Final answer:
To find the initial temperature of the metal, we can use the principle of heat transfer. The heat gained by the water is equal to the heat lost by the metal. By solving the equation, we can determine the initial temperature of the metal.
Step-by-step explanation:
To find the initial temperature of the metal, we can use the principle of heat transfer. The heat gained by the water is equal to the heat lost by the metal. We can use the formula:
Qwater = Qmetal
where Qwater = mass of water × specific heat of water × change in temperature of water, and Qmetal = mass of metal × specific heat of metal × change in temperature of metal.
Given that the mass of the water is 1.409 kg, the specific heat of water is 4.184 J/g°C, the change in temperature of the water is 6.67°C, and the mass of the metal is 288.4 g, we can calculate the initial temperature of the metal as follows:
Qwater = Qmetal
1.409 kg × 4.184 J/g°C × 6.67°C = 288.4 g × specific heat of metal × (29.615°C - initial temperature)
Solving for the initial temperature, we get:
Initial temperature = 29.615°C - (1.409 kg × 4.184 J/g°C × 6.67°C) / (288.4 g × specific heat of metal)