A sample of cereal grain has a thermal conductivity $k = 0.15\text{ W/(m}\cdot\text{K)}$, particle density $\rho = 1250\text{ kg/m}^3$, and specific heat capacity $c_p = 1500\text{ J/(kg}\cdot\text{K)}$. The thermal diffusivity of the grain in $10^{-8}\text{ m}^2\text{/s}$ is ________ (answer in integer).
Answer Key:
8
Step-by-Step Solution & Explanation
Thermal diffusivity $\alpha$ is given by:
$\alpha = \frac{k}{\rho c_p}$
Substitute values:
$\alpha = \frac{0.15\text{ W/(m}\cdot\text{K)}}{1250\text{ kg/m}^3 \times 1500\text{ J/(kg}\cdot\text{K)}} = \frac{0.15}{1875000} = 8.0 \times 10^{-8}\text{ m}^2\text{/s}$
Thus, the value in $10^{-8}\text{ m}^2\text{/s}$ is $8$.