Physics - Sound Wave Question with Solution | TestHub

${\text{T}}^{\gamma }{P}^{1-\gamma }$= constant

Differentiating

         $\gamma {\text{T}}^{\gamma -1}\text{dT}{P}^{1-\gamma }+{\text{T}}^{\gamma }\left(1-\gamma \right){\text{P}}^{-\gamma }\text{dP}=0$

or,  $\text{dT}=\frac{\left(\gamma -1\right)\text{T}}{\gamma \text{P}}\text{dP}$

or,  $\text{dT}=\left(\frac{\text{1.5}-1}{\text{1.5}}\right)\left(\frac{273}{76\times \text{13.6}\times 981}\times \text{0.001}\right)$

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