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A jacketed stirred tank with a provision for heat removal is used to mix sulphuric acid and water in a steady state flow process. $H_{2}SO_{4}$ $(l)$ enters at a rate of $4\:kg/h$ at $25^{\circ}C$ and $H_{2}O$ $(l)$ enters at a rate of $6\:kg/h$ at $10^{\circ}C$ . The following data are available:

Specific heat capacity of water = $4.2\;kJ\:kg^{-1}\:K^{-1}$

Specific heat capacity of aqueous solution of $40$ mass$\%$ $H_{2}SO_{4} = 2.8\:kJ$ ($kg$ solution)$^{-1}$ $K^{-1}$.

Assume the specific heat capacities to be independent of temperature.

Based on reference states of $H_{2}SO_{4}$ $(l)$ and $H_{2}O$ $(l)$ at $25^{\circ}C$, the heat of mixing for aqueous solution of $40$ mass$\%$  $H_{2}SO_{4}=-650\:kJ \left ( kg\:H_{2}SO_{4} \right )^{-1}.$

If the mixed stream leaves at $40^{\circ}C$ , what in the rate of heat removal (in $kJ/h$)?

  1. $1802$
  2. $2558$
  3. $5702$
  4. $6458$
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