MgO ceramic has heat capacity \( 940 \mathrm{~J} / \mathrm{kg} . \mathrm{K} \), coefficient of thermal expansion \( 13.5 \times 10^{-6} \) per \( { }^{\circ} \mathrm{C} \), thermal conductivity 37.7 W/m.K and density of \( 3.58 \mathrm{~g} / \mathrm{cm}^{3} \). Then the thermal diffusivity for MgO is \( \mathrm{cm}^{2} / \mathrm{s} \) (round off to two decimal places).

To calculate the thermal diffusivity (\(\alpha\)) of MgO ceramic, we use the formula: \[ \alpha = \frac{k}{\rho c} \] Where: - \(k\) is the thermal conductivity, - \(\rho\) is the density, - \(c\) is the specific heat capacity. **Given:** - Thermal conductivity, \(k = 37.7 \ \text{W/m·K}\) - Density, \(\rho = 3.58 \ \text{g/cm}^3\) - Specific heat capacity, \(c = 940 \ \text{J/kg·K}\) **Step-by-Step Calculation:** 1. **Convert Units to SI:** - **Density (\(\rho\))**: \[ 3.58 \ \text{g/cm}^3 = 3580 \ \text{kg/m}^3 \] - **Thermal Conductivity (\(k\))**: \[ 37.7 \ \text{W/m·K} = 0.377 \ \text{W/cm·K} \] 2. **Calculate Thermal Diffusivity (\(\alpha\)):** \[ \alpha = \frac{37.7 \ \text{W/m·K}}{3580 \ \text{kg/m}^3 \times 940 \ \text{J/kg·K}} \] \[ \alpha = \frac{37.7}{3,365,200} \ \text{m}^2/\text{s} \approx 1.119 \times 10^{-5} \ \text{m}^2/\text{s} \] 3. **Convert to \(\text{cm}^2/\text{s}\):** \[ 1 \ \text{m}^2 = 10^4 \ \text{cm}^2 \] \[ \alpha \approx 1.119 \times 10^{-5} \ \text{m}^2/\text{s} \times 10^4 = 0.1119 \ \text{cm}^2/\text{s} \] 4. **Round to Two Decimal Places:** \[ \alpha \approx 0.11 \ \text{cm}^2/\text{s} \] **Final Answer:** The thermal diffusivity of MgO ceramic is approximately **0.11 cm²/s**.