KE per unit volume is E. The pressure exerted by the gas is given by

Options

A. `E/3`
B. `(2E)/2`
C. `(3E)/2`
D. `E/2`

Explanation

To find the pressure exerted by a gas in terms of its kinetic energy per unit volume (E), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Kinetic Energy per Unit Volume (E)**:
- The kinetic energy per unit volume of a gas is denoted as \( E \).
- It is defined as the total kinetic energy of the gas divided by the volume of the gas.

2. **Using the Formula for Pressure**:
- The pressure \( P \) exerted by a gas can be derived from the kinetic theory of gases. The formula for pressure in terms of density \( \rho \) and average velocity \( V \) is given by:
\[ P = \frac{1}{3} \rho V^2 \]
- Here, \( \rho \) is the density of the gas, and \( V \) is the average velocity of the gas molecules.

3. **Relating Density to Mass and Volume**:
- The density \( \rho \) can be expressed as:
\[ \rho = \frac{m}{V} \]
- where \( m \) is the mass of the gas and \( V \) is its volume.

4. **Substituting Density into the Pressure Formula**:
- Substituting the expression for density into the pressure formula gives:
\[ P = \frac{1}{3} \left(\frac{m}{V}\right) V^2 \]
- Simplifying this, we get:
\[ P = \frac{1}{3} \frac{m V^2}{V} = \frac{1}{3} m \frac{V^2}{V} = \frac{1}{3} m V \]

5. **Expressing Kinetic Energy**:
- The kinetic energy \( KE \) of the gas can be expressed as:
\[ KE = \frac{1}{2} m V^2 \]
- The kinetic energy per unit volume \( E \) can therefore be expressed as:
\[ E = \frac{KE}{V} = \frac{\frac{1}{2} m V^2}{V} = \frac{1}{2} m V \]

6. **Relating Pressure to Kinetic Energy per Unit Volume**:
- From the previous steps, we can relate pressure \( P \) to kinetic energy per unit volume \( E \):
\[ P = \frac{2}{3} E \]

### Final Result:
Thus, the pressure exerted by the gas in terms of its kinetic energy per unit volume \( E \) is:
\[ P = \frac{2}{3} E \]