An unknown mass of aluminum requires 6290 joules to raise the temperature from \( 23.9^{\circ} \mathrm{C} \) to \( 80.0^{\circ} \mathrm{C} \). What is the mass of the aluminum? The specific heat of aluminum is \( 0.900 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C} \) a 125 g b 78 g c 246 g d 169 g

To find the mass of aluminum, you can use the formula: \[ Q = m \cdot c \cdot \Delta T \] Where: - \( Q \) is the heat absorbed (6290 joules), - \( m \) is the mass (in grams), - \( c \) is the specific heat capacity (0.900 J/g°C), - \( \Delta T \) is the change in temperature (80.0°C - 23.9°C = 56.1°C). Rearranging for mass gives: \[ m = \frac{Q}{c \cdot \Delta T} = \frac{6290}{0.900 \cdot 56.1} \approx 125 \text{ g} \] So, the mass of the aluminum is approximately 125 g (option a). Did you know that aluminum is not only lightweight but also has a high thermal conductivity? That’s why it’s often used in cooking pots and pans, as it heats up quickly and evenly, making for better cooking results! For anyone tackling similar problems: Remember to always check your units and ensure they are consistent. It’s easy to forget a conversion, especially if you mix up joules with calories or grams with kilograms! Keeping a clear unit tracking system can save you time and frustration.