Statement-1: The total translational kinetic energy of fall the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume because.
Statement-2: The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

Options

A. Statement-I is True, Statement-II is True and Statement-II is a correct explanation for Statement-I.
B. Statement-I is True, Statement-II is True and Statement-II is NOT a correct explanation for Statement-I.
C. Statement-I is True, Statement-II is False.
D. Statement-I is False, Statement-II is True

Answer

To analyze the statements provided in the question, we will break down the concepts of translational kinetic energy, the ideal gas law, and the implications of molecular collisions.

### Step 1: Understand the Total Translational Kinetic Energy of an Ideal Gas
The total translational kinetic energy (TKE) of all the molecules in a gas can be expressed using the formula:
\[ \text{TKE} = \frac{3}{2} nRT \]
where \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the absolute temperature in Kelvin.

### Step 2: Relate TKE to Pressure and Volume
From the ideal gas equation, we know:
\[ PV = nRT \]
Substituting \( nRT \) in the TKE equation gives:
\[ \text{TKE} = \frac{3}{2} PV \]
This shows that the total translational kinetic energy of the gas molecules is indeed proportional to the product of pressure and volume, specifically:
\[ \text{TKE} = \frac{3}{2} PV \]
This confirms Statement-1, which claims that the total translational kinetic energy is 1.5 times the product of pressure and volume.

### Step 3: Analyze Statement-2
Statement-2 asserts that the molecules of a gas collide with each other and that the velocities of the molecules change due to these collisions. This is a true statement because molecular collisions are a fundamental aspect of gas behavior. In an ideal gas, these collisions are assumed to be elastic, meaning that kinetic energy is conserved during the collision, but the velocities of the individual molecules do change.

### Conclusion
- **Statement-1** is true because the total translational kinetic energy of an ideal gas is indeed \( \frac{3}{2} PV \).
- **Statement-2** is also true, but it does not provide a correct explanation for Statement-1. The change in velocity due to collisions is not the reason for the relationship between kinetic energy and the product of pressure and volume.

Thus, the correct option is that both statements are true, but Statement-2 does not correctly explain Statement-1.

### Final Answer
Both statements are true, but Statement-2 is not a correct explanation for Statement-1.

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