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*Answer can only contain numeric values

QUESTION: 1

The capacity of a vessel in 3 litres. If contains 6gm oxygen, 8gm nitrogen and 5gm CO_{2} mixture at 27°C. If R = 7.31 J/mole-K, the pressure the vessel in units of 10^{3} N/m^{2} will be

Solution:

p = p_{1} + p_{2} + p_{3}

= 500 × 10^{3} N/m^{2}

The correct answer is: 500

*Answer can only contain numeric values

QUESTION: 2

22gm of CO_{2} at 27°C is mixed with 16 gm of O_{2} at 37°C. The temperature of the mixture (in °C) is?

Solution:

Let t be the temperature of mixture

Heat gained by CO_{2} = Heat lost by O_{2
}

⇒ t = 32°C

The correct answer is: 32

*Answer can only contain numeric values

QUESTION: 3

N molecule each of mass m of gas A and 2N molecules each of mass 2m of gas B are contained in the some vessel at temperature T. The mean square at temperature T. The mean square of the velocity of molecules of gas B is v_{2} and the mean square of x component of the velocity of molecules of gas A is w_{2} . The ratio w^{2}/v^{2 }upto 2 decimal plane is.

Solution:

Mean square velocity of molecule = 3kT/m

For gas A, x component of mean square velocity of molecule = w^{2} ...(1)

∴ Mean square velocity = ...(2)

For B gas, mean square velocity ...(3)

From (1) and (2),

So,

= 0.67

The correct answer is: 0.67

*Answer can only contain numeric values

QUESTION: 4

The gases occupy two containers A and B. Gas in A, of volume 0.1 m^{3} exerts a pressure of 1.40 MPa and that in B of volume 0.15 m^{2} exerts a pressure 0.7 MPa. The two containers are united by a tube of negligible volume and gases are allowed to intermingle. Then if the temperature remains constant the final pressure in the container will be (in MPa)

Solution:

µ_{A} + µ_{B} = µ

p = 0.98MPa

The correct answer is: 0.98

*Answer can only contain numeric values

QUESTION: 5

A gas mixture consists of 2 mole of oxygen and 4 mole of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system in the units of RT is given as?

Solution:

Total internal energy of system

= U_{oxygen} + U_{argon}

= 11RT (f_{1} = 5 for oxygen and f_{2} = 3 for argon.)

The correct answer is: 11

*Answer can only contain numeric values

QUESTION: 6

At standard temperature and pressure, the density of a gas is 1.3 kg/m^{3} and the speed of the sound and the speed of the sound in gas is 330 m/s. Then the degree of freedom of the gas will be?

Solution:

Velocity of sound v_{s} = 330 m/s

Density of gas ρ = 1.5kg/m^{3}

Atmosphere Pressure p = 1.01 × 10^{5} N/m^{2}

Substituting these values in

we get

Now

The correct answer is: 5

*Answer can only contain numeric values

QUESTION: 7

The mean free path of nitrogen molecules at a pressure of 1.0 atm and temperature 0°C is 0.8 × 10^{-7} m. If the number density of molecules is 2.7 × 10^{25} /m^{3} , then the molecular diameter (in Å) is.

Solution:

n = 2.7 × 10^{25} /m^{3}

d = 3.2 × 10^{-10} m

⇒ d = 3.2Å

The correct answer is: 3.2

*Answer can only contain numeric values

QUESTION: 8

The root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at 0°C is 3180 m/s. The pressure of hydrogen gas (in atm) is?

(density of hydrogen gas is 8.99 × 10^{-2} kg/m^{3} , 1 atm = 1.0 × 10^{5} N/m^{2} )

Solution:

As

p = 3.03 × 10^{5} N/m^{2}

p = 3 atm

The correct answer is: 3

*Answer can only contain numeric values

QUESTION: 9

A cylinder of capacity 20 litres is filled with H_{2} gas. The total average kinetic energy of translatory motion of its molecules is 1.5 × 10^{5} J. The pressure of hydrogen in the cylinder is (in 10^{6} N/m^{2}).

Solution:

Kinetic Energy E = 1.5 × 10^{5}J

Volume V = 20 litres = 20 × 10^{-3} m^{3}

Pressure =

p = 5 × 10^{6} N/m^{2}

The correct answer is: 5

*Answer can only contain numeric values

QUESTION: 10

If the mean free path of atoms is doubled, then the pressure of gas will change by what multiplicative factor?

Solution:

As

i.e. by increasing ρ two times, pressure will become half.

The correct answer is: 0.5

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