Kinetic Theory

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K the second vessel temperature is raised to 500 K. The final pressure in the vessels is kPa.

1. 100
2. 120
3. 90
4. 105

If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is :

1. 52T
2. 54T
3. 72T
4. 74T

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Choose the correct answer from the options given below :

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
3. (A) is true but (R) is false
4. (A) is false but (R) is true

An ideal gas at pressure P and temperature T is expanding such that PT3 = constant. The coefficient of volume expansion of the gas is .

1. 2T
2. 1T
3. 4T
4. 3T

One gas of n1 mole of molecules at temperature T1, volume V1, and pressure P1, and another gas of n2 mole of molecules at temperature T2, volume V2, and pressure P2, are mixed resulting in pressure P and volume V of the mixture. The temperature of the mixture is .

1. (T1+T2)2
2. T1T2PVT2P1V1+T1P2V2
3. (T2P1V1+T1P2V2)T1T2PV
4. |T1-T2|2

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Choose the correct answer from the options given below :

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
3. (A) is true but (R) is false
4. (A) is false but (R) is true

A mixture of carbon dioxide and oxygen has volume 8310 cm3, temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are . (Assume both carbon dioxide and oxygen gases behave like ideal gases) [R = 8.31 J/mol K]

1. 0.15 and 0.18
2. 0.25 and 0.08
3. 0.21 and 0.12
4. 0.13 and 0.20

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

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

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

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

1. [figure]
2. [figure]
3. [figure]
4. [figure]

The ratio of vapour densities of two gases at the same temperature is 425, then the ratio of r.m.s. velocities will be :

1. 52
2. 254
3. 425
4. 25

The kinetic energy of translation of the molecules in 50 g of CO2 gas at 17 is :

1. 4205.5 J
2. 3582.7 J
3. 3986.3 J
4. 4102.8 J

For a diatomic gas, if 1= ( CpCv ) for rigid molecules and 2= ( CpCv ) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? (Cp and Cv are specific heats of the gas at constant pressure and volume)

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

The temperature of a gas is -78 and the average translational kinetic energy of its molecules is K. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2 K is :

1. -78
2. 127
3. -39
4. 117

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27 ). The ratio of specific heat of gases at constant volume respectively is:

1. 32
2. 35
3. 75
4. 53

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

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