A flexible retort pouch is sterilized in a water-spray retort at $121.1^\circ\text{C}$ (pure steam saturation pressure $P_{\text{steam}} = 205.0\text{ kPa}$ absolute). The internal vapor and expanding air pressure inside the sealed pouch reaches $260.0\text{ kPa}$ absolute. To prevent pouch bursting or seam rupture, compressed air overpressure is injected into the retort. The minimum gauge overpressure required in the retort in $\text{kPa}$ to balance internal pouch pressure is ________ (answer in integer).
Answer Key:
159
Step-by-Step Solution & Explanation
Multi-Approach Solution:
**Method 1: Absolute to Gauge Pressure Balance**
Internal absolute pressure inside pouch $= 260.0\text{ kPa}$.
Atmospheric reference pressure $P_{\text{atm}} = 101.325\text{ kPa}$.
Required chamber absolute pressure to balance pouch $= 260.0\text{ kPa}$.
Chamber gauge pressure:
$P_{\text{gauge}} = P_{\text{abs}} - P_{\text{atm}} = 260.0 - 101.3 = 158.7\text{ kPa} \approx 159\text{ kPa}$
**Method 2: Steam vs Compressed Air Component**
Steam partial pressure at $121.1^\circ\text{C}$ is $205.0\text{ kPa}$ abs ($103.7\text{ kPa}$ gauge). Additional compressed air needed is $260.0 - 205.0 = 55.0\text{ kPa}$, making total gauge pressure $103.7 + 55.0 = 158.7\text{ kPa}$.