A cylindrical potato sample has a thermal conductivity of $k = 0.55\text{ W/(m}\cdot\text{K)}$, a density of $\rho = 1050\text{ kg/m}^3$, and a specific heat of $c_p = 3600\text{ J/(kg}\cdot\text{K)}$. The thermal diffusivity of the potato is:
Options:
(A) $1.45 \times 10^{-7}\text{ m}^2/\text{s}$
(B) $1.45 \times 10^{-5}\text{ m}^2/\text{s}$
(C) $6.87 \times 10^{6}\text{ m}^2/\text{s}$
(D) $2.12 \times 10^{-6}\text{ m}^2/\text{s}$
Answer Key:
A
Step-by-Step Solution & Explanation
Thermal diffusivity ($\alpha$) is defined as:
$\alpha = \frac{k}{\rho \cdot c_p}$
Substituting the given values:
$\alpha = \frac{0.55}{1050 \times 3600} = \frac{0.55}{3780000} \approx 1.455 \times 10^{-7}\text{ m}^2/\text{s}$
Therefore, $\alpha \approx 1.45 \times 10^{-7}\text{ m}^2/\text{s}$.