The pressure exerted by a gas enclosed within a room is due to:
1. | collisions of the gas molecules with the walls of the room. |
2. | repulsive force between molecules of the gas. |
3. | weight of the molecules of the gas. |
4. | angular momentum of the molecules. |
1. | \(2 P\) | 2. | \(P\) |
3. | \(\dfrac{P}{2}\) | 4. | \(4 P\) |
1. | \(T_{H_{2}}=T_{H e}\) | 2. | \(\dfrac{T_{H_2}}{2}=\dfrac{T_{He}}{4}\) |
3. | \(5 T_{H_2}=3 T_{He}\) | 4. | \(\dfrac{T_{H_{2}}}{5}=\dfrac{T_{{He }}}{3}\) |
Which of the following parameters is the same for molecules of all gases at a given temperature?
1. mass
2. speed
3. momentum
4. kinetic energy
Match Column I and Column II and choose the correct match from the given choices.
Column I | Column II | ||
(A) | root mean square speed of gas molecules | (P) | \(\dfrac13nm\bar v^2\) |
(B) | the pressure exerted by an ideal gas | (Q) | \( \sqrt{\dfrac{3 R T}{M}} \) |
(C) | the average kinetic energy of a molecule | (R) | \( \dfrac{5}{2} R T \) |
(D) | the total internal energy of \(1\) mole of a diatomic gas | (S) | \(\dfrac32k_BT\) |
(A) | (B) | (C) | (D) | |
1. | (Q) | (P) | (S) | (R) |
2. | (R) | (Q) | (P) | (S) |
3. | (R) | (P) | (S) | (Q) |
4. | (Q) | (R) | (S) | (P) |
A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of \(500~\text{ms}^{-1}\) in the vertical direction. The pressure of the gas inside the vessel as observed by us on the ground:
1. | remains the same because \(500~\text{ms}^{-1}\) is very much smaller than \(v_{rms}\) of the gas. |
2. | remains the same because the motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls. |
3. | will increase by a factor equal to \(\left(\dfrac{v_{rms}^2+(500)^2}{v_{rms}^2}\right) \) where \(v_{rms}^2\) was the original mean square velocity of the gas. |
4. | will be different on the top wall and bottom wall of the vessel. |