A 20-lb aluminum bar, initially at $T_a = 210^\circ F$, is placed in a tank together with 190 lb of liquid water, initially at $T_w = 70^\circ F$, and allowed to achieve thermal equilibrium. The aluminum bar and water can be modeled as incompressible with specific heats $c_a = 0.216 Btu/lb \cdot ^\circ R$ and $c_w = 0.998 Btu/lb \cdot ^\circ R$, respectively. Consider the aluminum bar and water as the system and ignore heat transfer between the system and its surroundings.
Determine the final temperature $T_f$, in $^\circ F$, and the amount of entropy produced within the tank, in $Btu/^\circ R$.
