When be container stopped suddenly , ordered kinetic energy gets converted into disordered kinetic energy which increases the temperature of gas. KE per unit volume is E, The pressure exerted by the gas is given by

Options

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

Explanation

To solve the problem, we need to derive the expression for the pressure exerted by the gas in terms of its kinetic energy per unit volume (E).

### Step-by-Step Solution:

1. **Understanding Kinetic Energy of Gas:**
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 absolute temperature.

2. **Kinetic Energy per Unit Volume:**
To find the kinetic energy per unit volume (E), we need to express the total kinetic energy in terms of volume. The number of moles \(n\) can be expressed as:
\[ n = \frac{PV}{RT} \]
Substituting this into the kinetic energy equation:
\[ KE = \frac{3}{2} \left(\frac{PV}{RT}\right) RT = \frac{3}{2} PV \]
Therefore, the kinetic energy per unit volume \(E\) is given by:
\[ E = \frac{KE}{V} = \frac{3}{2} P \]

3. **Relating Pressure and Kinetic Energy per Unit Volume:**
From the expression for \(E\), we can rearrange it to find the pressure \(P\):
\[ P = \frac{2E}{3} \]

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