Screen grab – interactive multimedia from the physical chemistry book (Click to enlarge)

Setting the Scene – Back to Basics
In order to understand the concept of thermal equilibrium (Chapter 1 section 1.4 of the physical chemistry textbook), we must first set the scene – by going back to basics.  And a good starting point for discussion is temperature and heat.
We all have a more or less well-developed sense of ‘hot’ and ‘cold’.  We understand the concept of temperature to mean that high values are linked to ‘hotness’ of a body or system whilst lower values are associated with ‘coldness’. Temperature is what the thermometer reads. However, the measurement of temperature on a numerical scale has always presented problems. The basic difficulty is that the measured temperature depends on the thermometer being used.
The Temperature Scale
We can define 100 º Celsius as the temperature of boiling water at 1 atmosphere pressure, and 0 ºC as the temperature of wet ice at 1 atmosphere in contact with air. In the United States, the Fahrenheit temperature scale is more commonly used. With this scale, the boiling point of water is designated as 212 ºF, and the freezing point of water is designated as 32 ºF. Temperatures expressed by the Fahrenheit scale can be converted to the Celsius scale equivalent using the equation below:

ºC = (ºF – 32º)/1.8

Conversely, temperatures expressed by the Celsius scale can be converted to Fahrenheit scale equivalent using the equation below:

ºF = 1.8 x ºC + 32º

A scale widely used among scientists is the Kelvin temperature scale where 0 ºC is 273.15 K (that is, zero Kelvin is equivalent to -273.15 ºC).  Conversions between the two scales can take place as below:

ºC = K – 273.15º

K = ºC + 273.15

The zero point on the Kelvin scale is known as absolute zero. It is the lowest temperature that can be achieved and it is at this temperature where atomic motion stops.
Temperature, Heat and the Zeroth Law of Thermodynamics
Temperature and heat are different. Temperature is a measure of the intensity (or degrees) of hotness in a system and heat is a measure of the quantity of heat energy in a system. Heat always flows from hot to cold and not vice versa. When two systems are placed together, the system with more heat energy will lose that energy to the system with less heat energy. This is because a hotter system contains more thermal energy and a cooler system contains less thermal energy. Systems or objects can either gain or lose heat but they cannot gain or lose cold.
Similarly in a thermal system, the hotter object loses heat energy to the cooler object until equilibrium is attained. Eventually, their temperatures will be equal and they will cease to exchange heat energy as neither object is warmer or cooler than the other. At this point, they are in a state of thermal equilibrium.
Thermal contact is an important concept that relates to thermal equilibrium. Multiple systems can be in thermal contact with each other if they are capable of affecting each other’s temperatures. This is where the Zeroth Law of Thermodynamics comes into the picture. The Zeroth Law is a concept that was used to establish temperature: it defines systems in equilibrium with each other as having the same temperature.
A rather straightforward example can be used to illustrate thermal equilibrium; A cup of hot coffee and a glass of cold orange juice are left on the kitchen bench. They are not in contact with each other. Over time, the coffee will cool down and the orange juice will warm up. Eventually both drinks will be at the same temperature, i.e. at room temperature. They have become in thermal equilibrium with their surroundings and with each other: they are in a state of thermal equilibrium.
Using the Zeroth Law of Thermodynamics, if two systems (the drinks) are in equilibrium with a third system (room temperature), then they must all be in equilibrium with each other (both drinks at room temperature).