Assertion (A): The average translational kinetic energy of the molecules in one mole of all ideal gases, at the same temperature is the same.
Reason (R): The average kinetic energy of one mole of any ideal gas at temperature T is given by \( \frac{3}{2}RT \).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The average translational kinetic energy per mole for any ideal gas is \( \frac{3}{2}RT \), dependent only on T.
So (A) is true. The formula in (R) represents this average translational kinetic energy per mole. So (R) is true and correctly explains (A).
Which of the following is not the correct assumption of kinetic theory of gases?
1. No intermolecular force acts between gas molecules.
2. The volume of molecules is negligible in comparison to the volume of gas.
3. Molecules only collide with the walls of container, there is no collision among the molecules.
4. All collisions are elastic.
View Answer
One of the postulates of the kinetic theory of gases is that gas molecules collide elastically with each other as well as with the walls of the container. Hence, the assumption that there are no collisions among molecules is incorrect.
If \(M\) is the molar mass of a gas, then the average speed of its molecules at temperature \(T\) is
1. \(\sqrt{\frac{3RT}{\pi M}}\)
2. \(\sqrt{\frac{8RT}{\pi M}}\)
3. \(\sqrt{\frac{2RT}{M}}\)
4. \(\sqrt{\frac{3RT}{M}}\)
View Answer
According to Maxwell-Boltzmann distribution, the average speed of molecules of an ideal gas is given by the expression \(v_{\text{avg}} = \sqrt{\frac{8RT}{\pi M}}\).
Which of the following is not the correct assumption of kinetic theory of gases?
1. No intermolecular force acts between gas molecules.
2. The volume of molecules is negligible in comparison to the volume of gas.
3. Molecules only collide with the walls of container, there is no collision among the molecules.
4. All collisions are elastic.
View Answer
Kinetic theory assumes that gas molecules undergo continuous random motion and collide with each other as well as with the walls of the container.
Consider the following statements out of which one is labelled as assertion and other as reason.
Assertion: The internal energy of an ideal monoatomic gas enclosed in a container does not change when there is no change in temperature.
Reason: Internal energy of a gaseous system is path function.
1. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
3. Assertion (A) is true and Reason (R) is false.
4. Assertion (A) is false and Reason (R) is true.
View Answer
Internal energy of an ideal gas depends only on its temperature, so the Assertion is true. However, internal energy is a state function, not a path function, so the Reason is false.
For an ideal gas, total energy is equally distributed in all possible energy modes, with each mode has an average energy equal to \(\frac{1}{2} k_B T\), and each vibrational mode has energy contribution of
1. \(\frac{1}{3} k_B T\)
2. \(k_B T\)
3. \(\frac{3}{2} k_B T\)
4. \(\frac{1}{4} k_B T\)
View Answer
Each vibrational mode has both kinetic energy and potential energy modes, thus having two degrees of freedom. Therefore, the average energy per vibrational mode is \(2 \times \frac{1}{2} k_B T = k_B T\).