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An unknown metal with a mass of 8.5 g was heated in boiling water to a temperature of 100°C. The metal was immediately transferred to an insulated cup containing 50.0 g of water at 22°C. At equilibrium (when the temperature became constant) the temperature of the system was 23.2°C. Calculate the specific heat of the metal and determine its identity. Explain how you arrived at your conclusion. You must show your work to receive credit for your answer.

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ardni313

The specific heat of the metal : 0.384 J/g° C,

and a metal with a specific heat of 0.384 is copper

Further explanation  

The law of conservation of energy can be applied to heat changes, i.e. the heat received / absorbed is the same as the heat released  

Q in = Q out  

Q lost(metal) = Q gained(water)

Heat can be calculated using the formula:  

Q = mc∆T  

Q = heat, J  

m = mass, g  

c = specific heat, joules / g ° C  

∆T = temperature difference, ° C / K  

[tex]\tt Q~metal=Q~water\\\\8.5\times c\times (100-23.2)=50\times 4.18\times(23.2-22)\\\\652.8\times c=250.8\Rightarrow c=\dfrac{250.8}{652.8}=0.384~J/g^oC[/tex]

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