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PHXI13:KINETIC THEORY

360277 Assertion :
If a gas container in motion is suddenly stopped, the temperature of the gas rises.
Reason :
The kinetic energy of ordered mechanical motion is converted into the kinetic energy of random motion of gas molecules.

1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

3 Assertion is correct but Reason is incorrect.

4 Both Assertion and Reason are incorrect.

AIIMS - 2010

PHXI13:KINETIC THEORY

360278 The total kinetic energy of 1 mole of oxygen at $27^{\circ} C$ is : [Use universal gas constant $(R) = 8.31 J / m o l e K]$

1

5942.0 J

2

5670.5 J

3

6232.5 J

4

6845.5 J

Explanation:

$K . E . = \frac{f}{2} n R T$
$K . E . = \frac{5}{2} (1) (\frac{25}{3}) (300)$
${f = 5 f o r d i a t o m i c g a s}$
$K . E . = 6232.5 J$

JEE - 2024

PHXI13:KINETIC THEORY

360279 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

1

4 R T

2

15 R T

3

9 R T

4

11 R T

Explanation:

Total internal energy of system
$\begin{aligned} = U_{oxygen} + U_{argon} = n_{1} \frac{F_{1}}{2} R T + n_{2} \frac{F_{2}}{2} R T \\ = 2 \frac{5}{2} R T + 4 \frac{3}{2} R T = 5 R T + 6 R T = 11 R T \end{aligned}$
[As $F_{1} = 5$ (for oxygen) and $F_{2} = 3$ (for argon) $]$ .

PHXI13:KINETIC THEORY

360280 Assertion :
Vibrational energy of diatomic molecule corresponding to each degree of freedom is $K_{B} T$ .
Reason :
For every molecule, vibrational degree of freedom is 2 .

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

According to law of equipartition energy in thermal equilibrium, at temperature $T$ . each degree of freedom of contributes an average energy equal to $\frac{1}{2} K_{B} T$ .
The vibrational motion has two types of energy associated with the vibrations along the length of the molecule-kinetic energy and potential energy. Thus it contributes two degrees of freedom. Thus vibration energy
$= 2 \times \frac{1}{2} K_{B} T = K_{B} T$
So correct option is (3).

PHXI13:KINETIC THEORY

360277 Assertion :
If a gas container in motion is suddenly stopped, the temperature of the gas rises.
Reason :
The kinetic energy of ordered mechanical motion is converted into the kinetic energy of random motion of gas molecules.

1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

3 Assertion is correct but Reason is incorrect.

4 Both Assertion and Reason are incorrect.

AIIMS - 2010

PHXI13:KINETIC THEORY

360278 The total kinetic energy of 1 mole of oxygen at $27^{\circ} C$ is : [Use universal gas constant $(R) = 8.31 J / m o l e K]$

1

5942.0 J

2

5670.5 J

3

6232.5 J

4

6845.5 J

Explanation:

$K . E . = \frac{f}{2} n R T$
$K . E . = \frac{5}{2} (1) (\frac{25}{3}) (300)$
${f = 5 f o r d i a t o m i c g a s}$
$K . E . = 6232.5 J$

JEE - 2024

PHXI13:KINETIC THEORY

360279 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

1

4 R T

2

15 R T

3

9 R T

4

11 R T

Explanation:

Total internal energy of system
$\begin{aligned} = U_{oxygen} + U_{argon} = n_{1} \frac{F_{1}}{2} R T + n_{2} \frac{F_{2}}{2} R T \\ = 2 \frac{5}{2} R T + 4 \frac{3}{2} R T = 5 R T + 6 R T = 11 R T \end{aligned}$
[As $F_{1} = 5$ (for oxygen) and $F_{2} = 3$ (for argon) $]$ .

PHXI13:KINETIC THEORY

360280 Assertion :
Vibrational energy of diatomic molecule corresponding to each degree of freedom is $K_{B} T$ .
Reason :
For every molecule, vibrational degree of freedom is 2 .

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

According to law of equipartition energy in thermal equilibrium, at temperature $T$ . each degree of freedom of contributes an average energy equal to $\frac{1}{2} K_{B} T$ .
The vibrational motion has two types of energy associated with the vibrations along the length of the molecule-kinetic energy and potential energy. Thus it contributes two degrees of freedom. Thus vibration energy
$= 2 \times \frac{1}{2} K_{B} T = K_{B} T$
So correct option is (3).

