Final answer:
To find the final temperature when gold and iron reach thermal equilibration, we apply the conservation of energy and set the heat lost by the iron equal to the heat gained by the gold, using the formula heat = mcΔT and solving for the final temperature.
Step-by-step explanation:
The student is dealing with a thermal equilibration problem where two metals, gold and iron, are brought into contact, and they reach a final temperature through heat exchange. To solve the problem, we need to apply the principle of conservation of energy, which states that the heat lost by the iron will be equal to the heat gained by the gold until thermal equilibrium is reached. The formula to use is heat = mcΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
To find the final temperature, we can set up the equation where the heat lost by the iron equals the heat gained by the gold:
- ΔT (gold) = T_final - T_initial (gold)
- ΔT (iron) = T_initial (iron) - T_final
- heat lost (iron) = heat gained (gold)
- m_iron * c_iron * ΔT (iron) = m_gold * c_gold * ΔT (gold)
By substituting the known values for mass and specific heat (from the provided table) for both metals, and solving for T_final, we can find the final temperature that both metals will reach in thermal equilibrium.