Question

Miners discover a new vein of metal in the mine they are excavating. They send a sample to your lab so you can determine what type of metal it is. You heat up a 2 kg block of the unknown metal from room temperature of 298 K until it melts at 1768 K. You measure that it takes 1.24 x 10^6 J of energy to melt the block. Use the specific heats of various metals shown below to determine what metal the miners have discovered.
Aluminum: 904 J kg-1 K-1
Nickel: 445 J kg-1 K-1
Copper: 384 J kg-1 K-1
Cobalt: 421 J kg-1 K-1
Titanium: 520 J kg-1 K-1
A. Cobalt
B. Copper
C. Aluminum
D. Nickel

Answer 1

Answer: option A. Cobalt

Explanation:

1) Data:

Q = 1.24 × 10⁶ J
m = 2 kg
Tf = 1768 K
Ti = 298 K
Cs = ?

2) Formula:

Q = m Cs ΔT
ΔT = Tf - Ti = 1,768K - 298K = 1,470K

3) Calculations:

i) Solve for Cs:

Cs = Q / [ m ΔT]

ii) Substitute the data:

Cs = 1.24 × 10⁵ J / [ 2kg (1768K - 298K) ] = 421 J / (kg K)

4) Compare with the specific heats (Cs) of the vaious metals given and you find that it is Cobalt.