A mass of 317.6 g with unknown composition is heated in an oven to a temperature

Question

A mass of 317.6 g with unknown composition is heated in an oven to a temperature of 307.61 °C. The mass is then dropped into a strong insulated calorimeter containing 804.9 g of water. The initial temperature of water is 12.07 °C. The final equlibrium temperature of the system is 17.19 °C. Assume that the mass and water are in an isolated system and the water does not vaporize. No heat is transferred to the water during this experiment. The specific heat of the water is 4190 J/kg-K. What is the specific heat of this unknown mass?

Explanation / Answer

The mass of the composition m = 317.6 g = 0.3176 kg The initial composition temperature Ti = 307.61C The mass of the water mw = 0.8049 kg The intial temperature of the water Ti = 12.07 C and the final temperature of the water Tf = 17.19C The specific heat of water Cw = 4190 J/kg K From calorimetery , the heat lost by compsotion is equal to the heat gained by water then        m CT = mw Cw T' Therefore the specific heat of composition        C = mw Cw T' / mT            = (0.8049kg) (4190 J/kg K) (17.19 - 12.07 ) / (0.3176 kg ) (307.61 - 17.19)                         = 17267.35 / 92.24                      = 187 J/kg 0C   or 187 J/kg K                      = 187 J/kg 0C   or 187 J/kg K           

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