The pressure `P_(1)` and density `d_(1)` of a diatomic gas `(gamma=(7)/(5))` change to `P_(2) and d_(2)` during an adiabatic operation .If `(d_(2))/(d_(1))=32, then (P_(2))/(P_(1))` is

Options

A. 76
B. 128
C. 168
D. 298

Answer

B

Explanation

In an adiabatic operation `P_(1)V_(1)^(gamma)=P_(2)V_(2)^(gamma)`
`(P_(2))/(P_(1))=(V_(1))/(V_(2))^(gamma)=((m)/(d_(1)))xx(d_(2))/(m)^(gamma)=((d_(2)/(d_(1)))^(gamma)`
`P_(2)/(P_(1)=(32)^(7//5)=(2^(5))^(7//5)=26(7)=128`
`(P_(2))/(P_(1))=128`