1. A solution containing 20% by mass of potassium sulfate (K₂SO₄) is cooled from 323 K to 303 K in a Swenson-Walker crystallizer to form crystals of K₂SO₄·2H₂O. The solubility of K₂SO₄ at 303 K is 12 kg/100 kg water, and the required product rate of crystals is 0.05 kg/s. The mean heat capacity of the solution is 3.1 kJ/kg·K, and the heat of crystallization is 160 kJ/kg. Cooling water enters at 290 K and leaves at 298 K, with an overall heat transfer coefficient of 120 W/m²·K.
Task:
Determine the length of the crystallizer required to achieve the cooling and crystallization.
2. A solution containing 25% by mass of magnesium sulfate (MgSO₄) is fed into a single- effect crystallizer at 350 K to form crystals of MgSO₄·7H₂O. The solution is cooled to 303 K, where the solubility of MgSO₄ is 18 kg MgSO₄ per 100 kg water. The desired product rate of crystals is 0.05 kg/s. Due to evaporation, part of the water is removed before cooling. The heat capacity of the solution is 3.5 kJ/kg·K, and the heat of crystallization for MgSO₄·7H₂O is 120 kJ/kg. The latent heat of vaporization for water is 2260 kJ/kg. Cooling water enters the system at 290 K and leaves at 295 K, and the overall heat transfer coefficient is 160 W/m²·K.
Task:
1. Calculate the mass of water evaporated before cooling.
2. Determine the heat required for evaporation.
3. Calculate the heat required for cooling and crystallization.
4. Determine the total heat transfer area required if the crystallizer operates at steady state.
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