1. | \(\dfrac{3}{2}k_BT\) | 2. | \(\dfrac{5}{2}k_BT\) |
3. | \(\dfrac{7}{2}k_BT\) | 4. | \(\dfrac{1}{2}k_BT\) |
A cylinder contains hydrogen gas at a pressure of \(249~\text{kPa}\) and temperature \(27^\circ\text{C}.\) 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 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. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}}\)
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. | 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 \(\gamma = \dfrac{C_P}{C_V}\) 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. | \(\dfrac{7}{5}, \dfrac{5}{3}, \dfrac{9}{7}\) | 2. | \(\dfrac{5}{3}, \dfrac{7}{5}, \dfrac{9}{7}\) |
3. | \(\dfrac{5}{3}, \dfrac{7}{5}, \dfrac{7}{5}\) | 4. | \(\dfrac{7}{5}, \dfrac{5}{3}, \dfrac{7}{5}\) |
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) | \(\dfrac13nm\bar v^2\) |
(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) |
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 |