Thermodynamics: Internal Energy

Internal Energy: An Introduction

The internal energy of a system is the total energy stored by the particles that make up the system.
It is the sum of the kinetic energy (due to the particles’ movement) and the potential energy (due to the forces between the particles).
Particles can have several types of kinetic energy including translational, vibrational, and rotational.
Internal energy is an example of a state function as it is independent of the path taken to achieve that state.
It’s important to note that we cannot measure internal energy directly but can only infer changes in internal energy.

Changes in Internal Energy

The change in internal energy (ΔU) of a system can be calculated using the formula ΔU = Q - W, where Q is the heat transferred to the system and W is the work done by the system.
If heat is added to the system or work is done to the system (compressing a gas, for instance), the internal energy of the system increases.
Conversely, if heat is taken away from the system or work is done by the system (expansion of a gas, for instance), the internal energy of the system decreases.
It’s worth noting that this formula is derived from the first law of thermodynamics which states that energy cannot be created or destroyed, only transferred or converted from one form to another.

Internal Energy and Temperature

There is a direct relationship between the internal energy of a system and its temperature.
For an ideal gas, any increase in internal energy comes through an increase in temperature, assuming the volume remains constant.
However, the internal energy is not equivalent to the temperature because it also depends on the quantity of matter (i.e., number of particles).
One must also keep in mind that the internal energy of a system can change even if the temperature remains constant (e.g., during a phase transition).

Specific Heat Capacity

The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of one kilogram of the substance by one degree Celsius.
Specific heat capacities can be used to calculate the heat energy transferred during a temperature change using the equation Q = mcΔT, where Q is the heat energy transferred, m is the mass, c is the specific heat capacity and ΔT is the change in temperature.

Latent Heat

Latent heat is the heat energy involved in a change of state and occurs at constant temperature.
The amount of latent heat energy can be calculated using the formula Q = mL, where Q is the heat energy transferred, m is the mass and L is the specific latent heat of the substance.
There are two types of latent heat: latent heat of fusion (change from solid to liquid or vice versa) and latent heat of vaporisation (change from liquid to gas or vice versa).

The top takeaway: understanding how particles’ kinetic and potential energy contribute to the internal energy of a system is crucial to grasping thermodynamics fundamentals. Practice applying these concepts to real-world examples as much as possible.