Question

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

The correct option is C $8.97\times {10}^{-8}K$

For adiabatic process, $T^{\gamma }{P}^{(1-\gamma )}=$ constant

Differentiate the equation we will get, $T^{\gamma }(1-\gamma )P^{-\gamma }dP+\gamma P^{1-\gamma }{T}^{(\gamma -1)}dT=0$

or $dT=\frac{(\gamma -1)T}{\gamma P}dP=\frac{(1.5-1)273}{1.5\times (1.013\times {10}^6)}\times 0.001=8.97\times {10}^{-8}K$