Subtopic: Preservation of food by cooling and freezing
Question Statement:
Which of the following thermo-physical properties of ice compared to liquid water explain why the thermal diffusivity of frozen food is roughly an order of magnitude higher than unfrozen food?
Options:
(A) The thermal conductivity of ice ($k_{\text{ice}} \approx 2.22\text{ W/(m}\cdot\text{K)}$) is approximately four times higher than liquid water ($k_{\text{water}} \approx 0.58\text{ W/(m}\cdot\text{K)}$)
(B) The specific heat capacity of ice ($C_{p,\text{ice}} \approx 2.05\text{ kJ/(kg}\cdot\text{K)}$) is roughly half that of liquid water ($C_{p,\text{water}} \approx 4.18\text{ kJ/(kg}\cdot\text{K)}$)
(C) The density of ice is slightly lower than liquid water ($\rho_{\text{ice}} \approx 917\text{ kg/m}^3$)
(D) Ice is a gas under standard food freezing conditions
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
Thermal diffusivity is $\alpha = \frac{k}{\rho C_p}$. Since ice has $4\times$ higher $k$ (A) and half the $C_p$ (B) with slightly lower density (C), $\alpha_{\text{ice}} = \frac{2.22}{917 \times 2050} \approx 1.18 \times 10^{-6}\text{ m}^2/\text{s}$ is nearly 8-9 times greater than $\alpha_{\text{water}} \approx 1.4 \times 10^{-7}\text{ m}^2/\text{s}$. This explains why freezing fronts advance much faster than thawing fronts under equivalent temperature driving forces.