The efficiency of a particular series of adiabatic gas turbines $($expanders$)$

correlates with power output according to the empirical expression: $=0\mathrm{.}065+$

$0\mathrm{.}080ln|W_{\text{d}\text{o}\text{t}}.$ Here, $W_{\text{d}\text{o}\text{t}}$ is the absolute value of the actual power output in $kW.$

Nitrogen gas is to be expanded from inlet conditions of $550K$ and $6$ bar to an

outlet pressure of $\frac{1\mathrm{.}2}{b}ar.$ For a molar flowrate of $175mo\frac{l}{s},$ what is the delivered

power in $kW?$ What is the efficiency of the turbine? What is the rate of entropy

generation $S_{\text{d}\text{o}\text{t}\text{G}}?$ Assume nitrogen to be an ideal gas with $c_p=(\frac{7}{2})R.$

Solution:

$W_{\text{d}\text{o}\text{t}}=-594\mathrm{.}716kW$

$=0\mathrm{.}576$

$(T_2=433\mathrm{.}213K)$

$Sdo{t}_G=1126\frac{J}{}Ks$

Solution:

please explain where each equation comes from