Answer
$L=4500\ ft$
Work Step by Step
From the energy balance:
$\dot{Q}+\dot{m}h_1=\dot{m}h_2$
$\dot{Q}=\dot{m}c_p(T_2-T_1)$
and since $\dot{m}=4\ lbm/s,\ c_p=1.0\ Btu/lbm.°F,\ T_2=180°F,\ T_1=55°F$:
$\dot{Q}=500\ Btu/s=1.8\times10^6\ Btu/h$
$\dot{Q}=\grave{Q}.L,\ \grave{Q}=400\ Btu/h.ft$
$L=4500\ ft$
