Assertion Pressure of a gas id given as `p=2/3E.`
Reason In the above expession, E represnts kinetic energy of the gas per unit volume.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explation os Assertion.
C. If Assertionis true bur Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the assertion and reason question, we need to analyze both statements step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that the pressure of a gas is given by the equation \( P = \frac{2}{3} E \). Here, \( P \) represents the pressure of the gas, and \( E \) represents the kinetic energy of the gas per unit volume.

2. **Understanding the Reason**:
The reason provided states that in the expression \( P = \frac{2}{3} E \), \( E \) represents the kinetic energy of the gas per unit volume.

3. **Relating Pressure and Kinetic Energy**:
To validate the assertion, we need to relate the pressure of a gas to its kinetic energy. The kinetic energy (KE) of an ideal gas can be expressed as:
\[ KE = \frac{3}{2} nRT \]
where \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.

4. **Using the Ideal Gas Law**:
From the ideal gas law, we know:
\[ PV = nRT \]
Rearranging this gives:
\[ nRT = PV \]

5. **Substituting into the Kinetic Energy Equation**:
Substituting \( nRT \) from the ideal gas law into the kinetic energy equation gives:
\[ KE = \frac{3}{2} PV \]

6. **Finding Kinetic Energy per Unit Volume**:
To find the kinetic energy per unit volume \( E \), we divide the total kinetic energy by the volume \( V \):
\[ E = \frac{KE}{V} = \frac{\frac{3}{2} PV}{V} = \frac{3}{2} P \]

7. **Relating Pressure to Kinetic Energy**:
Rearranging the equation \( E = \frac{3}{2} P \) gives:
\[ P = \frac{2}{3} E \]
This confirms the assertion that \( P = \frac{2}{3} E \).

8. **Conclusion**:
Since we have verified that the assertion \( P = \frac{2}{3} E \) is correct and that \( E \) indeed represents the kinetic energy per unit volume, we conclude that both the assertion and the reason are correct. Furthermore, the reason provides a correct explanation for the assertion.

### Final Answer:
Both the assertion and the reason are correct, and the reason is the correct explanation of the assertion.

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