Answer
$q=515\ Btu/lbm$
Work Step by Step
$q=\int Tds$
For 1-2:
$q_{1-2}=\frac{(T_1+T_2)}2(s_2-s_1)$
For 2-3:
$q_{2-3}=T_2(s_3-s_2)$
Given $T_1=515°R,\ T_2=T_3=820°R$
$s_1=1\ Btu/lbm.°R,\ s_2=3s_1,\ s_3=2s_1$
$q=515\ Btu/lbm$
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