1. The problem involves understanding the relationship between heat energy, specific heat, mass, and temperature change. 2. The specific heat capacity formula is given by $$Q = mc\Delta T$$ where: - $Q$ is the heat energy in joules, - $m$ is the mass in grams, - $c$ is the specific heat capacity in j/g°C, - $\Delta T$ is the temperature change in °C or K. 3. Given the specific heat $c = 0.902$ j/g°C, and heat energies $Q$ as 8500 J, 6000 J, and 80,000 J, and a temperature change $\Delta T = 7500$ K, we can find the mass $m$ for each case using: $$m = \frac{Q}{c \Delta T}$$ 4. Calculate mass for each heat energy: - For $Q = 8500$ J: $$m = \frac{8500}{0.902 \times 7500} = \frac{8500}{6765} \approx 1.256\text{ g}$$ - For $Q = 6000$ J: $$m = \frac{6000}{0.902 \times 7500} = \frac{6000}{6765} \approx 0.887\text{ g}$$ - For $Q = 80,000$ J: $$m = \frac{80000}{0.902 \times 7500} = \frac{80000}{6765} \approx 11.82\text{ g}$$ 5. These calculations show the mass of aluminum that would absorb the given heat energy with a temperature change of 7500 K. Final answers: - Mass for 8500 J: approximately 1.256 g - Mass for 6000 J: approximately 0.887 g - Mass for 80,000 J: approximately 11.82 g