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

Step-by-step 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=(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+(T_2C_2)/(C_1)`