Answer:
14.8°C
Explanation:
When the first two are mixed:
m C₁ (T₁ − T) + m C₂ (T₂ − T) = 0
C₁ (T₁ − T) + C₂ (T₂ − T) = 0
C₁ (9 − 15) + C₂ (24 − 15) = 0
-6 C₁ + 9 C₂ = 0
C₁ = 1.5 C₂
When the second and third are mixed:
m C₂ (T₂ − T) + m C₃ (T₃ − T) = 0
C₂ (T₂ − T) + C₃ (T₃ − T) = 0
C₂ (24 − 26.2) + C₃ (30 − 26.2) = 0
-2.2 C₂ + 3.8 C₃ = 0
C₂ = 1.73 C₃
Substituting:
C₁ = 1.5 (1.73 C₃)
C₁ = 2.59 C₃
When the first and third are mixed:
m C₁ (T₁ − T) + m C₃ (T₃ − T) = 0
C₁ (T₁ − T) + C₃ (T₃ − T) = 0
(2.59 C₃) (9 − T) + C₃ (30 − T) = 0
(2.59) (9 − T) + 30 − T = 0
23.3 − 2.59T + 30 − T = 0
3.59T = 53.3
T = 14.8°C
