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.
Explanation:
The motion of the container is known as the ordered motion of the gas and zig-zag motion of gas molecules within the container is called disordered/random motion, like brownian motion. When the container suddenly stops, ordered kinetic energy gets converted into disordered kinetic energy which increases the temperature of the gas.
AIIMS - 2010
PHXI13:KINETIC THEORY
360278
The total kinetic energy of 1 mole of oxygen at \(27^\circ \,C\) is : [Use universal gas constant \((R) = 8.31\;J/mole{\rm{ }}K]\)
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 \(\begin{aligned}& =U_{\text {oxygen }}+U_{\text {argon }}=n_{1} \dfrac{F_{1}}{2} R T+n_{2} \dfrac{F_{2}}{2} R T \\& =2 \dfrac{5}{2} R T+4 \dfrac{3}{2} R T=5 R T+6 R T=11 R T\end{aligned}\) [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 \(\dfrac{1}{2} K_{B} T\). 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 \(=2 \times \dfrac{1}{2} K_{B} T=K_{B} T\) So correct option is (3).
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.
Explanation:
The motion of the container is known as the ordered motion of the gas and zig-zag motion of gas molecules within the container is called disordered/random motion, like brownian motion. When the container suddenly stops, ordered kinetic energy gets converted into disordered kinetic energy which increases the temperature of the gas.
AIIMS - 2010
PHXI13:KINETIC THEORY
360278
The total kinetic energy of 1 mole of oxygen at \(27^\circ \,C\) is : [Use universal gas constant \((R) = 8.31\;J/mole{\rm{ }}K]\)
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 \(\begin{aligned}& =U_{\text {oxygen }}+U_{\text {argon }}=n_{1} \dfrac{F_{1}}{2} R T+n_{2} \dfrac{F_{2}}{2} R T \\& =2 \dfrac{5}{2} R T+4 \dfrac{3}{2} R T=5 R T+6 R T=11 R T\end{aligned}\) [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 \(\dfrac{1}{2} K_{B} T\). 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 \(=2 \times \dfrac{1}{2} K_{B} T=K_{B} T\) So correct option is (3).
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.
Explanation:
The motion of the container is known as the ordered motion of the gas and zig-zag motion of gas molecules within the container is called disordered/random motion, like brownian motion. When the container suddenly stops, ordered kinetic energy gets converted into disordered kinetic energy which increases the temperature of the gas.
AIIMS - 2010
PHXI13:KINETIC THEORY
360278
The total kinetic energy of 1 mole of oxygen at \(27^\circ \,C\) is : [Use universal gas constant \((R) = 8.31\;J/mole{\rm{ }}K]\)
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 \(\begin{aligned}& =U_{\text {oxygen }}+U_{\text {argon }}=n_{1} \dfrac{F_{1}}{2} R T+n_{2} \dfrac{F_{2}}{2} R T \\& =2 \dfrac{5}{2} R T+4 \dfrac{3}{2} R T=5 R T+6 R T=11 R T\end{aligned}\) [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 \(\dfrac{1}{2} K_{B} T\). 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 \(=2 \times \dfrac{1}{2} K_{B} T=K_{B} T\) So correct option is (3).
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.
Explanation:
The motion of the container is known as the ordered motion of the gas and zig-zag motion of gas molecules within the container is called disordered/random motion, like brownian motion. When the container suddenly stops, ordered kinetic energy gets converted into disordered kinetic energy which increases the temperature of the gas.
AIIMS - 2010
PHXI13:KINETIC THEORY
360278
The total kinetic energy of 1 mole of oxygen at \(27^\circ \,C\) is : [Use universal gas constant \((R) = 8.31\;J/mole{\rm{ }}K]\)
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 \(\begin{aligned}& =U_{\text {oxygen }}+U_{\text {argon }}=n_{1} \dfrac{F_{1}}{2} R T+n_{2} \dfrac{F_{2}}{2} R T \\& =2 \dfrac{5}{2} R T+4 \dfrac{3}{2} R T=5 R T+6 R T=11 R T\end{aligned}\) [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 \(\dfrac{1}{2} K_{B} T\). 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 \(=2 \times \dfrac{1}{2} K_{B} T=K_{B} T\) So correct option is (3).
