Question

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

• A. $8.97\times {10}^{-4}K$
• B. $8.97\times {10}^{-6}K$
• C. $8.97\times {10}^{-8}K$
• D. none of these

Answer 1

Answer: (C)

$8.97\times {10}^{-8}K$

T${}^{\gamma }$ P${}^{1-\gamma }$ = constant.
Differentiating above equation
$\gamma T^{\gamma -1}dT{P}^{1-\gamma }+T^{\gamma }(1-\gamma )P^{-\gamma }dP=0$
or, $dT=\frac{(\gamma -1)T}{\gamma P}dP$
or, $dT=\left(\frac{1.5-1}{1.5}\right)(\frac{273}{76\times 13.6\times 981}\times 0.001)$
= $8.97\times {10}^{-8}K$