Final answer:
To determine the mass of the metal, an equation based on the principle of conservation of energy is set up, equating the heat lost by the metal to the heat gained by the water. The mass is calculated by applying the formula q = m · c · (ΔT) for both substances and solving for m.
Step-by-step explanation:
To solve for the mass of the metal dropped into water using its specific heat and the principle of conservation of energy, we can set up an equation where the heat lost by the metal equals the heat gained by the water. The specific heat of water is generally known to be approximately 4.18 J/g°C, and this information, along with the masses and temperatures given, can be used to solve for the mass of the metal.
Let m be the mass of the metal we want to find. The amount of heat lost by the metal as it cools down from 1500°C to the final temperature of 75.0°C can be calculated using the formula: q = m · c · (ΔT), where q is the heat, m is the mass, c is the specific heat, and ΔT is the change in temperature. Similarly, the heat gained by the water can be calculated using a similar formula.
By setting the heat lost by the metal equal to the heat gained by the water, we have: m · 1.44 J/g°C · (1500°C - 75.0°C) = 1000 g · 4.18 J/g°C · (75.0°C - 40.0°C). Solving for m will give us the mass of the metal that was dropped into the water.