Physics · Kinetic Theory · NEET
In a gas the molecules are spread very far apart. At normal conditions the actual volume of the molecules is only about 0.1% of the container volume, so the empty space is huge compared to the molecules themselves. Because their own size is so small next to the space they move in, we assume each molecule is a point with mass but no volume. This makes the maths simple and gives correct results at low pressure. It fails only when the gas is squeezed to high pressure, where molecules are close and their size can no longer be ignored.
No. A key assumption is that molecules exert no force on one another when they are apart. There is no attraction and no repulsion between them except during the brief moment of a collision. Because there is no attractive force, an ideal gas has no potential energy — all its internal energy is kinetic. In a real gas weak attractive forces do exist, which is why real gases can be turned into liquids but an ideal gas cannot.
A perfectly elastic collision means no kinetic energy is lost when molecules hit each other or hit the container wall. The total kinetic energy of the molecules stays the same over time. If collisions were not elastic, the molecules would slowly lose speed and the gas would cool down and settle on the floor by itself — which never happens. Momentum is also conserved in each collision, and this is what lets us derive the gas pressure formula.
Between two collisions a molecule travels a fairly long straight path, but the actual contact time during a collision is extremely short. So a molecule spends almost all of its time moving freely and almost no time colliding. This lets us treat the motion as straight-line free motion interrupted by instant collisions. It also means the forces during collision act for such a tiny time that we do not track them individually — we only use the change in momentum at the wall.
Random motion means molecules move in every direction with equal chance, so no single direction is special. This is why the average velocity components in x, y and z directions are equal, and why gas pressure is the same on all walls of the container. If motion were not random, one wall would feel more pressure than another, which we never observe. Randomness is what makes the average of vx squared equal to one-third of the average of v squared — a step used to get the pressure formula P = (1/3) rho v squared.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
A gas has a very large number of identical molecules; they are point masses with negligible volume; they are in constant random motion in all directions; they exert no force on each other except during collisions; all collisions (with each other and with the walls) are perfectly elastic; and the time of a collision is negligible compared to the time between collisions.
Because the molecules do not attract or repel each other at a distance, there is no intermolecular potential energy. So the total internal energy is just the sum of the kinetic energies of all molecules, which depends only on the absolute temperature.
They break down at high pressure and low temperature. There the molecules are close together, so their own volume is no longer negligible and the attractive forces between them become important. A real gas then deviates from ideal behaviour and can even condense into a liquid.
Random motion gives average vx squared equal to one-third of average v squared. Elastic collisions with the wall conserve momentum, and negligible molecular size and collision time let us count wall hits simply. Combining these gives the pressure of an ideal gas as P = (1/3) rho v squared, where rho is density and v squared is the mean square speed.
Yes. For a pure gas the kinetic theory assumes all molecules are identical in mass and size. They are also assumed to be so small that their own volume is negligible compared with the volume of the container.
