A 175 g piece of iron and a 175 g piece of aluminum are placed in a hot water bath so that they are warmed to 99.7 o C. The metal samples are removed and cooled to 21.5 o C. Which sample undergoes the greater heat change

The Aluminium sample

Explanation:

From the question,

ΔQ of the iron = Cm(t₂-t₁) Equation 1

Given: C = specific heat capacity of iron, m = mass of iron, t₁ and t₂ = initial and final temperature respectively.

Given: m = 175 g = 0.175 kg, t₂ = 21.5°C, t₁ = 99.7°C

Constant: C = 444 J/kgK.

Substitute into equation 1

ΔQ = 0.175(444)(21.5-99.7)

ΔQ = -6076.14 J

Similarly, for aluminium,

ΔQ' = c'm'(t₂-t₁) Equation 2

Given: m' = 175 g = 0.175 kg,

Constant: 900 J/kgK

ΔQ' = 0.175(900)(21.5-99.7)

ΔQ' = -12316.5 J

Hence the aluminium sample undergoes the greater heat change