Molecular Agitation and Temperature

In physics, the temperature of an object is related to the degree of agitation of its molecules (and/or atoms). In this context, the thermal equilibrium between two bodies is associated with the exchange of heat between them, which takes place until the degree of agitation of the molecules of both bodies are equal, i.e., the bodies reach equal temperatures (thermal balance $$\iff$$ equal temperatures). The thermophysics (or thermology) is a branch of physics that studies the heat flows and their transformations, and how the temperatures of the bodies change these processes.

## Thermometry

The thermometry objects of study are: the different ways to measure the temperature of objects and the relationships between different temperature scales. Some important definitions for this study are:

Temperature
It is the quantitative measure of the physical quantity that is related to our sense of hot and cold. Microscopically, this magnitude is related to the degree of molecular agitation of the system (kinetic energy). The molecular agitation and the temperature are related as follows:
• A higher degree of molecular atomic agitation $$\Rightarrow$$ a higher temperature;
• A lower degree of molecular atomic agitation $$\Rightarrow$$ a lower temperature.
Macroscopically, it allows us to tell if two or more systems are in thermal equilibrium or not.
Heat exchange
It occurs when two objects (bodies) of different temperatures are put in direct contact or through a good thermal conductor.
Thermal Equilibrium
When two or more systems are in thermal equilibrium they do have the same temperature. Systems that are not in thermal equilibrium does not show any relationship between their temperatures.
Zeroth Law of Thermodynamics
If two bodies, $$A$$ and $$B$$ are in thermal equilibrium with a third body $$C$$, then $$A$$ and $$B$$ are also in thermal equilibrium with each other.
Thermometer
It is the instrument used to measure the temperature of objects. The thermometers use a scale that varies evenly with the temperature. Strictly speaking, we say that the variation is a bijection and changes monotonically with temperature.
Thermometric Function
It is the function that relates the thermometric magnitude $$g$$ of a thermometer to the temperature. For example, we know that the length of a column of mercury in a cylindrical vessel varies according to the temperature. In this case, the height of the column is the magnitude $$g$$. With this, we can find a function that relates the height of this column with the temperature, the thermometric function. Other quantities that may be used are: the pressure of a gas, the color of a material, the electrical resistance of a material etc. In general, the termometric function is a linear function of the form: $$T(g) = ag + b,$$ where $$T$$ is the system temperature, $$g$$ is the observed quantity (height of a column of mercury, for example) and the other parameters are constants.
Absolute Scale
The temperature measured in the International System of Units ($$IS$$) is the Kelvin scale. The absolute temperature is the average kinetic energy of the molecules of a body.
Temperature Scales
Typically, the temperature scales are made from the choice of an arbitrary value in the ice melting point and another in the boiling water point. Below we list several temperature scales, and in the $$IS$$ Kelvin is adopted.
The conversion formula between these various scales is: $$\frac{T_C}{5} = \frac{T_F - 32}{9} = \frac{T_K-273}{5},$$ where $$T_C$$, $$T_F$$ and $$T_K$$ are the temperatures in Celsius, Fahrenheit and Kelvin, respectively. Note that the relation between the temperature changes is $$\Delta T_C = \Delta T_K = \frac{5}{9} \Delta T_F.$$
 Some Temperatures Kelvin $$(K)$$ Fusion of helium nucleus $$10^8$$ Inside the Sun $$10^7$$ Sun's surface $$6000$$ Gold fusion $$1340$$ Boiling water at 1 atm $$373$$ Ambient highest recorded on Earth's surface $$331$$ Human body $$310$$ Freezing water at 1 atm $$273$$ Lowest ambient temperature recorded at the earth's surface $$185$$ Liquid helium $$4.2$$ Universe background radiation $$3$$