# Thermal energy

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Content – Forms of energy

Thermal energy refers to the internal energy present in a system by virtue of its temperature.

Temperature could be regarded as a measure of how much thermal energy a substance has. The higher the temperature, the more the molecules are moving and therefore the more kinetic and potential energy the molecules have.

Thermal energy is the combined kinetic energy and potential energy of the particles of a substance. These particles may be electrons, atoms and molecules.

In most substances thermal energy would partly be potential and partly kinetic energy. Kinetic energy by particles vibrating and potential energy by increased separation of particles having mutual force attraction.

The exception being, in ideal monatomic gases with no forces between the particles, where the thermal energy is entirely kinetic energy.

## Heat capcity

The specific heat capacity (c) of a substance is key to determining the thermal energy of the substance.

Specific heat capcity is defined by the amount of heat necessary to increase the temperature of one kilogram (kg) of the substance by one degree.

The specific heat capacity for a substance is not a constant value since it will vary with the actual temperature.

For gases the specific heat capcity is defined for constant volume (cv) and at constant pressure (cp) since the amount of heat needed will be different. More heat is needed to raise the temperature at constant pressure than for constant volume.

The relationship between cp and cv (cp/cv) is defined as k.
For monatomic gases k is 1,66 (eg. He, Ne, etc)
For biatomic gases k is 1,4 (eg, hydrogen H2, nitrogen N2, oxygen O2)
For threeatomic gases k is 1,3 (eg, carbon dioxide CO2)

## Heat transfer

Heat is only transferred or exchanged between systems if there are temperature differences. Heat that flow from a warm to a cold system reduces the thermal energy of the warm system and increases the thermal energy of the cold system. Equilibrium is reached when the systems have the same temperature.

## Formula for thermal energy

Q = mcT

Q = Thermal energy of a substance or a system
M = The mass of the substance or system
C = The specific heat capacity of the substance or system.
T = The absolute temperature of the substance or system
Δt = Temperature difference

In practical terms it is more relevant to calculate/measure the change in thermal energy (ΔQ) since this is related to the ability to do work or work needed.

The formula for change in thermal energy
ΔQ = Q = mcΔt

To cater for the heat capacity at the actual temperatures the formula would be:

$Q = \int_{t_1}^{t_2}mc\Delta t = m\int_{t_1}^{t_2}c\Delta t$

However for practical purposes the average specific heat capacity (cm) is used.

Q = mcm (t2 – t1)