Select the correct statement :

Options

A. The value of compressibility factor 'Z' for `H_(2)` gas is greater than one at room
B. The real gas behaves as an ideal gas at Boyle's temperature.
C. For a real gas following van der Waals' equation of state, the expression of critical temperature is `(8a)/(27R.b)`
D. AT low pressure, the compressibility factor 'Z'=1+`(P.b)/(RT)` for a van der Waals' gas.

Answer

To solve the question "Select the correct statement," we will analyze each statement provided in the video transcript step by step.

### Step 1: Analyze the first statement
**Statement:** The value of compressibility factor for H2 is greater than 1.

**Explanation:**
The compressibility factor (Z) is defined as Z = PV/nRT. For ideal gases, Z = 1. However, for real gases, Z can be greater than or less than 1 depending on the conditions. Hydrogen (H2) is a light gas, and under certain conditions, especially at high pressures, it can exhibit a compressibility factor greater than 1.

**Conclusion:** This statement is true.

### Step 2: Analyze the second statement
**Statement:** A real gas behaves like an ideal gas at its boiling temperature.

**Explanation:**
At the boiling point, the attractive and repulsive forces between molecules can balance out, allowing the gas to behave more ideally. This is a characteristic of real gases, where they tend to behave like ideal gases at certain conditions, including their boiling point.

**Conclusion:** This statement is true.

### Step 3: Analyze the third statement
**Statement:** For the real gas following the Van der Waals equation, critical temperature is given by 8A/(27Rb).

**Explanation:**
The Van der Waals equation accounts for the volume occupied by gas molecules and the intermolecular forces. The critical temperature (Tc) for a Van der Waals gas is indeed given by the formula Tc = 8A/(27Rb), where A and B are constants specific to the gas.

**Conclusion:** This statement is true.

### Step 4: Analyze the fourth statement
**Statement:** At low pressure, the compressibility factor is given by the equation P(Vm - B) = RT.

**Explanation:**
At low pressures, the volume of the gas is large, and the effects of the volume occupied by the gas molecules (B) become negligible. The equation simplifies to PVm = nRT, which implies Z = 1. However, the statement provided in the transcript suggests a different form that is not correct for low-pressure conditions.

**Conclusion:** This statement is false.

### Final Conclusion
The correct statements from the analysis are:
1. The value of compressibility factor for H2 is greater than 1. (True)
2. A real gas behaves like an ideal gas at its boiling temperature. (True)
3. For the real gas following the Van der Waals equation, critical temperature is given by 8A/(27Rb). (True)
4. At low pressure, the compressibility factor is given by the equation P(Vm - B) = RT. (False)

### Selected Correct Statements
- The value of compressibility factor for H2 is greater than 1.
- A real gas behaves like an ideal gas at its boiling temperature.
- For the real gas following the Van der Waals equation, critical temperature is given by 8A/(27Rb).