The flow rate of a hot coal/oil slurry in a pipeline is measured by injecting a small side stream of cool oil and measuring the resulting temperature change downstream in the pipeline. The slurry is initially at $300^{\circ} \mathrm{F}$ and has a density of $1.2 \mathrm{~g} / \mathrm{cm}^{3}$ and a specific heat of $0.7 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}}{ }^{\circ} \mathrm{F}\right)$. With no side stream injected, the temperature downstream of the mixing point is $298^{\circ} \mathrm{F}$. With a side stream at $60^{\circ} \mathrm{F}$ and a flow rate of $1 \mathrm{lb}_{\mathrm{m}} / \mathrm{s}$, the temperature at this point is $295^{\circ} \mathrm{F}$. The side stream has a density of $0.8 \mathrm{~g} / \mathrm{cm}^{3}$ and a $c_{p}$ of $0.6 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}}{ }^{\circ} \mathrm{F}\right)$. What is the mass flow rate of the slurry?