Kinetic theory of gases postulates and equations
According to kinetic theory of gases, a gas consists of a large number of molecules( or atoms) which are in continous random motion. These molecules are far apart from one another i.e their average separation is much greater than the diameter of each molecule. Therefore, the gas molecules can be considered as moving freely with respect to each other. However, when they come close to each other during the motion, their velocities change due to the inter-molecular forces between them. such changes may be understood as collisions at molecular level.
The various gas law and other important results can be obtained easily from the kinetic theory of gases. For this following assumptions are made:
1. All gases consist of molecules and the molecules of a gas are all alike but differ with molecules of other gases.
2. The Volume of molecules is negligible compared with the volume occupied by the gas.
3.The molecules are in random motion and the velocity in all directions are ranging from zero to a maximum.
4.During the motion, the molecules collide to each other and to the walls of the containing vessel. The collision of molecules is perfectly elastic.
5.The molecules behave as perfectly elastic sphere.
6.The duration of a collision between two molecules is negligible compared to the time between two successive collisions on the wall.
7. The attractive or repulsive force between the molecules is negligible, and no force is exerted by the molecules except during collisions.
Some important questions and their answers
1. Absloute zero temperature is not the zero energy temperature. Explain
ans. The kinetic energy of molecular translatory motion is represented by temperature. But other forms of energy such as intermolecular potential energy is not represented by the temperature so at absloute zero temperature, kinetic energy of the molecules is zero but intermolecular potenial energy is not zero. so, absloute zero tempertaure is not the zero energy temperature.
2.Eqall masses of monatomic and diatomic gases at same temperature are given eqall quantities of heat. which gas will undergo a large temperature rise and why?
ans. We know that the average translation K.E per molecule is directly proportional to absloute temperature. The monatomic gas molecules posses only translational K.E while diatomic gas molecules posses translational, rotational and vibration energies. Hence monatomic gas will undergo large temperature rise.
3. On which of the following factors does the average K.E of gas molecules depend?
ans. It depends only on the absloute temperature and is directly proportional to it. So its value is zero at absloute temperature.
4.Hydrogen gas is not found in the atomosphere, why?
ans.Root mean square speed of hydrogen gas is larger than escape velocity of earth. so hydrogen gas escape easily out frok the gravitional easily out from the gravitional field of earth. Hence hydrogen gas is not found in the atmosphere.
5.In the kinetic theory of gases, why do we take into account the change in gravitional potenial energy of the molecules?
ans.According to kinectic thoery gases, the pressure exerted by gases, the pressure exerted by gas molecules along each axis is same because gas molecules have eqall degree of freedom in each axis of their motion. Therefore, changes in the gravitional potenial energy of the molecules can be neglected. Hence in the kinetic theory of gases, we do not take into account changes in the gravitional potenial energy of the molecule.
6. Why do you consider an ideal gas while formulating pressure in terms of kinetic theory gases?
ans. While formulating the pressure in terms of kinetic theory of gases, we consider an ideal gas which simplifies the calculation. following assumptions are given as:
(i)There exists no force of attraction between the molecules i.e there is no potential energy between the molecules
(ii) The molecules of the gas collide elastically with themselves i.e there is no loss of kinetic energy during collisions.
some important questions for examinations
1.Give the molecular interpreation of temperature.
2.A gas is heated in a vessel at constant volume. pressure increases, why?
3.What is absloute zero temperature? explain it on basis of kinetic theory of gases.
4.Why do biycycles tube burst in summer? Explain.
5.What is an ideal gas
6.What do you mean by one mole of gas?
7.Explain Boyle’s law on the basis of kinetic theory gases.
8.What is the significance of Boltzman constant?
Long Discussion questions
1. Give the postulates of kinetic theory of gases. Hence derive an expression for the pressure exerted by an ideal gas.
2.Derive an expression for avergae kinetic energy per molecule of an ideal gas.
3. state and explain Daltons law of partial pressure. Obtain the law from kinetic theory of gases.