Consider a steady$-$flow turbine that extracts work from a mixture of $77\%$ carbon dioxide Expansion of a Perfect Gas Mixture

Consider a steady$-$flow turbine that extracts work from a mixture of $77\%$ carbon dioxide

$(C{O}_2)$ and $23.\%$ water $(H_{2}O)$ by mole. The mixture is expanded reversibly from

K and $11\mathrm{.}0$ bar to $1300$ K and $1\mathrm{.}10$ bar. Furthermore, the walls of the device are

isothermal with a temperature of $800.$ K$.$ Assume that these gases are thermally perfect

gases with specific heats $($for this temperature range$)$ given by

$\frac{c_{v,C{O}_2}}{R}=4\mathrm{.}296+1\mathrm{.}115{10}^{-3}T{K}^{-1}$ and $\frac{c_{v,H_2}}{2}=2\mathrm{.}569+1\mathrm{.}382{10}^{-3}T{K}^{-1}.$

a$.$ Determine the entropy change per kmol of mixture for the $C{O}_2$ and also for the

$H_{2}O.$

b$.$ Determine the amount shaft power per unit mass flowrate produced by the

turbine, and the rate of heat transfer per unit mass flowrate for the turbine $($and

indicate whether the heat transfer is entering or leaving the turbine$).$

$($CO$2)$ and $23.\%$ water $($H$2$O$)$ by mole. The mixture is expanded reversibly from

$1700.$ K and $11\mathrm{.}0$ bar to $1300.$ K and $1\mathrm{.}10$ bar. Furthermore, the walls of the device are

isothermal with a temperature of $800.$ K$.$ Assume that these gases are thermally perfect

gases with specific heats $($for this temperature range$)$ given by

cv$,$CO$2$

$/$R $=4\mathrm{.}296+1\mathrm{.}11510-3$T K

$-1$ and cv$,$H$2$

O$/$R $=2\mathrm{.}569+1\mathrm{.}38210-3$T K

$-1$