Subtopic: Preservation of food by cooling and freezing
Question Statement:
Plank's equation for freezing time of a slab of thickness $a = 0.05\text{ m}$ frozen from both sides is $t_f = \frac{\rho \lambda}{\Delta T} \left(\frac{P a}{h} + \frac{R a^2}{k}\right)$ with geometric factors $P = \frac{1}{2}$ and $R = \frac{1}{8}$. Given density of frozen food $\rho = 1000\text{ kg/m}^3$, latent heat $\lambda = 250\text{ kJ/kg} = 2.5 \times 10^5\text{ J/kg}$, temperature difference $\Delta T = 20.0\text{ K}$, surface heat transfer coefficient $h = 25.0\text{ W/(m}^2\cdot\text{K)}$, and frozen thermal conductivity $k = 1.25\text{ W/(m}\cdot\text{K)}$. The freezing time $t_f$ in seconds is ________ (answer in integer).