According to kinetic theory of gases,

Options

A. The velocity of molecules decreases for each collision
B. The pressure exerted by a diatomic gas is proportional to the mean velocity of the molecule.
C. The K.E of the gas decreases on expansion at constant temperature.
D. The mean translational K.E of diatomic gas increases with increses with increases in absolute temperature.

Explanation

To solve the question regarding the kinetic theory of gases, we will analyze each of the provided options step by step.

### Step 1: Analyze Option 1
**Statement:** The velocity of molecules decreases for each collision.

**Solution:** According to the kinetic theory of gases, all collisions between gas molecules are considered elastic. In elastic collisions, there is no loss of kinetic energy, which means that the velocities of the molecules do not decrease after collisions. Therefore, this statement is incorrect.

### Step 2: Analyze Option 2
**Statement:** The pressure exerted by the diatomic gas is proportional to the mean velocity of molecules.

**Solution:** The relationship between pressure (P), density (ρ), and mean velocity (V_mean) can be expressed as:
\[ V_{\text{mean}} = \sqrt{\frac{8P}{\pi \rho}} \]
From this equation, we can derive that pressure is proportional to the square of the mean velocity:
\[ P \propto V_{\text{mean}}^2 \]
Thus, the pressure is not directly proportional to the mean velocity, making this statement incorrect.

### Step 3: Analyze Option 3
**Statement:** Kinetic energy of gas decreases on expansion at constant temperature.

**Solution:** The kinetic energy of a gas is given by:
\[ KE = \frac{F}{2} RT \]
where F is the degrees of freedom, R is the gas constant, and T is the temperature. Since the kinetic energy depends only on the temperature and the type of gas (degrees of freedom), if the temperature remains constant during expansion, the kinetic energy also remains constant. Therefore, this statement is incorrect.

### Step 4: Analyze Option 4
**Statement:** Mean translational kinetic energy of diatomic gas increases with an increase in temperature.

**Solution:** The mean translational kinetic energy of a gas is directly proportional to its temperature:
\[ KE = \frac{F}{2} RT \]
As the temperature (T) increases, the kinetic energy also increases. Therefore, this statement is correct.

### Conclusion
Based on the analysis:
- Option 1: Incorrect
- Option 2: Incorrect
- Option 3: Incorrect
- Option 4: Correct

### Final Answer
The correct statement according to the kinetic theory of gases is Option 4.

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