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

Options

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

Answer

A

Explanation

The average translational kinetic energy of a gas molecule is `(1)/(2)mbar(u)^(2)` at a temperature, T. The total energy of the whole of the gas containing N molecules is
`E_(k)=(1)/(2)"m N"baru^(2)" …(i)"`
The kinetic gas equation is
`pV=(1)/(3)"m N"bar(u)^(2)" ...(ii)"`
`pV=(2)/(3)xx(1)/(2)mNbar(u)^(2)`
`pV=(2)/(3)E_(k)" ...(iii)"`
`"so, "p=(2)/(3)E_(k)" per unit volume"`