In a adiabatic process pressure 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

For an adiabatic process `PV^(gamma) = K`
Here, `gamma=3/2` and `K =` constant
`PV^(3//2)=K`
log `P + 3/2 log V = o log K`
`:. (DeltaP)/(P) +3/2 (DeltaV)/(V) = 0`
`:. (DeltaV)/(V) = -2/3 (DeltaP)/(P)`
`(DeltaV)/(V) xx 100 = -(2/3)((DeltaP)?(P)xx100)=-2/3 xx 2/3 = -4/9`
`:.` volume decreases by about `4/9 %`.