A 1.00 k g chunk of an unknown metal that has been in boiling water for several

Question

A 1.00kg   chunk of an unknown metal that has been in boiling water for several minutes is quickly dropped into an insulating Styrofoam beaker containing 1.00kg  of water at 18.0?C. After gently stirring for 5.00 minutes, you observe that the water's temperature has reached a constant value of 22.0?C . The specific heat capacity of water is cw = 4190J/(kg?K) . Assuming that the Styrofoam absorbs a negligibly small amount of heat and that no heat was lost to the surroundings, what is the specific heat capacity of the metal cm?Assuming that the Styrofoam absorbs a negligibly small amount of heat and that no heat was lost to the surroundings, what is the specific heat capacity of the metal, cm?

Explanation / Answer

temperature of metal = 100 degree celsius ( water boils at 100 degree celsius )

equilibrium temperature = 22 degree celsius

specific heat capacity of water Cw= 4190 J/kg-K

specific heat capacity of metal be Cm

mass of metal = Mm = 1 kg

mass of water = Mw = 1 kg

heat energy lost by metal = heat energy gained by water

(assuming no heat is lost to the surroundings)

heat energy lost by metal = Mm * Cm * (100 - 22)

heat energy lost by water = Mw * Cw * (22 - 18 ) given - initial temperature of water = 18 degree celsius

therefore

Mw * Cw * (22 - 18 ) =   Mm * Cm * (100 - 22)   

4190 * 4 = Cm * 78

Cm = 214.87 J/kg-k

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