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Q. Statement 1:
The total translational kinetic energy of all the molecules of a given mass of on ideal gas is 1.5 times the product of its pressure and volume.
Statement 2:
The molecules of a gas collide with each other and the velocities of the molecules change due to collision.

Statement-1 is true, Statement 2 is true; Statement-2 is the correct explotion for Statement 1
Statement-1 is true, Statement 2 is true; Statement-2 is not the correct explotion for Statement 1
Statement-1 is true, Statement 2 is false
Statement-1 is false, Statement 2 is true

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Q. A cylinder of capacity

20 L

is filled with

H_{2}

gas. The total average kinetic energy of translatory motion of its molecules is

1.5 \times 10^{5} J

. The pressure of hydrogen in the cylinder is

$2 \times 10^{6} {N/m}^{2}$
$3 \times 10^{6} {N/m}^{2}$
$4 \times 10^{6} {N/m}^{2}$
$5 \times 10^{6} {N/m}^{2}$

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Q. The translational kinetic energy of all the molecules of

1

mole of Helium gas having a volume

V

exerting a pressure

P

is

1000 J

. The total kinetic energy (in

Joule

) of all the molecules of

1

mole of

N_{2}

gas having the same volume

V

and exerting a pressure

2 P

is :

$4000 J$
$3000 J$
$2000 J$
$1000 J$

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Q. For ideal gas molecules the following quantities have zero average values.

Velocity
Momentum
Kinetic energy
Density

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Q. Statement 1:
The total translational kinetic energy of all the molecules of a given mass of on ideal gas is 1.5 times the product of its pressure and volume.
Statement 2:
The molecules of a gas collide with each other and the velocities of the molecules change due to collision.

Statement-1 is true, Statement 2 is true; Statement-2 is the correct explotion for Statement 1
Statement-1 is true, Statement 2 is true; Statement-2 is not the correct explotion for Statement 1
Statement-1 is true, Statement 2 is false
Statement-1 is false, Statement 2 is true

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Q. A closed container is filled with

20 moles

of an ideal diatomic gas at absolute temperature

T

. When heat is supplied to it, the temperature remains constant, but

8 moles

of the gas dissociate into atoms. The heat energy supplied to the gas is

$7 R T$
$6 R T$
$4 R T$
$5 R T$

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Q. If

2

moles of an ideal monoatomic gas at temperature

T_{0}

is mixed with

4

moles of another ideal monoatomic gas at temperature

2 T_{0}

, then the temperature of the mixture is

$\frac{5}{3} T_{0}$
$\frac{3}{2} T_{0}$
$\frac{4}{3} T_{0}$
$\frac{5}{4} T_{0}$

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Q. A tank used for filling helium balloons has a volume of

0.3 m^{3}

and contains

2 mol

of helium gas at

20^{\circ} C

. Assuming that the helium behaves like an ideal gas, find the total translational kinetic energy of the molecules of the gas

$7.3 kJ$
$10 kJ$
$3.65 kJ$
$2.4 kJ$

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Q. The translational kinetic energy of

1 mole

of an ideal gas at standard temperature is close to

$3403 J$
$3000 J$
$2342 J$
$1564 J$

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Q. If

2

moles of an ideal monoatomic gas at temperature

T_{0}

is mixed with

4

moles of another ideal monoatomic gas at temperature

2 T_{0}

, then the temperature of the mixture is

$\frac{5}{3} T_{0}$
$\frac{3}{2} T_{0}$
$\frac{4}{3} T_{0}$
$\frac{5}{4} T_{0}$

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Q. A gas mixture consists of

2

moles of oxygen and

4

moles of argon at temperature

T

. Neglecting all vibrational modes, the total internal energy of the system is

$14 R T$
$13 R T$
$15 R T$
$11 R T$

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Q.

N

molecules of an ideal gas at temperature

T_{1}

and pressure

P_{1}

are contained in a closed box. The molecules in the box gets doubled, Keeping total kinetic energy same. If new pressure is

P_{2}

and temperature is

T_{2}

, Then:

$P_{2} = P, T_{2} = T_{1}$
$P_{2} = P_{1}, T_{2} = \frac{T_{1}}{2}$
$P_{2} = 2 P_{1} . T_{2} = T_{1}$
$P_{2} = 2 P_{1}, T_{2} = \frac{T_{1}}{2}$

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Q. From the following statements , regarding an ideal gas at any given temperature

T

, choose the correct alternative

(s)

The coefficient of volume expansion at constant pressure is the same for all ideal gases
The average translational kinetic energy per molecule of oxygen gas is $3 k T$ , where $k$ being Boltzmann constant
The mean -free path of molecules increases with decrease in the pressure
In a gaseous mixture, the average translational kinetic energy of the molecules of each component is different.

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Q. Initially, the nucleus of

Radium - 226

is at rest. It decays by emitting an

α -

particle, and thus the nucleus of

Radon

is created. The released energy during the decay is

4.87 MeV

, which appears as the kinetic energy of the two resulted particles. The kinetic energy of

α -

particle &

Radon

nucleus are respectively.

[m_{α} = 4.002 u, m_{Rn} = 222.017 u]

$3.08 MeV, 0.09 MeV$
$0.09 MeV, 4.78 MeV$
$3.68 MeV, 1.09 MeV$
$4.78 MeV, 0.09 MeV$

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Q. From the following statements , regarding an ideal gas at any given temperature

T

, choose the correct alternative

(s)

The coefficient of volume expansion at constant pressure is the same for all ideal gases
The average translational kinetic energy per molecule of oxygen gas is $3 k T$ , where $k$ being Boltzmann constant
The mean -free path of molecules increases with decrease in the pressure
In a gaseous mixture, the average translational kinetic energy of the molecules of each component is different.

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Q.

N

molecules of an ideal gas at temperature

T_{1}

and pressure

P_{1}

are contained in a closed box. The molecules in the box gets doubled, Keeping total kinetic energy same. If new pressure is

P_{2}

and temperature is

T_{2}

, Then:

$P_{2} = P, T_{2} = T_{1}$
$P_{2} = P_{1}, T_{2} = \frac{T_{1}}{2}$
$P_{2} = 2 P_{1} . T_{2} = T_{1}$
$P_{2} = 2 P_{1}, T_{2} = \frac{T_{1}}{2}$

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Q. A gas mixture of

2

moles of

O_{2}

and

4

moles of

A r

are at temperature

T

. Neglecting all the vibrational modes, the total internal energy of the system is

$4 R T$
$15 R T$
$9 R T$
$11 R T$

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Q. What is the average translational kinetic energy of a gas molecule at

500 K

?

$1035 \times 10^{- 23} J$
$750 \times 10^{- 23} J$
$1725 \times 10^{- 23} J$
$1150 \times 10^{- 23} J$

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Q. A tank used for filling helium balloons has a volume of

0.3 m^{3}

and contains

2 mol

of helium gas at

20^{\circ} C

. Assuming that the helium behaves like an ideal gas, find the total translational kinetic energy of the molecules of the gas

$7.3 kJ$
$10 kJ$
$3.65 kJ$
$2.4 kJ$

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