If we fail to insulate the nozzle in the gas flow system of Problem 11.23, we allow heat transfer to occur as the gas flows from the reservoir. Show under these conditions that the entropy of the gas at any location in the nozzle can be given by:

\[S=S_{1}+C_{p} \ln \left[\left(ho_{1} / ho\right)\left(P / P_{1}\right)^{1 / \gamma}\right]\]