Step 1: Understanding the Concept:
Two-stage freezing thermodynamics of ice cream: in the dynamic scraped-surface continuous freezer (Phase 1, $-5^\circ ext{ to } -6^\circ ext{C}$), 33% to 67% (typically $pprox 50\%$) of water is frozen rapidly with air incorporation (overrun), followed by hardening room static freezing (Phase 2, $-25^\circ ext{ to } -30^\circ ext{C}$) to reach $> 85-90\%$ frozen water.
Key Formula or Approach:
\[ \text{Ice Cream Freezing: } \underbrace{\text{Phase 1 (Dynamic Freezer, } -5^\circ\text{C)}}_{\mathbf{33\% - 67\% \text{ Water Frozen (Rapid Micro-Crystals)}}} \longrightarrow \underbrace{\text{Phase 2 (Hardening Room, } -28^\circ\text{C)}}_{> 85\% \text{ Total Water Frozen}} \]
Step 2: Detailed Explanation:
In the physical thermodynamics of Ice Cream manufacturing:
- Freezing of ice cream mix occurs in two sequential thermodynamic stages:
1. First Phase (Dynamic Freezing in Scraped Surface Freezer) (C):
- Mix is chilled rapidly under high agitation from $+4^\circ ext{C}$ to extrusion temperature ($-5^\circ\text{ to } -6^\circ ext{C}$) within 15--30 seconds while whipping in air (overrun).
- In this initial phase, approximately 33% to 67% (average 50% to 55%) of the total water content is rapidly frozen into millions of microscopic ice crystal nuclei ($15 - 25\;\mu\text{m}$).
2. Second Phase (Static Hardening at $-25^\circ ext{ to } -30^\circ ext{C}$): Freezes the remaining unfrozen water without agitation to bring total frozen water to $85\% - 90\%$.
Step 3: Final Answer:
Therefore, the first phase of freezing accounts for freezing of water to about 33-67%, corresponding to option (C).