A sound wave passing through an ideal gas at NTP produces a pressure change of 0.001 `dyn e//cm^(2))` during adiabatic compression. The corresponding change in temperature `(gamma = 1.5` for the gas and atmospheric pressure is `1.013xx10^(6) dyn e//cm^(2))` is

Options

A. `8.97xx10^(-4)K`
B. `8.97xx10^(-6)`K
C. `8.97xx10^(-8)k`
D. `8.97xx10^(-9)K`

Answer

C

Explanation

For adiabatic process
`T^(gamma)P^(1-gamma)=` Constant
`T^(gamma)= P^(gamma - 1)`
` gamma log T = (gamma - 1) log p `
On differentiating on bith sides, we get ,
`gamma (Delta T)/(T) = (gamma - 1) (Delta p)/(p)`
` implies Delta T = ((1.5 - 1)/(1.5)) xx (0.001)/(1.013 xx 10^(6)) xx 20`
`therefore Delta T = 8.97 xx 10 ^(-8) K`