Question

Which of the following statements is NOT a correct assumption of the classicalmodel of an ideal gas?A. The molecules are in random motion.B. The volume of the molecules is negligible compared with the volume occupied bythe gas.C. The molecules obey Newton's laws of motion.D. The collisions between molecules are inelastic.E. The only appreciable forces on the molecules are those that occur duringcollisions.A sample of an ideal gas is in a tank of constant volume. The sample absorbsheat energy so that its temperature changes from 300 K to 600 K. If v1 is theaverage speed of the gas molecules before the absorption of heat and v2 is theiraverage speed after the absorption of heat, what is the ratio v2/ v1?A. 1/2 B. 1 C. 2 D. 2 E. 4

Answer 1

1) D. The collisions between molecules are inelastic

Step-by-step explanation:

The kinetic theory of the gases describe the property of the gases by looking at microscopic level. At these level, some assumptions are made on the motion/collisions of the molecules of the gas:

- Molecules move by random motion

- The volume of the molecules is negligible compared with the volume of the gas

- The molecules obey Newton's laws of motion

- The intermolecular forces between the molecules are negligible except during the collisions

- Collisions between molecules are elastic

Therefore, the following statement

D. The collisions between molecules are inelastic

is wrong.

2)
`√(2)`

The kinetic energy Ek of a gas is directly proportional to its absolute temperature T:

`E_k = (3)/(2)kT`

where k is the Boltzmann's constant. However, the kinetic energy depends on the square of the average velocity of the particles,
`v^2`:

`E_k = (1)/(2)mv^2=(3)/(2)kT`

where m is the mass of the particles. This means that the velocity is proportional to the square root of the temperature:

`v \propto √(T)`

So, if the temperature of the gas is doubled, the average speed increases by a factor
`√(2)`, and the ratio v2/v1 is

`(v_2)/(v_1)=√(2)`