Question

A piece of unknown metal has a heat capacity of 222 J for 1⁰C and a mass of 246 g. Calculate the specific heat of this metal. Identify the metal.

Answer 1

Answer:

When a problem asks you to find a substance's specific heat, c, it's essentially telling you to find how much heat is needed in order to increase the temperature of 1 g of said substance by 1∘C.

In your case, you know that you need 178.1 J in order to increase the temperature of 15.0 g of your unknown metal by 7∘C, since

ΔT=32.00∘C−25.00∘C=7.00∘C

So, how much heat would be needed to increase the temperature of 1 g of this metal by 7.00∘C ?

1g⋅178.1 J15.0g=11.873 J

Since this much heat is needed to increase the temperature of 1 g by 7.00∘C, it follows that you can increase temperature by 1∘C by adding

1∘C⋅11.873 J7.00∘C=1.70 J

Since you need 1.70 J to increase the temperature of 1 g of this metal by 1∘C, you can say that the metal's specific heat will be

c=∣∣ ∣∣¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯aa1.70 J g−1∘C−1aa∣∣−−−−−−−−−−−−−−−−−−→ rounded to three sig figs

ALTERNATIVELY

You can also use the following equation

Answer 2

The specific heat is 0.902 J/KKg

The element with 0.902 J/KKg specific heat is ALUMINIUM.