$2\mathrm{.}21.$ A list of common unit operations follows:

$($a$)$ Single$-$pipe heat exchanger

$($b$)$ Double$-$pipe heat exchanger

$($c$)$ Pump

$($d$)$ Gas compressor

$($e$)$ Gas turbine

$($f$)$ Throttle valve

$($g$)$ Nozzle

Develop a simplified form of the general steady$-$state energy balance appropriate for

each operation. State carefully, and justify, any assumptions you make.