Question

I'm beginning to revise the basic concepts of statistical mechanics and I came across the definition of thermal equilibrium.

'Two thermodynamic systems are in thermal equilibrium with each other if there is no net flow of thermal energy between them.'

There's also this:

'A system is said to be in thermal equilibrium with itself if the temperature within the system is spatially uniform and temporally constant.'

My question is simple: does the absence of exchange of thermal energy mean that both systems are at the same temperature?

Answer 1

The absence of exchange of thermal energy between two systems indicates that they are at the same temperature, by the Zeroth law of thermodynamics.

Step-by-step explanation:

Understanding Thermal Equilibrium and Temperature

When exploring the basic principles of statistical mechanics, an important concept to grasp is the nature of thermal equilibrium. As defined, two systems are in thermal equilibrium with each other if no net flow of thermal energy exists between them, essentially meaning that their temperatures are identical. The Zeroth law of thermodynamics plays a fundamental role in explaining this concept. It states that if system A is in thermal equilibrium with system B, and B is with system C, then A is also in thermal equilibrium with C.

The underlying reason why systems at thermal equilibrium do not exchange heat is that they are at the same temperature. This temperature uniformity implies an operational definition, which is based on the measurement of a thermometer. This device does not directly measure the temperature of the object it comes in contact with but rather its temperature. However, due to the systems reaching an equilibrium state upon contact, allowing enough time guarantees that the measured temperature of the thermometer corresponds to that of the object it is in touch with.

In essence, the absence of an exchange of thermal energy signifies that the two systems have matched their temperatures. To sum up, an attribute of thermodynamic systems at thermal equilibrium is that they share the same temperature, whether or not they are in actual physical contact. The Zeroth law of thermodynamics solidifies this concept, ensuring predictability and consistency within the realm of thermal dynamics.