Final answer:
To determine the final temperature at thermal equilibrium for the lead weight and water without the specific heat capacities provided, you must use the conservation of energy principle. The energy lost by water will equal the energy gained by the lead, but without specific heat values, we cannot solve for the final temperature.
Step-by-step explanation:
To calculate the final temperature of both the lead weight and water at thermal equilibrium, we use the principle of conservation of energy. The energy lost by the hot water as it cools will be equal to the energy gained by the lead weight as it warms up, assuming no heat is lost to the surroundings. The equation for this process can be written as:
mass of lead × specific heat of lead × (final temperature - initial temperature of lead) = mass of water × specific heat of water × (initial temperature of water - final temperature)
Given that the specific heat capacities are constant for the scenario and the system is insulated, solving the above equation for the final temperature will give us the answer.
However, the specific heat capacities of lead and water are needed to solve this equation. Usually, these values can be found in a physics textbook or reliable scientific resource. For the sake of this exercise, let's assume that each material's specific heat capacity is known and perform the calculation accordingly. But since we don't have the exact values here, we cannot provide the final temperature. The student is encouraged to plug in the specific heat values into the equation to find the final temperature.