Question

The value of specific heat for copper is 390 J/kg⋅C∘, for aluminun is 900 J/kg⋅C∘, and for water is 4186 J/kg⋅C∘.

What will be the equilibrium temperature when a 235 g block of copper at 255 ∘C is placed in a 135 g aluminum calorimeter cup containing 825 g of water at 16.0 ∘C? Express your answer using three significant figures.

Answer 1

Basic equation for final (f) state of an N-component mixture expresses the equality of final and initial heats:

(m_fc_f)T_f = Σ(i=1,N)(m_ic_iT_i)

(0.235*390 + 0.135*900 + 0.825*4186)T_f = 0.235*390*255 + 0.135*900*16 + 0.825*4186*16

Equilibirium Temperature, T_f = 80569.95/3666.6 = 21.974 ⁰C

Answer 2

mc(ti - tf) = mc(tf - ti) + mc(tf - ti)

c for copper = 0.390 J/gC
c for water = 4.186 J/gC
c for aluminum = 0.900 J/gC
235(0.390)(255 - Tf) = 825(4.186)(Tf - 16) + 145(0.900)(Tf - 16)

Tf = 21.96 C