Derive the 1-D energy equation for adiabatic compressible flow staring from the first law of thermodynamics and Euler's equation, that is, derive \(c_{p} T+\frac{1}{2} u^{2}=C\) from \(d e=\delta q+\delta w\) and \(u d u=-\frac{d P}{ho}\), where \(C\) is a constant.