Kinetic Theory

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

1. Statement I is false but Statement II is true
2. Both Statement I and Statement II are true
3. Statement I is true but Statement II is false
4. Both Statement I and Statement II are false

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :

1. 12 2
2. 14
3. 2 21
4. 132

Energy of 10 non rigid diatomic molecules at temperature T is :

1. 35 RT
2. 72 RT
3. 70 KBT
4. 35 KBT

If the collision frequency of hydrogen molecules in a closed chamber at 27 is Z, then the collision frequency of the same system at 127 is :

1. 32Z
2. 2 3Z
3. 34Z
4. 43Z

If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

1. 1 2n d2
2. 1 2n2 2d2
3. 1 2n d2
4. 2n d2

P-T diagram of an ideal gas having three different densities 1, 2, 3 (in three different cases) is shown in the figure. Which of the following is correct : [figure]

1. 1> 2
2. 2< 3
3. 1= 2= 3
4. 1< 2

The translational degrees of freedom (ft) and rotational degrees of freedom (fr) of CH4 molecule are:

1. ft = 2 and fr = 2
2. ft = 3 and fr = 3
3. ft = 3 and fr = 2
4. ft = 2 and fr = 3

Two moles of a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :

1. 32R
2. 74R
3. 52R
4. 94R

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km/s, the root mean square velocity of oxygen at the same condition in km/s is :

1. 1.0
2. 1.5
3. 2.0
4. 0.5

The parameter that remains the same for molecules of all gases at a given temperature is :

1. kinetic energy
2. mass
3. momentum
4. speed