A high pressure dairy homogenizer operates under upstream and downstream pressures of 200 and 40 bar respectively homogenizing 30 L of whole milk per hour. Density and specific heat capacity of whole milk are 1030 kg m⁻³ and 3.8 kJ kg⁻¹K⁻¹, respectively. Assuming complete energy conservation, the temperature rise of whole milk in degree Celsius is _______________
Official Answer Key:
4.09
Step-by-Step Solution & Explanation
Pressure drop, ΔP = (200−40) bar = 160×10⁵ Pa.
Volumetric flow, Q = 30 L/h = 30×10⁻³/3600 = 8.333×10⁻⁶ m³/s.
Mechanical power dissipated (converted entirely to heat, per problem statement) = ΔP×Q = 160×10⁵ × 8.333×10⁻⁶ = 133.3 W.
Mass flow rate = Q×ρ = 8.333×10⁻⁶×1030 = 8.583×10⁻³ kg/s.
Temperature rise, ΔT = Power/(ṁ×c_p) = 133.3/(8.583×10⁻³×3800) = 133.3/32.6 = ≈4.09°C.
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