For an ideal gas, pressure `(p)` and interal energy `(E )` per unit volume are related as

Options

A. `p = (3)/(2) E`
B. `p = (2)/(3)E`
C. `p = (1)/(2) E`
D. `p = (1)/(3)E`

Answer

B

Explanation

According to the kinetic gas equation , `pV = (1)/(3) mnc^(2)`
` = (1)/(3) Mc^(2)` `(M = mn)`
` = (2)/(3).(1)/(2) Mc^(2)`
` = (2)/(3) E_(K)` `(E_(K) = (1)/(2) MC^(2))`
Dividing both sides by volume `(V)` , we get
`p = (2)/(3)E` `(E = (E_(K))/(V)`
Note that the internal energy of an ideal gas is equal to its kinetic energy because the potential energy of an ideal gas is zero as there is no intermolecular interaction between gas particles.