Answer:
Tբ = (C₁T₁ + C₂T₂)/(C₁ + C₂) = (C₁T₁)/(C₁ + C₂) + (C₂T₂)/(C₁ + C₂)
Explanation:
Let's Assume that T₁ > T₂, this means that, T₁ > Tբ > T₂
The zeroth law of thermodynamics explains that two bodies in thermal equilibrium will eventually end up with the same final body temperature.
Heat lost by body 1 = Heat gained by body 2
C₁ (T₁ - Tբ) = C₂ (Tբ - T₂)
C₁T₁ - C₁Tբ = C₂Tբ - C₂T₂
C₁Tբ + C₂Tբ = C₁T₁ + C₂T₂
Tբ(C₁ + C₂) = C₁T₁ + C₂T₂
Tբ = (C₁T₁ + C₂T₂)/(C₁ + C₂)
Tբ = (C₁T₁)/(C₁ + C₂) + (C₂T₂)/(C₁ + C₂)
