Saturated steam at 121°C sterilizes pineapple juice by direct steam injection. Initial juice temperature = 80°C; blended juice exits at 95°C. Enthalpies: hf(95°C)=397.9, hg(121°C)=2707.1 kJ/kg; specific heat of juice = 3.9 kJ/kg·°C. Find the ratio of juice sterilized to steam utilized.
Options:
(A) 34.79
(B) 37.94
(C) 39.47
(D) 43.97
Official Answer Key:
C
Step-by-Step Solution & Explanation
Steam condenses fully and cools to the blend exit temperature, releasing heat = hg(121)−hf(95) = 2707.1−397.9 = 2309.2 kJ/kg. This heats the juice from 80 to 95°C: heat absorbed per kg juice = cp×ΔT = 3.9×15 = 58.5 kJ/kg. Energy balance: m_steam×2309.2 = m_juice×58.5 ⇒ m_juice/m_steam = 2309.2/58.5 ≈ 39.47.
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