1. The problem requires calculating the maximum allowable temperature rise for a material under thermal shock conditions, which depends on the material properties such as thermal stress limits. 2. To solve this, we use the formula for thermal stress: $$\sigma = E\alpha \Delta T$$ where $\sigma$ is the stress, $E$ is the Young's modulus, $\alpha$ is the coefficient of thermal expansion, and $\Delta T$ is the temperature rise. 3. The maximum allowable temperature rise $\Delta T_{max}$ before the material cracks or yields is found by rearranging the formula: $$\Delta T_{max} = \frac{\sigma_{allowable}}{E\alpha}$$ 4. Using given values for silicone nitride: assume - Young's modulus $E = 310 \times 10^9$ Pa - Coefficient of thermal expansion $\alpha = 3.2 \times 10^{-6} \text{°C}^{-1}$ - Allowable stress $\sigma_{allowable} = 700 \times 10^6$ Pa 5. Substitute the values: $$\Delta T_{max} = \frac{700 \times 10^6}{310 \times 10^9 \times 3.2 \times 10^{-6}} = \frac{700 \times 10^6}{992000} \approx 705.65 \text{°C}$$ 6. The maximum allowable temperature rise rounded to the nearest 10 °C is **710 °C**. Final answer: 710 °C