Q. No.When a large bubble rises from the bottom of a lake to the surface, its radius doubles. The atmospheric pressure is equal to that of a column of water of height H. The depth of the lake is:
1. H
2. 2H
3. 7H
4. 8H
1. \(\frac{400}{\sqrt{3}}\)
2. \(\frac{100\sqrt{2}}{3}\)
3. \(\frac{100}{3}\)
4. \(100\sqrt{2}\)
The change in the internal energy of an ideal gas does not depend on?
| 1. | Number of moles |
| 2. | Change in temperature |
| 3. | Specific heat at constant pressure \(C_p\) of the gas |
| 4. | Specific heat at constant volume \(C_v\) 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. | \(l\propto \dfrac{1}{d}\) |
The translational kinetic energy of \(n\) moles of a diatomic gas at absolute temperature \(T\) is given by:
1. \(\frac{5}{2}nRT\)
2. \(\frac{3}{2}nRT\)
3. \(5nRT\)
4. \(\frac{7}{2}nRT\)
If the mean free path of atoms is doubled, then the pressure of the gas will become:
1. \(\frac{P}{4}\)
2. \(\frac{P}{2}\)
3. \(\frac{P}{8}\)
4. \(P\)
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) |
If at a pressure of \(10^6\) dyne/cm2, one gram of nitrogen occupies \(2\times10^4\) c.c. volume, then the average energy of a nitrogen molecule in erg is:
| 1. | \(14\times10^{-13}\) | 2. | \(10\times10^{-12}\) |
| 3. | \(10^{6}\) | 4. | \(2\times10^{6}\) |
| 1. | \(2 P\) | 2. | \(P\) |
| 3. | \(\dfrac{P}{2}\) | 4. | \(4 P\) |
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