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o determine whether a shiny gold-colored rock is actually gold, a chemistry student decides to measure its heat capacity. She first weighs the rock and finds it has a mass of 4.7 g. She then finds that upon absorption of 57.2 J of heat, the temperature of the rock rises from 25 °C to 57 °C. Find the specific heat capacity of the substance composing the rock and determine whether the value is consistent with the rock being pure gold.

Respuesta :

Answer: The specific heat capacity of the substance composing the rock is [tex]0.38J/g^0C[/tex] and the value is not consistent with the rock being pure gold.

Explanation:

[tex]Q=m\times c\times \Delta T[/tex]

Q = Heat absorbed= 57.2 Joules

m= mass of substance = 4.7 g

c = specific heat capacity = ?

Initial temperature of the rock = [tex]T_i[/tex] = 25.0°C

Final temperature of the rock = [tex]T_f[/tex]  = 57.0°C

Change in temperature ,[tex]\Delta T=T_f-T_i=(57-25)^0C=32^0C[/tex]

Putting in the values, we get:

[tex]57.2=4.7\times c\times 32^0C[/tex]

[tex]c=0.38J/g^0C[/tex]

The specific heat for the rock is [tex]0.38J/g^0C[/tex] and for pure gold the specific heat is [tex]0.128J/g^0C[/tex], thus the rock is not pure gold.

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