Question

A sound wave passing through an ideal gas at NTP produces a pressure change of $0.001$ dyne/ $cm ^{2}$ during adiabatic compression. The corresponding change in temperature $(\gamma=1.5$ for the gas and atmospheric pressure is $1.013 \times 10^{6}$ dyne/cm $^{2}$ ) is

• A. $8.97 \times 10^{-4} K$
• B. $8.97 \times 10^{-6} K$
• C. $8.97 \times 10^{-8} K$
• D. $8.97 \times 10^{-9} K$

Answer 1

Answer: (C)

$T^{\gamma} p^{1-\gamma}=$ constant
or $T^{\gamma}=p^{\gamma-1}$
$T=p^{\left(\frac{\gamma-1}{\gamma}\right)}$
$ \therefore \frac{\Delta T}{T} =\frac{\gamma-1}{\gamma} \times \frac{\Delta p}{p} $
$ \frac{\Delta T}{T} =\left(\frac{1.5-1}{1.5}\right) \times \frac{0.001}{1.013 \times 10^{6}} $
$ \Delta T=8.98 \times 10^{-8}\, K $