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, we can follow these steps:

### Step 1: Understand the total kinetic energy
The total kinetic energy (KE) of an ideal gas can be expressed as:
\[ KE = \frac{3}{2} nRT \]
where:
- \( n \) = number of moles of the gas,
- \( R \) = universal gas constant,
- \( T \) = absolute temperature in Kelvin.

### Step 2: Relate the number of moles to pressure and volume
From the ideal gas law, we know:
\[ PV = nRT \]
where:
- \( P \) = pressure,
- \( V \) = volume.

### Step 3: Substitute \( nRT \) in the kinetic energy equation
We can substitute \( nRT \) from the ideal gas law into the kinetic energy equation:
\[ KE = \frac{3}{2} (PV) \]

### Step 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 \( V \):
\[ KE \text{ per unit volume} = \frac{KE}{V} = \frac{\frac{3}{2} PV}{V} \]
This simplifies to:
\[ KE \text{ per unit volume} = \frac{3}{2} P \]

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