# Kinetic Theory - Online Test

Q1. Kinetic theory explains the behavior
Explaination / Solution:

The theory for ideal gases makes the following assumptions 1. Gases consist of particles in constant, random motion. They continue in a straight line until they collide with something—usually each other or the walls of their container. 2. Particles are point masses with no volume. The particles are so small compared to the space between them, that we do not consider their size in ideal gases. 3. No molecular forces are at work. This means that there is no attraction or repulsion between the particles. 4. Gas pressure is due to the molecules colliding with the walls of the container. All of these collisions are perfectly elastic, meaning that there is no change in energy of either the particles or the wall upon collision. No energy is lost or gained from collisions. 5. The time it takes to collide is negligible compared with the time between collisions. 6. The kinetic energy of a gas is a measure of its Kelvin temperature. Individual gas molecules have different speeds, but the temperature and kinetic energy of the gas refer to the average of these speeds. 7. The average kinetic energy of a gas particle is directly proportional to the temperature. An increase in temperature increases the speed in which the gas molecules move. 8. All gases at a given temperature have the same average kinetic energy. 9. Lighter gas molecules move faster than heavier molecules.

Q2. Kinetic theory
Explaination / Solution:

The kinetic theory describes a gas as a large number of submicroscopic particles (atoms or molecules), all of which are in constant rapid motion that has randomness arising from their many collisions with each other and with the walls of the container. It will applicable only for gases

Q3. Kinetic theory relates measurable properties.
Explaination / Solution:

Kinetic theory explains the behaviour of gases based on the idea that the gas consists of rapidly moving atoms or molecules. It also relates measurable properties of gases such as viscosity, conduction and diffusion with molecular parameters, yielding estimates of molecular sizes and masses.

Q4. According to Atomic Hypothesis:
Explaination / Solution:

atomic hypothesis that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.

Explaination / Solution:

Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules"

For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

Q6. In which case are the atoms relatively rigidly fixed?
Explaination / Solution:

Atoms in a gas are well separated with no regular arrangement. Atoms vibrate and move freely at high speeds Atoms in a liquid are close together with no regular arrangement. Atoms vibrate, move about, and slide past each other. Atoms in a solid are tightly packed, usually in a regular pattern. Atoms vibrate (jiggle) but generally do not move from place to place.

Q7. The order of inter atomic distance in liquids is about
Explaination / Solution:

Using the assumption of little spheres (for interatomic space) the spacing between the molecules at about 2X10-10 m i.e.

The size of an atom is about an angstrom (10 -10 m) . In solids, which are tightly packed, atoms are spaced about a few angstroms (2 Å) apart.

Q8. The average distance a molecule can travel without colliding is called the
Explaination / Solution:

the mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties

Q9. In dynamic equilibrium, molecules collide and change their speeds during the collision
Explaination / Solution:

All collisions between molecules among themselves or between molecules and the walls are elastic. So that total kinetic energy and total momentum is conserved. Also the average properties of gas are remains constant.

Q10.

Considering a gas in a parallelopiped, in a small time interval , a molecule with x-component of velocity  will hit the wall

Explaination / Solution:

Collision by moleculeto the wall of conntainer assumed to be perfectly elastic.

By the principle of conservation of momentum, the momentum imparted to the wall in the collision = 2mvx

So the magnitude of the force on the wall from each collision is

distance travelled in time

$\mathrm{x=vx\Delta t}$