The mean free path for a gas, with molecular diameter \(d\) and number density \(n,\) can be expressed as:
1. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}^2} \)
2. \( \frac{1}{\sqrt{2} n^2 \pi \mathrm{d}^2} \)
3. \(\frac{1}{\sqrt{2} n^2 \pi^2 d^2} \)
4. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}}\)
A cylinder contains hydrogen gas at a pressure of \(249~\text{kPa}\) and temperature \(27^\circ~\mathrm{C}.\) Its density is: (\(R=8.3~\text{J mol}^{-1} \text {K}^{-1}\))
1. \(0.2~\text{kg/m}^{3}\)
2. \(0.1~\text{kg/m}^{3}\)
3. \(0.02~\text{kg/m}^{3}\)
4. \(0.5~\text{kg/m}^{3}\)
The average thermal energy for a mono-atomic gas is:
(\(k_B\) is Boltzmann constant and T absolute temperature)
1. \(\frac{3}{2}k_BT\)
2. \(\frac{5}{2}k_BT\)
3. \(\frac{7}{2}k_BT\)
4. \(\frac{1}{2}k_BT\)
The mean free path \(l\) for a gas molecule depends upon the diameter, \(d\) of the molecule as:
1. \(l\propto \frac{1}{d^2}\)
2. \(l\propto d\)
3. \(l\propto d^2 \)
4. \(l\propto \frac{1}{d}\)
An ideal gas equation can be written as where and are respectively:
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 value \(\gamma = \frac{C_P}{C_V}\) for hydrogen, helium, and another ideal diatomic gas \(X\) (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to:
1. \(\frac{7}{5}, \frac{5}{3}, \frac{9}{7}\)
2. \(\frac{5}{3}, \frac{7}{5}, \frac{9}{7}\)
3. \(\frac{5}{3}, \frac{7}{5}, \frac{7}{5}\)
4. \(\frac{7}{5}, \frac{5}{3}, \frac{7}{5}\)
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) | \(\frac13nm\bar v^2\) |
(B) | the pressure exerted by an ideal gas | (Q) | \( \sqrt{\frac{3 R T}{M}} \) |
(C) | the average kinetic energy of a molecule | (R) | \( \frac{5}{2} R T \) |
(D) | the total internal energy of 1 mole of a diatomic gas | (S) | \(\frac32k_BT\) |
(A) | (B) | (C) | (D) | |
1. | (Q) | (P) | (S) | (R) |
2. | (R) | (Q) | (P) | (S) |
3. | (R) | (P) | (S) | (Q) |
4. | (Q) | (R) | (S) | (P) |
An increase in the temperature of a gas-filled in a container would lead to:
1. | decrease in intermolecular distance. |
2. | increase in its mass. |
3. | increase in its kinetic energy. |
4. | decrease in its pressure. |
The temperature at which the rms speed of atoms in neon gas is equal to the rms speed of hydrogen molecules at \(15^{\circ} \mathrm{C}\) is: (Atomic mass of neon\(=20.2\) u, molecular mass of hydrogen\(=2\) u)
1. \(2.9\times10^{3}\) K
2. \(2.9\) K
3. \(0.15\times10^{3}\) K
4. \(0.29\times10^{3}\) K