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A sample of brass, which has a specific heat capacity of 0.375 J*g^-1*°C^-1 is put into a calorimeter (see sketch at right) that contains 250.0 g of water. The brass sample starts off at 85.7°C and the temperature of the water starts off at 16.0 °C. When the temperature of the water stops changing it's 17.5 °C. The pressure remains constant at 1atm.Calculate the mass of the brass sample. Be sure your answer is rounded to 2 significant digits.

Respuesta :

Answer:

The mass of the brass sample is 0.061 grams.

Explanation:

Treating the calorimeter as an isolated system (no heat lost to the surroundings), we write  

qsystem = qwater + qbrass

qwater = -qbrass

The heat gained by the water is given by qwater = m.s.ΔT

Where ΔT is the temperature change: ΔT= tfinal - tinitial, m the mass and s the specific heat. Therefore:

qwater = 250.0 g x 4.184 J/g.ÂșC x (17.5 - 16.0)ÂșC  

qwater = 1569 J

Because the heat lost by the sample of brass is equal to the heat gained by the water, so

qbrass = -1569 J

Solving for the specific heat of brass, we write:

qbrass = m.s.ΔT

-1569 = m x 0.375 J/g.ÂșC x (17.5 - 85.7)ÂșC  

m= 0.061 g

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