KE per unit volume is:

Options

A. `(3)/(2) P`
B. `(3)/(2) RT`
C. `(3)/(2) (RN)/(N_(0))`
D. `(3)/(2) (RT)/(n)`

Explanation

To find the kinetic energy per unit volume (KE per unit volume) for an ideal gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Kinetic Energy of Gas:**
The kinetic energy (KE) of an ideal gas can be expressed in terms of the number of moles (n) and temperature (T) using the formula:
\[ KE = \frac{3}{2} nRT \]
where R is the gas constant.

2. **Relate Number of Moles to Pressure and Volume:**
According to the ideal gas law, we have:
\[ PV = nRT \]
This means we can express \(nRT\) in terms of pressure (P) and volume (V):
\[ nRT = PV \]

3. **Substitute into the Kinetic Energy Formula:**
Now, substituting \(nRT\) in the kinetic energy formula gives us:
\[ KE = \frac{3}{2} PV \]

4. **Calculate Kinetic Energy per Unit Volume:**
To find the kinetic energy per unit volume, we need to divide the total kinetic energy by the volume (V):
\[ KE \text{ per unit volume} = \frac{KE}{V} = \frac{\frac{3}{2} PV}{V} \]

5. **Simplify the Expression:**
The volume (V) cancels out:
\[ KE \text{ per unit volume} = \frac{3}{2} P \]

### Final Answer:
Thus, the kinetic energy per unit volume (KE per unit volume) is:
\[ \text{KE per unit volume} = \frac{3}{2} P \]