Problem $3.$ Mixing of sulfuric acid and water: A pure sulfuric acid stream flowing at $2\mathrm{.}0k\frac{g}{m}in$ is mixed in an isothermal vessel with an aqueous solution which flows at $1\mathrm{.}8kg/$ min and contains $40\%$ by weight of sulfuric acid. Estimate the rate of heat that must be added or removed to maintain the temperature of the exit stream at $294K.$ The inlet streams are at $294K$ and the mixer operates at steady state. The heat of mixing data for the sulfuric acid and water mixture at $294K$ was reported by Ross $(1952)$ as follows:

$widetilde(H{)}_{\text{m}\text{i}\text{x}}=x_1{x}_2[-53\mathrm{.}5+20\mathrm{.}9(x_1-x_2)]$

where $x_1$ and $x_2$ are mole fractions of sulfuric acid and water, respectively, and, $widetilde(H{)}_{\text{m}\text{i}\text{x}}$ is the enthalpy change of mixing in $k\frac{j}{m}ol.$