Repeating the developments in the text examples $2\mathrm{.}11$ and $2\mathrm{.}12,$ filling in any

missing steps, and using $C_P=C_V+R,$ use the first law to derive all six of

the expressions in equations $41,42$ and $43$ in the posted equation sheet. Note

that isentropic can be taken to mean reversible and adiabatic.

EXTRA INFO:

Example $2\mathrm{.}12.$ Continuous adiabatic, reversible compression of an ideal

gas

Suppose $1$ kmol$/$h of air at $5$ bars and $298$ K is adiabatically and reversibly

compressed in a continuous process to $25$ bars. What will be the outlet

temperature and power requirement for the compressor in hp$?$

Example $2\mathrm{.}11.$ Adiabatic, reversible expansion of an ideal gas

Suppose an ideal gas in a piston $+$ cylinder is adiabatically and reversibly

expanded to twice its original volume. What will be the final temperature?

$41$: $\backslash$gamma $($gamma$)=$ CP$/$CV if isentropic

$42$: $\backslash$gamma $($gamma$)=$ k if polytropic

$43$: $($T$2/$T$1)=($V$1/$V$2)^(\backslash$gamma $-1)=($V$1/$V$2)^($R$/$Cv$)$