Question

Which of the following is an intensive variable for an ideal gas?
A. V
B. P
C. n
D. T

Answer 1

Intensive variable is defined as a quantity measured in a macroscopic system that has a well defined value at every point inside the system and that remains more or less constant when the size of the system is increased or changed.

Complete step by step answer:
Later a theory was given called kinetic molecular theory of gases to provide a sound theoretical basis for the various gas laws. The kinetic theory of gases is based on the following assumptions or postulates:
(i) Actual volume of gas molecules is negligible in comparison to the total volume of the gas : Postulate says that all the gases are made up of extremely small particles called molecules dispersed throughout the container. These particles are so small that they are regarded as point masses. As they are point masses, so the actual volume occupied by the gas molecules is negligible in comparison to the total volume of the gas.
Support for assumption:This assumption explains the great compressibility of gases, because there is a lot of empty space between the gas molecules.
(ii) No force of attraction between the gas molecules : As the distance between the gas molecules is very large, so it is assumed that there is no force of attraction between the gas molecules at ordinary temperature and pressure.
Support for assumption : Due to no force of attraction between the gas molecules, therefore the gases easily expand and occupy all the space available to them on heating.
(iii) Particles of gas are in constant random motion : Particles of gas are in a state of constant random motion.
Support for Assumption :This assumption is supported by the fact that gases do not have a fixed shape because of their random motion.
(iv) Particles of gas collide with each other and with the walls of the container : Particles of gas
move in the straight line with high velocities in all the possible directions. During this motion, they collide with each other and with the walls of the container in which gas is enclosed and even change direction upon collisions.
(v) Collisions are perfectly elastic : When the gas molecules collide with each other they pass on their energies. There is transfer of energy from one colliding molecule to the other but the total energy of molecules before and after the collision remains the same therefore, the collisions are called perfectly elastic. So, there is no net loss of energy.
Support for Assumption : As there is no loss of kinetic energy, therefore the motion of molecules does not cease so, the gases never settle down.
(vi) Different particles of the gas have different speeds Different particles of gas possess different kinetic energies, therefore they have different speeds at a particular time. Support for Assumption : This postulate is reasonable as when the molecules collide, they change their speed. Even though the initial speeds are the same, after collisions there is transfer of energy from one molecule to the other. So, as the energy changes after the collisions, so do the speeds. But the distribution of speeds remains constant at a particular temperature. Temperature is independent of the quantity of matter, hence it is an intensive variable.

So the correct option is (D).

Note: All the gas laws that we have discussed like Boyle's law, Charles' Law, Avogadro's Law are merely based on the experimental evidence. There was no theoretical background to justify them. So, the scientists were curious to know why the gases behave in a peculiar manner under certain set of conditions. From Charles' Law we got to know that the gases expand on heating. But there was no theory to give the reason for such a fact. So, there was a need for some theory which could tell about the happenings at the molecular level and so could answer all the questions arising regarding the behaviour of gases.