Which of these statements is not necessarily true for two objects in thermal equilibrium?

The objects are made of tiny particles that are moving at the same rate.

The objects' temperatures are not changing.

The objects have the same temperature.

The objects' temperatures have both changed by the same amount.

The objects' temperatures have both changed by the same amount

Explanation:

Two objects are said to be in thermal equilibrium if their temperature is the same.

Therefore, we can already state that the option

"The objects have the same temperature"

is true.

Furthermore, the temperature of an object is a measure of the average kinetic energy of its particles (in fact, temperature is directly proportional to the average kinetic energy of its particles): so the following option

The objects are made of tiny particles that are moving at the same rate.

is also true (if the two objects have same temperature, then their particles have same average kinetic energy, so they are moving at the same rate).

From the laws of thermodynamics, we also know that for two objects in contact, heat is always transferred from the hotter object to the colder object, until the two objects reach thermal equilibrium. When they reach thermal equilibrium, their temperatures are the same, therefore they no longer exchange heat. So, the following option

The objects' temperatures are not changing

is also correct.

Therefore, the option that is NOT necessarily correct is

The objects' temperatures have both changed by the same amount.

In fact, it is possible that the magnitude of the change in temperature of the two objects was different: we only know that their final temperature is the same, however we don't know what was their initial temperature.