"Why 100-Degree Span between the Melting and Boiling Points of Water"?

Brief background

Is it coincidental or science? It is a science. Anders Celsius, invented centigrade temperature scale in 1742. Because of the 100-degree interval between the freezing and boiling point in water he named the scale centigrade scale. In 1848, Lord Kelvin defined an absolute temperature scale and linked temperature with kinetic energy. He worked with Boltzmann, who contributed the theoretical foundation linking kinetic energy and temperature through the Boltzmann constant, KE = 3/2KT, K is Boltzmann constant and T is kelvin. In Kelvin's scale, the zero point is 273.15 below that of the Celsius scale. As part of the 2019 redefinition of SI base units, the Boltzmann constant was defined to be exactly 1.380649×10^?23 J?K^?1 and connected with Kelvin and temperature and kinetic energy were linked.

What creates the difference between melting and boiling points of water

Fundamentals of water molecule

The gap between freezing and boiling points of water is not coincidental but rather is a result of the physical properties and molecular structure of water itself.

Water molecules are made up of two hydrogen atoms and one oxygen atom, with a unique bent structure. The bent structure as you can see above stretches the O-H bonds as the bonds bend and polarise the bonds with H acquiring partial positive charge and oxygen with two lone pairs of electrons which is more electronegative than H acquires two negative charges. These charge centres are the points for water molecule to form H bonds with opposite charge atoms of another water molecule. One water molecule can form four hydrogen bonds and the cluster of water molecules grow into a huge network with complete different thermodynamic properties than a single water molecule. This molecular arrangement allows for the formation of hydrogen bonds between water molecules.

How H bonds play role in melting and boiling point of water?

At lower temperatures, these hydrogen bonds become stronger and hold the molecules in a more rigid, organized structure, leading to the solid phase or ice. The freezing point of water, at 0 degrees Celsius, is the temperature at which the kinetic energy of water molecules decreases enough for them to become locked into this organized structure.

At higher temperatures, the kinetic energy of water molecules increases, causing the hydrogen bonds to break more easily. This leads to greater molecular motion and the transition from the liquid phase to the gas phase or vapor. The boiling point of water, at 100 degrees Celsius, is the temperature at which the kinetic energy becomes sufficient to overcome the intermolecular forces and convert water into steam.

The key differences between centigrade and Kelvin scale

The Celsius scale was initially based on observations of the freezing and boiling points of water, which provided easily reproducible reference points for measuring temperature. However, it was later redefined in a more scientific manner. The Celsius scale is not linked to the kinetic energy which is an important property of temperature.

The Kelvin scale, on the other hand, is derived from the absolute thermodynamic temperature scale. It is based on the concept of absolute zero and the behaviour of gases at different temperatures. The Kelvin scale is tied to the fundamental properties of gases and is a more scientifically rigorous scale.

The Kelvin scale is defined in relation to the triple point of water, which is the temperature and pressure at which water coexists in three phases (solid, liquid, and gas) in equilibrium. The triple point of water is assigned a value of exactly 273.16 Kelvin. Absolute zero, the coldest possible temperature, is defined as 0 Kelvin.

The Kelvin scale is also linked to the Boltzmann constant (k), which relates the average kinetic energy of particles in a gas to temperature. The relationship between temperature in Kelvin and energy is more fundamental in nature, making the Kelvin scale important in scientific and mathematical calculations involving temperature and energy. Kelvin is the thermodynamic temperature.

Overall, while the Celsius scale has its origins in empirical observations, the Kelvin scale is based on a more scientific and absolute foundation, incorporating concepts like the triple point and the Boltzmann constant.

What is Boltzmann constant and how it relates to Kelvin?

The Boltzmann constant (k) relates the average kinetic energy of particles in a gas to temperature through the equation:

KE = (3/2) kT

Where KE is the average kinetic energy, k is the Boltzmann constant, and T is the temperature in Kelvin.

At absolute zero (0 Kelvin), according to the equation, the average kinetic energy of particles would theoretically be zero. This is because at the lowest possible temperature, the particles would have minimal or no motion.

The Boltzmann constant provides the proportionality between temperature and average kinetic energy, allowing us to make quantitative calculations involving these quantities.

How does one calculate temperature from kinetic energy using Boltzmann equation?

T = KE/ (3/2) K, is rearranged from the equation, KE = (3/2)kT, where k is the Boltzmann constant. In this equation, KE represents the average kinetic energy of particles in the system, and T represents the temperature in Kelvin.

The Boltzmann constant, k, has a specific value of approximately 1.38 x 10^-23 joules per kelvin. By multiplying the average kinetic energy, KE, by the reciprocal of (3/2)k, you can calculate the temperature, T, in Kelvin.

For example, if you have a system with an average kinetic energy of 1 joule, you would divide 1 by (3/2)k to obtain the temperature in Kelvin.

T = KE / [(3/2)k]

T = (1 joule) / [(3/2)(1.38 x 10^-23 joules per kelvin)]

T ≈ 4.31 x 10^22 Kelvin

So, dividing the average kinetic energy by (3/2) times the Boltzmann constant gives you the temperature in Kelvin.

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