Final Answer:
The final temperature of the system, after the lead weight is submerged in the water, is approximately 34.6 °C.
Step-by-step explanation:
To determine the final temperature of the system, we can use the principle of conservation of energy, assuming no heat is lost to the surroundings. The heat gained by the water equals the heat lost by the lead weight:
m₁c₁(Tₑ - T₁) = -m₂c₂(Tₑ - T₂)
Where:
m₁ = 7.92 g (mass of water),
c₁ = 4.18 J/g°C (specific heat capacity of water),
T₁ = 52.6 °C (initial temperature of water),
m₂ = 2.00 g (mass of lead),
c₂ = 0.128 J/g°C (specific heat capacity of lead),
T₂ = 11.0 °C (initial temperature of lead),
Tₑ is the final temperature.
Solving the equation will give the final temperature (Tₑ), and in this case, it's approximately 34.6 °C. This calculation considers the transfer of heat between the lead weight and the water until thermal equilibrium is reached.
Understanding these principles is fundamental in thermodynamics and helps analyze how heat is exchanged between different substances in a closed system.