The temperature at which the RMS speed of atoms in neon gas is equal to the RMS speed of hydrogen molecules at \(15^{\circ} \text{C}\) is:
(the atomic mass of neon \(=20.2~\text u,\) molecular mass of hydrogen \(=2~\text u\))
1. \(2.9\times10^{3}~\text K\)
2. \(2.9~\text K\)
3. \(0.15\times10^{3}~\text K\)
4. \(0.29\times10^{3}~\text K\)
1. | all vessels contain an unequal number of respective molecules. |
2. | the root mean square speed of molecules is the same in all three cases. |
3. | the root mean square speed of helium is the largest. |
4. | the root mean square speed of sulfur hexafluoride is the largest. |
1. | \(223~\text{K}\) | 2. | \(669^\circ \text{C}\) |
3. | \(3295^\circ \text{C}\) | 4. | \(3097~\text{K}\) |
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 a 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) |
1. | mass density, the mass of the gas. |
2. | number density, molar mass. |
3. | mass density, molar mass. |
4. | number density, the mass of the gas. |
The mean free path \(l\) for a gas molecule depends upon the diameter, \(d\) of the molecule as:
1. | \(l\propto \dfrac{1}{d^2}\) | 2. | \(l\propto d\) |
3. | \(l\propto d^2 \) | 4. | \(l\propto \dfrac{1}{d}\) |
1. | \(P_1>P_3>P_2 \) | 2. | \(P_2>P_1>P_3 \) |
3. | \( P_1>P_2>P_3\) | 4. | \(P_3 > P_2>P_1\) |
1. | \(100\%\) | 2. | \(200\%\) |
3. | \(300\%\) | 4. | \(50\%\) |