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Temperature. The Zeroth Law of Thermodynamics Revision Notes

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13.1Temperature. The Zeroth Law of Thermodynamics


In these revision notes for Temperature. The Zeroth Law of Thermodynamics, we cover the following key points:

  • What is temperature?
  • How the speed of molecules is related to temperature?
  • What are the devices used to measure the temperature?
  • What are the units of temperature?
  • How is the temperature related to the thermal energy of objects?
  • What is thermal equilibrium?
  • What does the Zeroth Law of Thermodynamics say?

Temperature. The Zeroth Law of Thermodynamics Revision Notes

All particles of any object in whatever state it may be are in unceasing motion. In general, they vibrate around some fixed points known as "equilibrium positions." Faster the particles' vibration, greater their kinetic energy.

We use an indirect way to estimate the kinetic energy of an object's particles (in other words its heat energy), which is one of the main components of their internal energy (the other is the chemical energy generated during chemical reactions). A more direct measurement than the measurement of particles' average kinetic energy was therefore invented a few centuries ago. In this way, the concept of temperature was introduced.

By definition, temperature represents a measure of the ability of a substance, or more generally of any physical system, to transfer heat energy to another physical system.

Temperature as a concept is closely related to the average kinetic energy of all particles of the object or system. This means temperature is a more suitable quantity related to the measurements of objects' warmth than heat energy, because its value can be measured directly through devices called thermometers. But first, a thermometer needs to be graded. For this, a lower fixed point and an upper fixed point are needed. The process of assigning different values to different heights of liquid column in a thermometer is known as "calibration of thermometer."

Celsius Scale (invented by the Swedish scientist Anders Celsius) uses the melting and boiling points of water as a lower and upper fixed points respectively. The range of temperatures between these two fixed points is divided in 100 equal parts. Each division is called 1-Celsius degree (1°C).

Daniel Gabriel Fahrenheit, a German scientist, used the temperatures in the coldest and the hottest days in his country to calibrate thermometers. In this way, he invented the Fahrenheit Scale. The conversion formula between Celsius and Fahrenheit scales is:

t (°F) = 1.8 × t (°C) + 32°

However, the official SI unit of temperature is the Kelvin Scale. It is named after the Lord Kelvin, alias William Thompson, the Scottish famous scientist. Kelvin degree is the SI unit of temperature as it offers a great advantage compared to the other units: it has only positive (or zero) values because the lower fixed point of this scale refers to the lowest temperature in the universe, i.e. the temperature in which particles of matter stop vibrating around their equilibrium positions. When measured in Celsius degree, this minimum temperature is equal to -273.16°C. Thus, we have:

0 K = - 273.16°C ≈ - 273°C

or more generally,

T(K) = t (°C) + 273°

Internal energy is composed by two main subcategories: chemical and thermal energy. The first involves the energy generation or absorption during chemical reactions. The later involves the energy generation during the local movements (like vibrations) of objects' particles due to their hotness. Thermal energy is somehow related to temperature, i.e. hot objects possess more thermal energy than cold objects as their particles vibrate more rapidly. The part of this thermal energy that is transferred to another object, is known as heat energy.

The heat "flow" eventually stops when two objects in contact have reached the same temperature. This means the average speeds of particles vibration in both objects are already equal. This is the base of the Zeroth Law of Thermodynamics, which says:

If a thermodynamic system A is in thermal equilibrium with another thermodynamic system B and the thermodynamic system B is in thermal equilibrium with a third thermodynamic system C, then the thermodynamic system A is also in thermal equilibrium with the thermodynamic system C.

In simpler words, the Zeroth Law of Thermodynamics says:

If an object A has the same temperature with another object B and the object B has the same temperature with a third object C, then the object A has the same temperature with the object C.

For example, the object in the factory in which a thermometer was originally placed in contact to do its calibration represents the system A, the thermometer itself is the system B and the patient's body is the system C.

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