Which of the following relationships is valid ?
where `K` is a proportionality constant.

Options

A. `(pV)/(T) = (2)/(3)K`
B. `(pV)/(T) = (3)/(2)K`
C. `(pV)/(T) = 2K`
D. `(pV)/(T) = 3K`

Answer

A

Explanation

According to the kinetic gas equation,
`pV = (1)/(3) mnc^(2) = (1)/(3) Mc^(2)`
` = (2)/(3).(1)/(2) Mc^(2)`
`= (2)/(3).KE`
Since `KE` (kinetic energy ) is directly proportional to the absolute temperature `(T)`, we have
`pV prop (2)/(3) T`
`pV = (2)/(3) KT`
where `K` is a proportionality constant. Dividing both sides by `T`, we have
`(pV)/(T) = (2)/(3)K`