Thermal Equilibrium Temperature

Our sense of touch can usually tell us if an object is hot or cold. We know that to
make a cold object warmer, we can place it in contact with a hot object, and to make a hot object cooler, we can place it in contact with a cold object.

When an object is heated or cooled, some of its physical properties change. If a
solid or liquid is heated, its volume usually increases. If a gas is heated and its pressure is kept constant, its volume increases. However, if a gas is heated and its volume is kept constant, its pressure increases. If an electrical conductor is heated, its electrical resistance changes. 

A physical property that changes with temperature is called a thermometric property. Achange in a thermometric property indicates a change in the temperature of the object.

Suppose that we place a warm copper bar in close contact with a cold iron bar so that the copper bar cools and the iron bar warms. We say that the two bars are in thermal contact. The copper bar contracts slightly as it cools, and the iron bar expands slightly as it warms. 

This process eventually stops and the lengths of the bars remain constant. The two bars are then in thermal equilibrium with each other. Suppose instead that we place the warm copper bar in a cool running stream of water. The bar cools until it stops contracting, at the point at which the bar and the water are in thermal equilibrium. 



Next, we place a cold iron bar in the stream, near but not touching the copper bar. The iron bar will warm until the iron bar and the water are also in thermal equilibrium. If we remove the bars and place them in thermal contact with each other, we find that their lengths do not change. 

They are in thermal equilibrium with each other. Although it is common sense, there is nological way to deduce this fact, which is called the zeroth law of thermodynamics :

If two objects are in thermal equilibrium with a third object, then all three of the objects are in thermal equilibrium with each other.

                                                           

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