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Answer :
The heat flowed into the water is 56376.96 J.
The heat flowed into the water when a metal sample weighing 450 g and at a temperature of 99.1 c was placed in a 38.6 g of water in a calorimeter at 25.0 c and the calorimeter reached a final temperature of 32.8 c is 57919.42 J.
The heat flowed into the water can be calculated using the formula, q=mcΔT, where q = heat, m = mass of the substance, c = specific heat of the substance, and ΔT = change in temperature.
The specific heat of water is 4.184 J/(g°C).
The specific heat of metal is 0.385 J/(g°C).
Given that,mass of metal = 450 g
Temperature of metal = 99.1 c
Mass of water = 38.6 g
Temperature of water = 25.0 c
Final temperature of the calorimeter after placing the metal into the water = 32.8 c
Now, to find the heat flowed into the water, we can use the formula,
q = mcΔT
q = (38.6 g) (4.184 J/(g°C)) (32.8 c - 25.0 c)
q = 1157.584 J
The amount of heat that the water gained is 1157.584 J.
As per the principle of the conservation of energy, the amount of heat lost by the metal is equal to the amount of heat gained by the water and calorimeter.
q lost = q gained
q lost = (450 g) (0.385 J/(g°C)) (99.1 c - 32.8 c)
q lost = 56376.96 J
Therefore, the heat flowed into the water is equal to the heat lost by the metal.
Therefore, the heat flowed into the water is 56376.96 J.
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