First, design an experiment you could conduct that might measure how thermal equilibrium occurs. what materials would you use? what would you measure? what results would you expect? what if the results were different; what would that indicate?

What material would you use: I would use a beaker, water, heated metal

What would you measure: Measure the changes in temperature before and after pouring the metal.

What results would you expect: Whether Thermal Equilibrium has occurred or not.

What if the results were different; what would that indicate : The Beaker might absorb some of the heat causing an error in the reading.

Explanation:

step 1: Take a well insulated beaker and pour water of known mass in it.

step 2: Record its initial temperature.

step 3:  Place heated metal into the beaker and make sure that the beaker is tightly packed so that no heat escapes from the beaker.

step 4: Record temperature of the beaker at different intervals and after temperature has become constant ( No heat is being gained) , note the final temperature

In end we will check whether thermal equilibrium is established or not.

heat lost by the metal = heat gained by water + heat gained by the beaker    

Possible Error:

There might be disparities in the values acquired as the beaker will absorb some heat.