Question

Is it possible for two objects to be in thermal equilibrium with each other if they are not in contact with each other? Explain.

Answer 1

Yes, it is possibe. Let's denote these two objects as A and B, and they can not be brought in contact with each other. Suppose, we have the third object C that can be brought in contact with both A and B. Object C should be small enough compared with A and B, so their contact does not change the states of A and B much.

Let's then bring C in contact with A and wait until they come in termal equilibrium. If we then transfer C to B and observe that they are already in termal equilibrium, it means that A is in termal equilibrium with B as well. Mathematically it will be writen as follows:

$$(T_A = T_C \space \text {and} \space T_C = T_B) \Rightarrow T_A = T_B$$

where $T$ denotes absolute temperature of corresponding objects.