This question is incomplete, the complete question is;
A sample of polystyrene, which has a specific heat capacity of 1.880 J.g⁻¹, is put into a calorimeter (see sketch at right) that contains 300.0 g of water. The polystyrene sample starts off at 94.9 °C and the temperature of the water starts off at 22.0. When the temperature of the water stops changing it's 27 °C . The pressure remains constant at 1 atm.
Calculate the mass of the polystyrene sample. Be sure your answer is rounded to 2 significant digits.
Answer:
the mass of the polystyrene sample is 57 g
Explanation:
Given the data in the question;
mass of water m[tex]_{water[/tex] = 300 g
Temperature of water T[tex]_{water[/tex] = 22 °C
Specific heat capacity of water C[tex]_{water[/tex] = 4.184 J/g°C
mass of the polystyrene sample m[tex]_{polystyrene[/tex] = ?
T[tex]_{polystyrene[/tex] = 94.9 °C
Specific heat capacity of polystyrene; C[tex]_{polystyrene[/tex] = 1.880 J.g⁻¹.°C⁻¹
T = 27.7 °C
Now, using heat conservation equation
heat lost by polystyrene = heat gained by water
m[tex]_{polystyrene[/tex] × C[tex]_{polystyrene[/tex] × ( T[tex]_{polystyrene[/tex] - T ) = m[tex]_{water[/tex] × C[tex]_{water[/tex] × ( T - T[tex]_{water[/tex] )
We substitute
m[tex]_{polystyrene[/tex] × 1.880 × ( 94.9 - 27.7 ) = 300 × 4.184 × ( 27.7 - 22 )
m[tex]_{polystyrene[/tex] × 1.880 × 67.2 = 300 × 4.184 × 5.7
m[tex]_{polystyrene[/tex] × 126.336 = 7154.64
m[tex]_{polystyrene[/tex] = 7154.64 / 126.336
m[tex]_{polystyrene[/tex] = 56.63 ≈ 57 g { 2 significant figures }
Therefore, the mass of the polystyrene sample is 57 g
