Select the incorrect statement(s) :

Options

A. The product of pressure and volume of fixed amount of a gas is independent of temperature.
B. The value of universal gas constant depends upon temperature, volume and number of gaseous molecules
C. The gas constant also known as Boltzmann's constant
D. The average kinetic energy of molecules depends only on temperature

Explanation

To solve the question of identifying the incorrect statements regarding the gaseous state, we will analyze each statement one by one.

### Step 1: Analyze Statement 1
**Statement 1:** The product of pressure and volume of a fixed amount of gas is independent of temperature.

- According to the Ideal Gas Law, \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is temperature.
- For a fixed amount of gas (constant \( n \)), the product \( PV \) is directly proportional to \( T \).
- Therefore, this statement is incorrect because \( PV \) is dependent on temperature.

### Step 2: Analyze Statement 2
**Statement 2:** The value of the universal gas constant depends upon temperature, volume, and number of gaseous molecules.

- The universal gas constant \( R \) is a constant value that does not change with temperature, volume, or the number of molecules.
- It is a fixed value used in the Ideal Gas Law.
- Thus, this statement is also incorrect.

### Step 3: Analyze Statement 3
**Statement 3:** The gas constant is also known as the Boltzmann constant.

- The gas constant \( R \) is related to the Boltzmann constant \( k \) by the equation \( R = k \cdot N_A \), where \( N_A \) is Avogadro's number.
- Therefore, \( R \) is not the same as \( k \), making this statement incorrect.

### Step 4: Analyze Statement 4
**Statement 4:** The average kinetic energy of a molecule depends only on temperature.

- The average kinetic energy of gas molecules can be expressed as \( KE = \frac{3}{2} k T \) or \( KE = \frac{3}{2} R T \) for one mole of gas.
- In both expressions, the average kinetic energy is directly proportional to temperature \( T \) and does not depend on other factors.
- Therefore, this statement is correct.

### Conclusion
The incorrect statements are:
- Statement 1
- Statement 2
- Statement 3

### Final Answer
The answer to the question is that statements 1, 2, and 3 are incorrect.

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