Question

Two bodies, with heat capacities C₁ and C₂ (assumed independent of temperature) and initial temperatures T₁ and T₂ respectively, are placed in thermal contact. Show that their final temperature $T_f$ is given by T₁ = (C₁T₁ + C₂T₂)/(C₁ + C₂). If C₁ is much larger than C₂ . show that $T_f$ = T₁ + C₂(T₂ -T₁)/C₁.

Answer 1

Explanation:

Given:

• Initial Temperature of the body(1) with heat capacity $C_1$ is $T_1$

• Initial Temperature of the body(2) with heat capacity $C_2$ is $T_2$

The heat lost by one body will be equal to the heat gained by other body by first law of thermodynamics.

Let assume that  $T_1$ is greater than $T_2$ and $T_f$ be the final temperature of both body.

$C_1(T_1-T_f)=C_2(T_f-T_2)\\T_f=\dfrac{C_1T_1+C_2T_2}{C_1+C_2}$

If $C_1$ is much larger than $C_2$ then final temperature   $T_f$ will be

$T_f=T_1+\dfrac{T_2C_2}{C_1}$