

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For any development of theory the scientific community needs specific proof and in most cases derivation of the relationship between the components. The experimental ideas and observation needs specific definition of the idea.
  • The kinetic theory of gas which takes up the relationship between kinetic energy and temperature are based on certain assumptions:
  • Gaseous matter is made up of several number of atoms or molecules and these are separated by distances that are considered to be bigger in comparison to their inter particle distance.
  • These gaseous particles are always in random motion
  • The collisions between these particles and against the container wall is found to be elastic, and kinetic energy is transferred from one particle to another, but is never converted into another form
  • Interactions between molecules is negligible or absent
From the ideal gas equation we get,

PV = nRT 

Where, P is the pressure of the gaseous matter, V is the volume of the gaseous matter, n is the moles of gaseous matter, R is the universal gas constant, T is the absolute temperature.

PV = (N / NA) RT

Where, NA is the Avogadro number. 

$\frac{2 N}{3 V}$ $E_{trans}$ = $\frac{N RT}{NA V}$ 
This relationship is given out for kinetic energy for 1 mole of the gas. Here, R = $K_{B} N_{A}$ 

$K_{B}$ is the Boltzmann constant equivalent to $1.380658 x 10^{-23} JK^{-1}$

The mean kinetic energy of one molecule is proportional to absolute temperature. The significance of this relationship is that it gives an idea of temperature of a gas in terms of molecular motion. Random molecular motion is hence sometimes referred to as thermal motion.

The Etrans is independent of molecular properties such as size or molar mass or amount of the gas present as long as N is a large number.
$\frac{1}{2}$ $mv^{2}$ = $\frac{3}{2}$ kb t

$v^{2}$ = $\sqrt{\frac{3 RT}{M}}$
M = $m N_{A}$

Kinetic Energy and Temperature Change

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Chemical energy related to the development of the chemical reactions between atoms or molecules within the system, relates to more extreme temperature and pressure conditions which are given out in the form of radiation and nuclear energy considered to be essential quantities. 

The description of changes of internal energy ∆U of the system. The internal energy U in a system of matter can be kinetic energy Ek connected with movement of atoms or molecules. The kinetic form of energy exists in two qualitatively different forms. 
  • The molecular kinetic form of energy is connected with disorder and random thermal movements of these atoms and molecules. The temperature T of the system of matter is considered to be the measure of average molecular kinetic energy of the system.
  • The macroscopic kinetic energy created by an ordered simultaneous movement of a system of matter. The macroscopic kinetic energy of the system is often used quantity in calculations within mechanical discipline of physics.
The molecular kinetic energy is an important quantity in thermodynamic in systems of matter and any temperature change indicates a change in average kinetic energy of the molecules.  

Average Kinetic Energy and Temperature

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The collision of gas particles with each other and with the container walls are found to be elastic which means there is no loss in kinetic form of energy, and the average kinetic energy of these gas particles is proportional to the temperature on the kelvin scale. 

Effusion is the escape of gas molecules through a small hole and gases effuse faster than others due to its higher kinetic energy of the particles. As temperature is the measure of average kinetic energy of these gas molecules, the average kinetic energy is proportional to thermodynamic temperature. The average kinetic energy of the molecules in the gas is constant at a given temperature. 

Average KE = ½ mv2 = constant

Or, mv2 = constant, or, v2 = (constant) / m and also v ∝ 1/√m

The speed of the molecules in a gas and also the rate of effusion is inversely proportional to the square root of the mass of the participating molecule. This shows that lighter gases effuse faster at a given temperature as these molecules can move faster. The mathematical condition of the kinetic theory of gas and energy can be used to determine the relative number of gas particles that have particular speed. Some of the particles have lower speeds, while the rest can move at the same speed or rapidly and hence the average kinetic energy relationship comes into picture.

The plotting of these are considered under Maxwell Boltzmann distribution curve. The mean speed is little higher than most probable speed because the graphs are not symmetric. If the temperature increase, the average speed increase which results in a broader curve. This results in the most probable speed and Urms shifting to greater values.

The average kinetic energy of the gas molecules is found to be proportional to temperature and kinetic molecular theory shows that ‘rms’ speed is related to temperature and molar mass given out by the relation, Urms = √ 3RT / M

Where, R = 8.314 J / mol / K and molar mass M is in Kg / mole.

In Maxwell Boltzmann distribution of molecular energies curve at fixed temperature, the highest point on the curve represent most probable energy. The greatest fraction of molecules have this energy at any given instant. None of the molecules are stationary and few molecules have exceptional high energy. 

The area under curve is never symmetrical and end part of the curve shows higher energy, while the graph drops off sharply on low energy side. At higher energy, the average energy of molecules is found to be more and the range of energy is also greater with better chances of very high energy. The peak is broad and can show lower curve at high temperature. 

Kinetic Energy and Temperature

Distinguish Between Kinetic Energy and Temperature

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 Kinetic energy 
 Kinetic energy gives the indication of how fast a molecule moves  Temperature indicates the thermal condition of a body
 The kinetic energy is a scalar form
 Temperature is scalar quantity
 The total kinetic energy of a molecule is given out in form of heat  Temperature is the average kinetic energy per molecule of a body
 Kinetic energy of a molecule do not decide the direction of heat flow from body  Temperature of a body decides the direction of heat flow from the body
 Most of the kinetic energy possessed by a molecule either converts to heat or remain as it is in case the collision is elastic 
 The exchange of heat between particles results in the sum total temperature which is different before and after the exchange
 The SI unit is joule (J)  The SI unit is kelvin (K)

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