Q. No.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. \(0.5~\text{kg/m}^{3}\)
(\(R=8.3~\text{J mol}^{-1} \text {K}^{-1}\))
1. \(0.2~\text{kg/m}^{3}\)
2. \(0.1~\text{kg/m}^{3}\)
3. \(0.02~\text{kg/m}^{3}\)
4. \(0.5~\text{kg/m}^{3}\)
(\(k_B\) is Boltzmann constant and \(T\) absolute temperature)
| 1. | \(\dfrac{3}{2}k_BT\) | 2. | \(\dfrac{5}{2}k_BT\) |
| 3. | \(\dfrac{7}{2}k_BT\) | 4. | \(\dfrac{1}{2}k_BT\) |
The mean free path for a gas, with molecular diameter \(d\) and number density \(n,\) can be expressed as:
| 1. | \( \dfrac{1}{\sqrt{2} n \pi {d}^2} \) | 2. | \( \dfrac{1}{\sqrt{2} n^2 \pi {d}^2} \) |
| 3. | \(\dfrac{1}{\sqrt{2} n^2 \pi^2 d^2} \) | 4. | \( \dfrac{1}{\sqrt{2} n \pi {d}}\) |
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 \(\gamma = \frac{C_P}{C_V}\) 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. | \(\dfrac{7}{5}, \dfrac{5}{3}, \dfrac{9}{7}\) | 2. | \(\dfrac{5}{3}, \dfrac{7}{5}, \dfrac{9}{7}\) |
| 3. | \(\dfrac{5}{3}, \dfrac{7}{5}, \dfrac{7}{5}\) | 4. | \(\dfrac{7}{5}, \dfrac{5}{3}, \dfrac{7}{5}\) |
If \(C_P\) and \(C_V\) denote the specific heats (per unit mass) of an ideal gas of molecular weight \(M\) (where \(R\) is the molar gas constant), the correct relation is:
1. \(C_P-C_V=R\)
2. \(C_P-C_V=\frac{R}{M}\)
3. \(C_P-C_V=MR\)
4. \(C_P-C_V=\frac{R}{M^2}\)
To find out the degree of freedom, the correct expression is:
1. \(f=\frac{2}{\gamma -1}\)
2. \(f=\frac{\gamma+1}{2}\)
3. \(f=\frac{2}{\gamma +1}\)
4. \(f=\frac{1}{\gamma +1}\)
The equation of state for 5g of oxygen at a pressure P and temperature T, when occupying a volume V, will be: (where R is the gas constant)
1. PV = 5 RT
2. PV = (5/2) RT
3. PV = (5/16) RT
4. PV = (5/32) RT
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) |
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