Final answer:
The first law of thermodynamics states that the heat lost by the metals is equal to the heat gained by the water. The heat transfer for each component is calculated with the formula q = mcΔT, summing up to be equal to zero, with the water's heat gain equation being qwater = mwatercwaterΔTwater.
Step-by-step explanation:
From the first law of thermodynamics, the heat lost by the metal samples will be equal to the heat gained by the water, assuming no heat is lost to the surroundings. This can be represented by the equation qmetal + qwater = 0, where q is the heat transfer. The heat transfer q can be calculated using the formula q = mcΔT, where m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature. For a specific example, when a hot piece of metal is dropped into water, the final temperature is reached when the heat lost by the metal equals the heat gained by the water.
In the question, if the specific heat capacity of the substances are known, the equation would be set up as follows for each substance: qiron = mironcironΔTiron and qgold = mgoldcgoldΔTgold, then the sum of these qmetal's would be equal to qwater = mwatercwaterΔTwater.