Select correct statement(s)

Options

A. Kinetic energy is zero at `0^(@)C`
B. RMS velocity of `O_(2) " at" 27^(@)C " is " = sqrt((3 xx 8.314 xx 300)/(32)) ms^(-1)`
C. Distribution of molecules is very small when `u rarr 0 or u rarr oo`
D. All the statements are correct

Explanation

To solve the question of selecting the correct statements regarding kinetic energy, RMS velocity, and molecular distribution, we will analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement:** Kinetic energy is 0 at 0°C.

- **Conversion of Temperature:** 0°C = 273 K.
- **Kinetic Energy Formula:** The kinetic energy (KE) of a gas is given by the formula:
\[ KE = \frac{3}{2} RT \]
where \( R \) is the gas constant (8.314 J/(mol·K)) and \( T \) is the temperature in Kelvin.

- **Calculation:**
\[ KE = \frac{3}{2} \times 8.314 \times 273 \]
This value is not equal to 0. Therefore, the first statement is **incorrect**.

### Step 2: Analyze the second statement
**Statement:** RMS velocity of O2 at 27°C is equal to \(\sqrt{\frac{3 \times 8.314 \times 300}{32}}\) m/s.

- **Conversion of Temperature:** 27°C = 300 K.
- **Molecular Mass of O2:** The molecular mass of O2 is 32 g/mol.
- **RMS Velocity Formula:** The root mean square (RMS) velocity is given by:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]
where \( R \) is the gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass in kg/mol (32 g/mol = 0.032 kg/mol).

- **Calculation:**
\[ v_{rms} = \sqrt{\frac{3 \times 8.314 \times 300}{0.032}} \]
This calculation gives a valid RMS velocity value. Therefore, the second statement is **correct**.

### Step 3: Analyze the third statement
**Statement:** Distribution of molecules is very small when \( u \) tends to 0 or \( u \) tends to infinity.

- **Understanding Distribution:** The distribution of molecular speeds in a gas can be represented by a curve (Maxwell-Boltzmann distribution).
- **Behavior at Extremes:**
- As \( u \) (velocity) approaches 0, very few molecules have negligible speed.
- As \( u \) approaches infinity, again, very few molecules can reach extremely high speeds.

- **Conclusion:** The distribution of molecules is indeed very small at both extremes (0 and infinity). Therefore, the third statement is **correct**.

### Step 4: Conclusion
- The first statement is incorrect.
- The second statement is correct.
- The third statement is correct.
- Since the first statement is incorrect, the option "all statements are correct" is also incorrect.

**Final Answer:** The correct statements are the second and third statements.

---