Kinetic Theory

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

A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

1. 29 RT
2. 27 RT
3. 20 RT
4. 21 RT

At which temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47 ?

1. 20 K
2. 80 K
3. 4 K
4. -73 K

If three moles of monoatomic gas ( = 53 ) is mixed with two moles of a diatomic gas ( = 75 ), the value of adiabatic exponent for the mixture is

1. 1.35
2. 1.52
3. 1.40
4. 1.75

Two vessels A and B are of the same size and are at same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen. PA and PB are the pressures of the gases in A and B respectively, then PAPB is:

1. 4
2. 32
3. 8
4. 16