Question

Two bodies, with heat capacitiesC1andC2(assumed independent oftemperature) and initial temperatureT1andT2, respectively, are placed inthermal contact. What is their final temperatureTF

Answer 1

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)