# Clarification on the macroscopic intensive parameter "Temperature"

As I understood, the condition to be in a thermal equilibrium is that the temperature is well defined. But what does "well defined" mean? is it the fact that I can measure the temperature by thermometer? if yes, why is most of our everyday activities is not quasi static process? When I boiling water I can always measure the temp'.

Well-defined in this context means the temperature isn't changing with time, or with position within the body being measured. This means a thermometer will produce a meaningful measurement of the system.

Everyday thermodynamic processes are usually not quasistatic because they weren't designed to be so from the outset, either because they are natural and not engineered or because the machine containing that process would not be useful if operated in a quasistatic mode- as for instance in the case of an internal combustion engine or a steam turbine.

• Thank you I realized what I have missed, even in natural process I can get values for the temperature but they will not be stable during the process and that is mean not well defined. Commented Feb 16, 2021 at 7:31

As I understood, the condition to be in a thermal equilibrium is that the temperature is well defined. But what does "well defined" mean?

A definition of the temperature of an object can be associated with the concept of thermal equilibrium, essentially that objects that are no longer transferring net heat with one another are in thermal equilibrium with one another and therefore temperature is a property of these objects which means they will no longer transfer net energy to one another. This definition is associated with the Zeroth law of thermodynamics.

A common definition you will see is the so called "kinetic temperature", which says that the temperature of an object is a measure of the average translational kinetic energy of molecules of the object. A shortcoming of this definition is that it assumes an object consists only of independently moving particles having translational kinetic energy. It ignores the fact that there are more forms of kinetic energy besides translational, namely, the kinetic energy associated with molecular rotation and vibrational. These modes become important when considering the specific heats of materials.

A more reliable definition of temperature is in terms of the partial derivative of entropy with respect to internal energy, with the number of particles (N) and the volume (V) constant, per the equation.

$$\frac{1}{T}=\biggr(\frac {\partial S}{\partial U}\biggl)_{N,V}$$

For a more detailed description of the above, see :http://www.hyperphysics.de/hyperphysics/hbase/thermo/temper2.html#c1

is it the fact that I can measure the temperature by thermometer? if yes, why is most of our everyday activities is not quasi static process?

The measurement of temperature by a temperature measuring device, be it with a thermometer, thermocouple, or IR detection device does not define temperature. Depending on the technology, reading is an indirect measure of the average translational kinetic energy of the molecules, the kinetic temperature described above.

Regarding everyday activities, or everyday natural processes, they are generally not quasi static. That's because natural processes occur because of some form of disequilibrium, be it thermal (temperature difference), mechanical (pressure and force differences), or chemical disequilibrium.

Hope this helps.

• It indeed helped me thank you, just to make sure, you meant "the partial change in entropy divided by the partial change in internal energy" right? I mean $\frac{1}{T}=\biggr(\frac {\partial S}{\partial U}\biggl)_{N,V}$ Commented Feb 16, 2021 at 7:29
• Yes of course, as shown in the link. That's what happens when you're tired. Corrected, thanks. Commented Feb 16, 2021 at 13:52