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 statement(s) regarding the kinetic energy and properties of gases, we will analyze each statement step by step.

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

- **Conversion to Kelvin**: 0 degrees Celsius is equivalent to 273 Kelvin (0 + 273).
- **Kinetic Energy Formula**: The formula for kinetic energy (KE) of a gas is given by:
\[ KE = \frac{3}{2} k T \]
where \( k \) is the Boltzmann constant and \( T \) is the temperature in Kelvin.
- **Calculation**: Substituting \( T = 273 \) K into the formula:
\[ KE = \frac{3}{2} \times (1.38 \times 10^{-23} \text{ J/K}) \times 273 \text{ K} \]
This value will not equal 0. Thus, the first statement is **incorrect**.

### Step 2: Analyze the second statement
**Statement**: RMS velocity of O2 at 27 degrees Celsius is given as \( \sqrt{3 \times 8.314 \times 300 / 32} \).

- **RMS Velocity Formula**: The formula for the root mean square (RMS) velocity is:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]
where \( R \) is the universal gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass in kg/mol.
- **Temperature Conversion**: 27 degrees Celsius is 300 Kelvin (27 + 273).
- **Molar Mass Conversion**: The molar mass of O2 is 32 g/mol, which is equivalent to 0.032 kg/mol.
- **Calculation**: Substituting the values:
\[ v_{rms} = \sqrt{\frac{3 \times 8.314 \times 300}{0.032}} \]
The statement incorrectly uses 32 g/mol instead of 0.032 kg/mol. Therefore, the second statement is **incorrect**.

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

- **Maxwell-Boltzmann Distribution**: This distribution describes the speeds of particles in a gas.
- **Graph Analysis**: At \( u = 0 \) (no speed), the number of molecules is indeed very small. As \( u \) approaches infinity, the number of molecules also approaches zero.
- **Conclusion**: This statement is **correct**.

### Step 4: Analyze the fourth statement
**Statement**: All the statements are correct.

- Since we have determined that the first and second statements are incorrect while the third statement is correct, this statement is also **incorrect**.

### Final Conclusion
The only correct statement is the third one regarding the distribution of molecules.

### Summary of Correct Statements
- **Correct Statement**: The distribution of molecules is very small when \( u = 0 \) or \( u = \infty \).
- **Incorrect Statements**: Kinetic energy at 0 degrees Celsius is not 0, and the RMS velocity calculation contains an error in molar mass.