# 5.1.5 Internal Energy

## Internal Energy

• Energy can be classified into two forms: kinetic or electrostatic potential energy
• The molecules of all substances contain both kinetic and electrostatic potential energies
• Kinetic energy is determined by the speed and mass of the molecules and gives the material its temperature
• Electrostatic potential energy is due to the separation between the molecules and their position within the structure

• The amount of kinetic and electrostatic potential energy a substance contains depends on its phase of matter (solid, liquid or gas)
• This is known as internal energy

• The internal energy of a substance is defined as:

The sum of the randomly distributed kinetic and potential energies of atoms or molecules within a substance

• The symbol for internal energy is U, with units of Joules (J)
• Particles are randomly distributed, meaning they all have different speeds and the separation between each molecule varies
• The internal energy of a system is determined by:
• Temperature
• Higher temperature means greater kinetic energy
• Lower temperature means less kinetic energy
• The random motion of molecules
• The phase of matter: gases have the highest internal energy, solids have the lowest
• Intermolecular forces between the particles
• Stronger intermolecular forces mean higher potential energy
• Weaker intermolecular forces mean lower potential energy
• The strength of the intermolecular forces is linked to the phase (solid, liquid, gas) of the substance

• The internal energy of a system increases by:
• Doing work on it

• The internal energy of a system decreases by:
• Losing heat to its surroundings
• Changing phase from a gas to liquid or liquid to solid

#### Exam Tip

Always remember internal energy is made up of both the kinetic and electrostatic potential energy of the particles in a substance.

## Absolute Zero

• On the thermodynamic (Kelvin) temperature scale, absolute zero is defined as:

The lowest temperature possible. Equal to 0 K or -273.15 °C

• It is not possible to have a temperature lower than 0 K
• This means a temperature in Kelvin will never be a negative value

• Absolute zero is defined as:

The temperature at which the molecules in a substance have zero kinetic energy

• This means for a system at 0 K, it is not possible to remove any more energy from it
• Even in space, the temperature is roughly 2.7 K, just above absolute zero

## Internal Energy and Temperature

• When a substance is heated, its internal energy (sometimes referred to as thermal energy or heat) increases
• As a substance’s internal energy increases, so will its temperature
• The higher the temperature of a substance, the more internal energy it possesses

As the temperature of a substance is increased, the total energy of the molecules (the internal energy) increases

• Since temperature is a measure of the average kinetic energy of the molecules, only an increase in the average kinetic energy of the molecules will result in an increase in temperature of the substance
• Due to thermal expansion, when the temperature of a substance increases, the potential energy of the molecules also increases
• Temperature and internal energy are directly proportional to each other
• A decrease in temperature will result in a proportional decrease in internal energy

ΔU ΔT

• Where:
• ΔU = change in internal energy (J)
• ΔT = change in temperature (K)

#### Worked example

A student suggests that when an ideal gas is heated from 50 oC to 150 oC, the internal energy of the gas is trebled.

State and explain whether the student’s suggestion is correct.

Step 1: State the relationship between internal energy and temperature

• The internal energy of an ideal gas is directly proportional to its temperature, when the temperature is in Kelvin

ΔU  ΔT

Step 2: Determine whether the change in temperature is in Kelvin

50 oC + 273.15 = 323.15 K

150 oC + 273.15 = 423.15 K

Step 3: Calculate the ratio between the two temperatures

Step 4: State a conclusion

• The temperature change, in Kelvin, does not treble
• Since ΔU ∝ ΔT, the internal energy also does not treble
• Therefore, the student's conclusion is incorrect

#### Exam Tip

Remember that a change in internal energy does not necessarily correspond to a change in temperature.

• A change in the average kinetic energy of the molecules corresponds to a change in temperature
• A change in the average electrostatic potential energy of the molecules does not affect temperature

## Internal Energy and Phase Change

• A phase change is another way of saying a change of state
• The states of matter are solid, liquid and gas
• When a substance reaches a certain temperature, the kinetic energy of the molecules will stop increasing and the energy will go into increasing its electrostatic potential energy instead
• This breaks the bonds between the molecules, causing them to move further apart and
• This leads to a change of phase
• For example, liquid to gas
• When a substance changes its state from solid to liquid, or liquid to gas:
• The electrostatic potential energy of the molecules increases,
• The bonds between molecules break and the molecules move further apart
• The kinetic energy remains the same, meaning that the temperature will remain the same, even though the substance is still being heated

• When a substance changes its state from gas to liquid, or liquid to solid:
• The electrostatic potential energy of the molecules decreases,
• Bonds form between molecules and the molecules move closer together
• The kinetic energy remains the same, meaning that the temperature will remain the same, even though the substance is still being cooled

An increase in internal energy from heating can cause a change of state

• In different phases the atoms or molecules of a substance have different electrostatic potential energies
• Solid: The electrostatic forces between atoms are very large, so electrostatic potential energy has a large negative value
• It is negative because it requires a large amount of energy to break apart the bonds between the atoms
• Liquid: The electrostatic forces between atoms are small but present, so electrostatic potential energy has a small negative value
• Gas: The electrostatic forces between atoms are negligible, so the electrostatic potential energy is zero

#### Exam Tip

Remember that whilst a substance changes phase it does so at a constant temperature.

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