If 100.0 grams of each of the following metals absorb the same amount of heat, which metal will show the smallest temperature increase?

Question

Silver = (c = 0.235 J/g°C)

Aluminum = (c = 0.897 J/g°C)

Lead = (c = 0.129 J/g°C)

Lead

Aluminum

Silver

They will all have the same increase in temperature

Answer 1

The change in temperature is dependent on the mass of the metal, the amount of heat and the specific heat. Since the masses are all the same (100 g), and the amount of heat absorbed is the same, the change in temperature will be dependent only on the specific heat. The equation that shows this is q = mC∆T

q = heat

m = mass

C = specific heat

∆T = change in temperature

∆T = q / (m)(C) and since q and m are the same for all metals, this reduces down to ∆T = 1/ C

So, the metal that shows the smallest change in temperature will be the metal with the greatest specific heat.

The answer would be Aluminum

To prove this, calculate the change in temperature for all three metals (use 100 J of heat)

Silver: ∆T = q/mC = 100 J / 100 g (0.235 J/gº) = 4.25º

Aluminum: ∆T = 100 J / 100 g (0.897 J/gº) = 1.11º'

Lead: ∆T = 100 J / 100 g (0.129 J/gº) = 7.75º