Final answer:
The final temperature at which a 32.5g sample of iron and 105.3g of water reach thermal equilibrium is determined by using the conservation of energy formula, taking into account the masses and specific heats of both substances.
Step-by-step explanation:
To find the final temperature of both iron and water when they reach thermal equilibrium, we can use the principle of conservation of energy which states that heat lost by the hot substance will be equal to the heat gained by the cooler substance. Since no energy is lost to the surroundings, the equation is set up as:
mironcironΔTiron = -mwatercwaterΔTwater
Let:
- miron = 32.5g (mass of the iron)
- mwater = 105.3g (mass of the water)
- ciron = 0.449 J/g°C (specific heat of iron)
- cwater = 4.184 J/g°C (specific heat of water)
- Tfinal = unknown final temperature
- ΔTiron = Tfinal - 45.8°C
- ΔTwater = Tfinal - 15.4°C
Plugging these values into our equation:
(32.5g)(0.449 J/g°C)(Tfinal - 45.8°C) = -(105.3g)(4.184 J/g°C)(Tfinal - 15.4°C)
This equation is then solved for Tfinal to determine the final temperature at which the iron and water reach equilibrium.