Final answer:
To warm 1.92 x 10⁵g of aluminum from 73°C to 165°C, one would need 1.56 x 10⁸ joules of energy, calculated using the specific heat capacity of aluminum and the temperature change.
Step-by-step explanation:
To calculate the amount of energy needed to warm a given mass of aluminum, one can use the formula: Q = m × c × ΔT, where Q represents the amount of heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, the specific heat capacity (c) of aluminum is 0.89 J/g°C. The mass of aluminum (m) is 1.92 x 10⁵g, and the temperature change (ΔT) is the final temperature minus the initial temperature, which is 165°C - 73°C = 92°C.
By plugging these values into the formula, we get:
Q = (1.92 x 10⁵g) × (0.89 J/g°C) × (92°C).
Solving for Q gives us the amount of energy required:
Q = 1.92 x 10⁵g × 0.89 J/g°C × 92°C = 1.56 x 10⁸ J
Therefore, 1.56 x 10⁸ joules of energy is needed to warm 1.92 x 10⁵g of aluminum from 73°C to 165°C.