Answer
$m_e=99.41\ lbm$
$Q_i=3328\ Btu$
Work Step by Step
From the material balance:
$m_e=m_1-m_2$
$PV=mRT$
Given $P_1=1500\ psia,\ P_2=300\ psia,\ V=15\ ft³,\ R=0.3353\ psia.ft³/lbm.°R$
$\ \ \ \ \ \ T_1=540°R,\ T_2=540°R$
$m_1=124.3\ lbm,\ m_2=24.85\ lbm,\ m_e=99.41\ lbm$
From the energy balance:
$Q_i-m_eh_e=m_2u_2-m_1u_1$
$Q_i=c_v(m_2T_2-m_1T_1)+m_ec_pT_e$
With $c_p=0.219,\ c_v=0.157\ Btu/lbm.°R$:
$Q_i=3328\ Btu$