PHXI13:KINETIC THEORY

360277 Assertion :
If a gas container in motion is suddenly stopped, the temperature of the gas rises.
Reason :
The kinetic energy of ordered mechanical motion is converted into the kinetic energy of random motion of gas molecules.

1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

3 Assertion is correct but Reason is incorrect.

4 Both Assertion and Reason are incorrect.

AIIMS - 2010

PHXI13:KINETIC THEORY

360278 The total kinetic energy of 1 mole of oxygen at $27^{\circ} C$ is : [Use universal gas constant $(R) = 8.31 J / m o l e K]$

1

5942.0 J

2

5670.5 J

3

6232.5 J

4

6845.5 J

Explanation:

$K . E . = \frac{f}{2} n R T$
$K . E . = \frac{5}{2} (1) (\frac{25}{3}) (300)$
${f = 5 f o r d i a t o m i c g a s}$
$K . E . = 6232.5 J$

JEE - 2024

PHXI13:KINETIC THEORY

360279 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

1

4 R T

2

15 R T

3

9 R T

4

11 R T

Explanation:

Total internal energy of system
$\begin{aligned} = U_{oxygen} + U_{argon} = n_{1} \frac{F_{1}}{2} R T + n_{2} \frac{F_{2}}{2} R T \\ = 2 \frac{5}{2} R T + 4 \frac{3}{2} R T = 5 R T + 6 R T = 11 R T \end{aligned}$
[As $F_{1} = 5$ (for oxygen) and $F_{2} = 3$ (for argon) $]$ .

PHXI13:KINETIC THEORY

360280 Assertion :
Vibrational energy of diatomic molecule corresponding to each degree of freedom is $K_{B} T$ .
Reason :
For every molecule, vibrational degree of freedom is 2 .

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

According to law of equipartition energy in thermal equilibrium, at temperature $T$ . each degree of freedom of contributes an average energy equal to $\frac{1}{2} K_{B} T$ .
The vibrational motion has two types of energy associated with the vibrations along the length of the molecule-kinetic energy and potential energy. Thus it contributes two degrees of freedom. Thus vibration energy
$= 2 \times \frac{1}{2} K_{B} T = K_{B} T$
So correct option is (3).

PHXI13:KINETIC THEORY

360277 Assertion :
If a gas container in motion is suddenly stopped, the temperature of the gas rises.
Reason :
The kinetic energy of ordered mechanical motion is converted into the kinetic energy of random motion of gas molecules.

1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

3 Assertion is correct but Reason is incorrect.

4 Both Assertion and Reason are incorrect.

AIIMS - 2010

PHXI13:KINETIC THEORY

360278 The total kinetic energy of 1 mole of oxygen at $27^{\circ} C$ is : [Use universal gas constant $(R) = 8.31 J / m o l e K]$

1

5942.0 J

2

5670.5 J

3

6232.5 J

4

6845.5 J

Explanation:

$K . E . = \frac{f}{2} n R T$
$K . E . = \frac{5}{2} (1) (\frac{25}{3}) (300)$
${f = 5 f o r d i a t o m i c g a s}$
$K . E . = 6232.5 J$

JEE - 2024

PHXI13:KINETIC THEORY

360279 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

1

4 R T

2

15 R T

3

9 R T

4

11 R T

Explanation:

Total internal energy of system
$\begin{aligned} = U_{oxygen} + U_{argon} = n_{1} \frac{F_{1}}{2} R T + n_{2} \frac{F_{2}}{2} R T \\ = 2 \frac{5}{2} R T + 4 \frac{3}{2} R T = 5 R T + 6 R T = 11 R T \end{aligned}$
[As $F_{1} = 5$ (for oxygen) and $F_{2} = 3$ (for argon) $]$ .

PHXI13:KINETIC THEORY

360280 Assertion :
Vibrational energy of diatomic molecule corresponding to each degree of freedom is $K_{B} T$ .
Reason :
For every molecule, vibrational degree of freedom is 2 .

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

According to law of equipartition energy in thermal equilibrium, at temperature $T$ . each degree of freedom of contributes an average energy equal to $\frac{1}{2} K_{B} T$ .
The vibrational motion has two types of energy associated with the vibrations along the length of the molecule-kinetic energy and potential energy. Thus it contributes two degrees of freedom. Thus vibration energy
$= 2 \times \frac{1}{2} K_{B} T = K_{B} T$
So correct option is (3).

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