Question

Prove that P = Energy/Volume​

Answer 1

Answer:

We have to prove that the dimension of energy per unit volume is equal to the dimension of pressure. Now, energy / volume = [ML^2T^−2] / [L^3] = [L^-1M T^-2] which is equal to the dimension of pressure.

Hence proved.

Answer 2

Explanation:

The main result of kinetic theory of gases is the following expression for pressure ,P of the ideal gas.

P=(1/3)d<v^2>……………(1)

d is density that is mass per unit volume.

<v^2> is average, over all molecules ,of squares of velocities of molecules of the gas.

Now, energy of an ideal gas per unit volume, E=(1/2) d<v^2>……………..(2)

Using equation (2) in equation (1), we get

P=(2/3)E.

Note: Ideal gas molecules have only kinetic energy . They do not have potential energy of interaction with each other.