Question

Вывести T из равенства

$\frac{P}{Po} = (\frac{T}{To} )^{\frac{-g}{k*R} }$

Answer 1

$\frac{P}{P_{0}}=(\frac{T}{T_{0}})^{\frac{-g}{k*R}} \Leftrightarrow (\frac{P}{P_{0}})^{\frac{k*R}{-g}}=((\frac{T}{T_{0}})^{\frac{-g}{k*R}})^{\frac{k*R}{-g}} \Leftrightarrow \frac{T}{T_{0}}=(\frac{P}{P_{0}})^{\frac{k*R}{-g}} \Leftrightarrow T=T_{0}*(\frac{P}{P_{0}})^{\frac{k*R}{-g}}$