Answer:
The final temperature aluminium-water system is 24° C
Step-by-step explanation:
Heat energy, H = mcθ
Where m is mass of substance, c is specific heat capacity, θ is temperature difference
Using the principle, Heat lost = Heat gained
Let the final temperature of the aluminium-water system be Tfinal
Heat lost by aluminium, H₁ = -m₁c₁(Tfinal - 40)
Heat gained by water, H₂ = m₂c₂(Tfinal -21)
Heat lost by aluminium, H = -[30 × 0.21 × (Tfinal - 40)]
H₁ = -6.3Tfinal + 252
Heat gained by water, H₂ = 50 × 1.0 × (Tfinal - 21)
H₂ = 5Tfinal - 21
Equating H₁ and H₂
-6.3Tfinal + 252 = 5 Tfinal - 21
5Tfinal + 6.3Ffinal = 252 + 21
11.3 Tfinal = 273
Tfinal = 273/11.3
Tfinal = 24° C
Therefore, the final temperature aluminium-water system is 24° C