Question

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.

Answer 1

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

`\tt Q~metal=Q~water\\\\8.5* c* (100-23.2)=50* 4.18*(23.2-22)\\\\652.8* c=250.8\Rightarrow c=(250.8)/(652.8)=0.384~J/g^oC`