If E is the translational kinetic energy, then which of the following relation holds good

CONCEPT:

Translational Kinetic Energy and Pressure-Volume Relation

Translational kinetic energy is the energy possessed by an object due to its motion from one place to another.

In thermodynamics, the relationship between the pressure (P), volume (V), and the translational kinetic energy (E) of an ideal gas can be derived from the ideal gas law.

EXPLANATION:

Let's examine the given options:

Option 1: PV = E

This is incorrect. The pressure-volume product is not equal to the translational kinetic energy.

Option 2: PV = 323232 $\frac{3}{2}$ E

This is incorrect. While 323232 $\frac{3}{2}$ E is related to the total kinetic energy per mole of gas, it is not the correct relation for PV.

Option 3: PV = 3E

This is incorrect. The factor of 3 is not applicable in this context.

Option 4: PV = 232323 $\frac{2}{3}$ E

This is correct. The pressure-volume product (PV) of an ideal gas is directly proportional to the translational kinetic energy (E) with the relation PV = 232323 $\frac{2}{3}$ E.

Therefore, the correct answer is option 4: PV = 232323 $\frac{2}{3}$ E.