Kinetic Theory · Question 7

The mean free path of a molecule of diameter 5 10-10 m at the temperature 41 C and pressure 1.38 105 Pa, is given as m. (Given kB = 1.38 10-23 J/K).

1. 2 2 10-10
2. 10 2 10-8
3. 2 2 10-8
4. 2 10-8

Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is 32 1018 /s then collision frequency in gas A is /s.

1. 8 1018
2. 2 1018
3. 32 1018
4. 4 1018

An insulated cylinder of volume 60 cm3 is filled with a gas at 27 and 2 atmospheric pressure. Then the gas is compressed making the final volume as 20 cm3 while allowing the temperature to rise to 77 . The final pressure is atmospheric pressure.

The r.m.s. speed of oxygen molecules at 47 is equal to that of the hydrogen molecules kept at . (Mass of oxygen molecule/mass of hydrogen molecule = 32/2)

1. -100
2. -253
3. -20
4. -235

Match the List I with List II Choose the correct answer from the options given below:

1. A-III, B-IV, C-I, D-II
2. A-II, B-IV, C-I, D-III
3. A-IV, B-II, C-III, D-I
4. A-III, B-II, C-IV, D-I

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is: (Given: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)

1. 1 : 10
2. 10 : 1
3. 1 : 10
4. 1 : 1

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are 3 10-7 m and 600 m/s, respectively. Find the frequency of its collisions.

1. 5 108/s
2. 9 105/s
3. 2 1010/s
4. 2 109/s

There are two vessels filled with an ideal gas where volume of one is double the volume of the other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa).

1. 24
2. 4.4
3. 18
4. 6

A is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. B is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If A B = (1 + 1n ), then the value of n is .

The internal energy of air in 4 m 4 m 3 m sized room at 1 atmospheric pressure will be 106 J (Consider air as diatomic molecule)