A sound wave passing through air at `NTP` produces a pressure of `0.001` dyne/`cm^(2)` during a compression. The corresponding change in temperature (given `gamma = 1.5` and assume gas to be ideal) is

Options

A. `8.97 xx 10^(-4) K`
B. `8.97 xx 10^(-6) K`
C. `8.97 xx 10^(-8) K`
D. None of these

Answer

C

Explanation

Differentiating
`gammaT^(gamma-1) dT P_(1-gamma)+T^(gamma)(1-gamma)P^(-gamma)dP = 0`
or `dT = ((gamma-1)T)/(gamma P) dP`
`or dT = ((1.5-1)/(1.5))((273)/(76xx13.6xx981)xx0.001)`
`=8.97xx10^(-8)K`.