Introduction
There are five states of matter and gas is one of them. Empty spaces are filled by gases. The atmosphere is full of gas molecules. It contains different gas molecules. The oxygen gas molecule which is necessary for breathing is also in our atmosphere along with many other gas molecules. Every matter in the universe is composed of tiny particles called molecules. They attract each other with some attractive force. There exists an intermolecular force of attraction between molecules.
Based on the force of attraction between the molecules, matters are classified into five categories. They are solid, liquid, gas, plasma, and Bose-Einstein. Solids are the matter in which the distance between the molecules is very small and they are tightly bound to each other. Liquids are matter having molecules at a small distance and they bound less tightly than solids. Plasma state molecules have high kinetic energy.
Assumptions of Kinetic Theory of Gases
The kinetic theory of gases shows the thermodynamic behavior of gases. They have some basic assumptions as,
- There are many tiny particles in the gas known as particles.
- They make an elastic collision with each other and also with the walls of the container.
- The particles are identical to each other and can move in all possible directions.
- The time of collision is very small as compared with the time between the collision.
- The volume of the molecule is very much smaller when comparing it with the total volume of the gas.
- Molecules do not apply any force on the other except during collision.
- The separation between the molecules is greater compared to the size of the molecule.
- All the molecules obey the laws of motion.
Explore our latest online courses and learn new skills at your own pace. Enroll and become a certified expert to boost your career.
What do you mean by Kinetic Interpretation of Temperature ?
Let us consider a gas-filled container of volume V. Let the molecules move at all possible velocities. Then the pressure applied by the gas molecules on the walls is given by,
P=13mnc2vP=13mnc2v
Where m denotes the mass of one molecule. n denotes the number of molecules. C2C2 denotes the root mean square velocity of the molecules. V denotes the volume of the gas.
The 1 mole of gas contains N number of molecules.
PV=13mNC2PV=13mNC2
By gas law PV=RT
RT=13mNC2RT=13mNC2
RTN=13mC2RTN=13mC2
multiply and divide the right-hand side by 2 we get,
RTN=23×12mC2RTN=23×12mC2
The kinetic energy of the molecule is K.E=12mC2K.E=12mC2
RTN=23×K.ERTN=23×K.E
K.E=32×RTNK.E=32×RTN
K.E=32KTK.E=32KT
where K=RNK=RN denotes Boltzmann’s constant.
Relation between Kinetic Energy and Temperature
The work that is done on the body is its energy. The body which possesses the energy due to its motion is called its kinetic energy. It can be transformed from one object to another and also into other forms of energy. This energy depends on its mass and velocity. The S.I unit of kinetic energy is Joule. Thus the kinetic energy of the object is given by,
K.E=12mc2K.E=12mc2
Degrees of freedom of the molecules are different by the law of equipartition of energy; the total energy of the system is equally allocated for each degree of freedom of the molecule. And the energy allocated equally is 1/2 kT. This is called the law of equipartition of energy. Thus the temperature of the gas is directly related to the kinetic energy of the molecules.
Gas laws
Many laws were proposed to know about the behavior of gas. Gas laws give the relation between pressure, temperature, and volume. They are Charle’s law, Gay Lussac’s law, Avogadro’s law, Boyle’s law, and Grahm’s law.
- Boyle’s law: Boyle’s law clearly says that the pressure of the gas is controversial with the volume of the gas. (i.e) when pressure increases volume will decrease. This will be maintained as long as the temperature is constant. Mathematical representation gives,
P∝1vP∝1v
PV=k(constant)PV=k(constant)
- Charle’s law: When temperature increases the gas gets expanded. This was explained by Charle’s law. It shows that the volume of the gas changes directly with temperature change when pressure is maintained constant.
V∝TV∝T
vT=k(constant)vT=k(constant)
- Gay Lussac’s law: Pressure of the gas changes directly by the change in temperature when the volume of the gas is kept constant. This is known as Gay Lussac’s law.
P∝TP∝T
PT=k(constant)PT=k(constant)
- Avogadro’s law: Avogadro’s law says that in an equal volume of gases the number of molecules will be the same when the same temperature and pressure are the same.
V∝nV∝n
vn=kvn=k
- Graham’s law: According to his principle lighter molecules move faster than heavier molecules. I.e. effusion of molecules with low molecular mass is faster than the higher molecular mass at constant pressure and temperature. The molecules diffusing for time are the reciprocal of the square root of their mass density.
r∝1P√r∝1P
Conclusion
In this tutorial, the assumption of the kinetic theory of gases and the kinetic interpretations of temperature are discussed in detail. The relation between the kinetic energy and the temperature and gas laws is also discussed.
Leave a Reply