In an adiabatic process on a gas with `(gamma = 1.4)` the pressure is increased by `0.5%` . The volume decreases by about

Options

A. `0.36%`
B. `0.5%`
C. `0.7%`
D. `1%`

Answer

A

Explanation

`PV^(gamma)=P(1+(0.5)/(100))V'^(gamma)`
`((V')/(V))^(gamma)=(1+(0.5)/(100))^-1`
`(V')/(V)=(1+(0.5)/(100))^((-1)/(gamma))=(1+(0.5)/(100))^(-(1)/(1.4))`
`=(1-(0.5)/(1.4)xx(1)/(100))`
`((V')/(V)-1)xx100=-(0.5)/(1.4)=-0.36%`
`0.36%` decrease.