Apiece of a newly synthesized material of mass 25.0 g at 80.0◦c is placed in a calorime- ter containing 100.0 g of water at 20.0◦c. if the final temperature of the system is 24.0◦c, what is the specific heat capacity of this material? 1. 4.76 j · g−1 · (◦c)−12. 1.19 j · g−1 · (◦c)−13. 0.84 j · g−1 · (◦c)−14. 0.30 j · g−1 · (◦c)−15. 7.46 j · g−1 · (◦c)−1

the correct answer is b) c mat = 1.19 J/ g°C

Explanation:

if the calorimeter is isolated, all the heat absorbed by water is due to the heat released by the material:

Q water = - Q material

since Q= m * c * (T final - T inicial) , m=mass , c= specific heat capacity , T final and T initial = final and initial temperature

denoting w as water , mat as material:

m w * c w * (T final - T i w) = - m mat * c mat * (T final - T i mat) = m mat * c mat * (T i mat- T final )

c mat =   m w * c w * (T final - T i w) / [ m mat * (T i mat- T final ) ]

replacing values , assuming c water = 4.186 J/g°C

c mat =   100 g* 4.186 J/g°C * (24°C - 20°C)/[ 25 g * (80°C- 24°C )  ] = 1.19°J/g°C

therefore the correct answer is b) c mat = 1.19 J/ g°C

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