NEET
- Exam
- NEET
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- Physics
- Chapter
- Kinetic Theory of Gases
NEET · Physics · Kinetic Theory of Gases
Match the quantities in Column I with their corresponding...
Match the quantities in Column I with their corresponding expressions in Column II.
(
)
| Column I | Column II | ||
| (a) | Root mean square speed | (p) | \tfrac{1}{2} m v_{rms}^{2} = \tfrac{3}{2} k_{B} T |
| (b) | Mean free path | (q) | \tfrac{1}{\sqrt{2 \pi d^{2} n}} |
| (c) | Ideal gas equation | (r) | P V = n R T |
| (d) | Degrees of freedom | (s) | 5 |
| of a diatomic gas | |||
| (e) | Pressure of an ideal gas | (t) | P = \tfrac{1}{3} \rho v_{rms}^{2} |
Options
- A
- B(a - p), (b - r), (c - q), (d - s), (e - t)
- C(a - t), (b - q), (c - r), (d - s), (e - p)
- D(a - t), (b - q), (c - s), (d - r), (e - p)
Correct answer
A.
Step-by-step solution
1. (a) Root mean square speed corresponds to the relation where the kinetic energy is given by (m v_{\mathrm{rms}}^2=k_B T), which shows the connection between temperature and molecular speed.
2. (b) Mean free path is the average distance a molecule travels before colliding, and it is given by (), where is the diameter of the molecules, and is the number density.
3. (c) Ideal gas equation is represented by the familiar equation , which relates pressure, volume, and temperature of an ideal gas.
4. (d) Degrees of freedom of a diatomic gas is typically 5, accounting for 3 translational and 2 rotational degrees of freedom at normal temperatures.
5. (e) Pressure of an ideal gas is related to the root mean square speed by (P=\frac{1}{3} \rhov_{\mathrm{rms}}^2), where (\rho) is the density of the gas.