Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
The values of C and n for raisin are 1.283×10⁻⁴ K⁻¹ and 1.02, respectively in the Henderson equation. The equilibrium moisture content of raisin in percent dry basis corresponding to the air with 70% relative humidity at 40 °C is _____.
Official Answer Key:
26 to 30
Step-by-Step Solution & Explanation
Henderson's equation: 1 − RH = exp(−C·T·Mⁿ), with T in absolute temperature (K) and M in % dry basis.
T = 40 + 273.15 = 313.15 K. 1 − 0.70 = 0.30.
ln(0.30) = −C·T·Mⁿ ⇒ −1.204 = −1.283×10⁻⁴ × 313.15 × M^1.02
M^1.02 = 1.204/(1.283×10⁻⁴×313.15) = 1.204/0.04018 = 29.97
M = 29.97^(1/1.02) = 28.0% (dry basis). This lies within the accepted range 26–30.
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