JoAnna and Joseph Gibbs, twin cousins of the famous Connecticut thernodynamicist, J$.$

Willard Gibbs, have designed a heat exchanger for heating supercritical organic fluids

with geothermal heat. They claim that by proper design of tubes$/$baffles and other internal

components, they can eliminate heat transfer coefficient variations and reduce the

tendency of the exchanger to "pinch." According to the Gibbs twins, the pressure drop

for both streams is negligible. A hot, pressurized $(300C,14$MPa$)$ water stream at $100$

$k\frac{g}{s}$ is available from a geothermal well. In their design, heat is transferred to an entering

supercritical ammonia $(N{H}_3)$ stream that is exiting from a Rankine cycle feed pump at

$P=12\mathrm{.}5$MPa and $T=40C.$ Steam tables or charts are available for the water properties,

and an equation of state is available for $N{H}_3$ with $P_r=f(T_r,V_r).$ The critical

compressibility, pressure, and temperature and $C_p^o$ for $N{H}_3$ are: $Z_c=0\mathrm{.}242,P_c=11\mathrm{.}28$

MPa,$T_c=405K,$ and $\frac{C_p^0}{R}=4\mathrm{.}3-1\mathrm{.}84T_r+3\mathrm{.}20r_r^2.$

$($a$)$ For any specified minimun $T$ condition, is it possible to set the temperatures of

either the exiting wath or the exiting ammonia, or both exiting streams?

$($b$)$ Incorporating your answer from part $($a$),$ sketch the temperature profiles for both

streams in the heat exchanger.