In a adiabatic process is increased by `2//3%` if `C_(P)//C_(V) = 3//2`. Then the volume decreases by about

Options

A. `(4)/(9)%`
B. `(2)/(3)%`
C. `4%`
D. `(9)/(4)%`

Answer

A

Explanation

a. For a adiabatic process, `Pv^(gamma) = K`
Here,
`gamma = 3//2` and `K =` constant
`:. PV^(3//2) = K`
`log P + (3)/(2) log V = log K`
`(Delta P)/(P) + (3)/(2) (Delta V)/(V) = 0`
`:. (Delta V)/(V) = (2)/(3) = (Delta P)/(P)`
`:. (Delta V)/(V) xx 100 = - ((2)/(3)) ((Delta P)/(P) xx 100) = - (2)/(3) xx (2)/(3) = - (4)/(9)`
Therefore volume decrease decrease by about `(4//9) %`.