Thermal concepts

📝 Mini-cours GRATUIT

Kinetic theory describes the differences in the properties of solids, liquids, and gases on the basis of the different movement and arrangement of the particles.

The absolute temperature in kelvin is a measure of average kinetic energy.

	Particles in a solid vibrate about fixed position as held together by attractive forces.
	Particles in a liquid move in fixed volume as particles held closely together by attractive forces.
	Particles in a gas can move freely as negligible attractive forces

Every substance changes state by melting/freezing and boiling/condensing at a defined temperature at constant pressure. During a phase change the temperature does not change although the substance continues to be heated. The heat is used to change the separation between the particles rather than their kinetic energy.
More heat is needed to convert a liquid into a gas than a solid into a liquid as more separation occurs in boiling than melting.

Temperature is a measure of how hot or cold a body is.
The average random kinetic energy of the molecules of a substance is proportional to the absolute temperature of the substance.
The average $\rm KE$ of a molecule of monatomic gas $\rm = 3/2 k_BT$ ($\rm T$ measured in kelvin).
$\rm k_B$ is Boltzmann’s constant $\rm = 1.38 \times 10^{-23}~J~K^{-1}$.
The Kelvin (absolute) and Celsius scales are related by $\rm T(K) = t(°C) + 273$.
Note that $\rm\Delta T$ is the same if measured in $\rm K$ or $\rm °C$.
Molecules have no kinetic energy at absolute zero $\rm 0~K$.
Heat, $\bf Q$, is energy that is transferred from one body to another due to a difference in temperature. Heat flows from a body with high temperature to a body with low temperature until they reach thermal equilibrium.

A liquid boil at a specific temperature but a liquid can evaporate at any temperature.

When a liquid boils molecules escape from anywhere in the liquid but only molecules at the surface escape during evaporation.

Evaporation leads to a reduction in temperature as the escape of the faster molecules reduces the average kinetic energy and thus the temperature.

The Internal energy $\bf (U)$ is the sum of the total random kinetic energy of the molecules and their intermolecular potential energy.

For an ideal gas (see $3.2$) the intermolecular forces are zero and so internal energy only consists of random kinetic energy.

There are (electrostatic) forces between molecules. They decrease with increasing separation.

Work has to be done to separate molecules, which increases the intermolecular potential energy, and the internal energy of the substance.

Gases have more potential energy than liquids. Liquids have more potential energy than solids.

The heat capacity $\bf (C)$ of a body is the energy required to change the temperature by one degree. Its units are $\mathrm{J} \mathrm{K}^{-1}$.
$\rm Q=C \Delta T$
The specific heat capacity (c) of a material is the energy needed to increase the temperature of a unit mass of the material by one degree.
$\mathrm Q=m c \Delta \rm T$
The heat capacity of a body made from one material of mass $m$ is related to specific heat capacity:
$\mathrm C=m c$.
For water, $c=4~200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$ . $~4200 \mathrm{~J}$ is needed to change the temperature of $1.0 \mathrm{~kg}$ of water by $1° \mathrm{C}$.

Specific latent heat $\bf (L)$ is the energy needed required to change the phase of a unit mass of a substance at constant temperature.
$\mathrm Q = m\rm L$
At the melting point: $\rm L$ is the specific latent heat of fusion $\rm L_{fusion}$.
At the boiling point: L.is the specific latent heat of vaporisation $\rm L_{vaporisation}$.
The units are $\rm J~ kg^{-1}$.
The specific latent heat of vaporisation of a substance is greater than the specific latent heat of vaporisation as the change in particle separation is greater when a liquid is boiled than when a solid is melted.