In thermodynamics, the internal energy (U) of a system refers to the total energy it possesses due to the motion and interactions of its particles at the microscopic level. It is not a quantity of energy that can be observed directly, but is manifested through changes in the state of the system, such as temperature variations or phase changes.
Every substance contains internal energy, even if it appears to be doing nothing. A block of metal, a glass of water, or the air in a room all have internal energy because their atoms and molecules are constantly moving and interacting with each other.
Internal energy formula
The internal energy of a system can change in two ways:
- By providing or extracting heat (Q) , that is, by transferring thermal energy due to a temperature difference with the environment.
- By doing work (W) on the system or allowing it to do work on the surroundings , for example, by compressing a gas in a cylinder or allowing it to expand.
The first law of thermodynamics, which is a formulation of the principle of conservation of energy, expresses this relationship as follows:
\[ \Delta U = Q - W \]
This means that any change in the internal energy (\( \Delta U \)) of a system is the result of the energy it receives in the form of heat minus the work it does on the surroundings.
If the system is isolated, i.e. it does not exchange heat or work with the outside, its internal energy remains constant. This occurs, for example, in a perfectly sealed thermos that prevents heat loss.
Properties of internal energy
Internal energy has some key characteristics:
- It is a state function , meaning that its value depends only on the current state of the system (its temperature, pressure, volume, and chemical composition) and not on how it got to that state.
- It is an extensive property , that is, its magnitude depends on the amount of matter in the system. A system with twice the mass will have twice the internal energy.
- In many systems, internal energy is difficult to measure directly, but its variations can be calculated by measuring heat and work flows.
Units of measurement
In the International System (SI), internal energy is measured in joules (J).
To describe internal energy as a function of the amount of matter, intensive properties can be defined:
- Specific internal energy (\(u\)): It is the internal energy per unit of mass (J/kg).
- Molar internal energy (\(U_m\)): It is the internal energy per mole of substance (J/mol).
Microscopic explanation of internal energy
If we analyze internal energy at a microscopic level, we will see that it has two fundamental contributions:
Internal kinetic energy
Internal kinetic energy refers to the motion of the particles that make up a system.
In gases, molecules are in constant random motion, moving, rotating and vibrating at high speeds. This movement generates a large amount of kinetic energy, which directly depends on the temperature of the system: the higher the temperature, the greater the kinetic energy of the molecules.
In liquids and solids, although the molecules do not move as freely as in gases, they still vibrate around fixed positions due to intermolecular forces.
The temperature of these systems is also related to the internal kinetic energy, but in this case it is mainly due to the vibrational motion of the molecules.
Internal potential energy
Internal potential energy is associated with the interactions between the particles of a system.
In solids and liquids, molecules exert both attractive and repulsive forces on each other. These interactions contribute to the internal potential energy of the system.
During phase changes, such as the evaporation of a liquid or the melting of a solid, internal potential energy plays a crucial role. Although the temperature of the system may remain constant during these processes, energy is used to break intermolecular bonds or overcome the forces holding molecules together in their previous phase.
This phenomenon occurs without any increase or decrease in temperature, since all the energy is used to change the structure of the material instead of increasing the movement of the molecules.
Internal energy in ideal gases
To simplify the study of thermodynamic systems, the ideal gas model is used, which is a useful approximation in many situations.
An ideal gas is defined as a gas whose particles:
- They do not have their own volume, that is, they are considered points without size.
- They do not exert intermolecular forces, except when they collide with each other (perfectly elastic collisions).
In an ideal gas, the internal energy depends only on temperature and not on pressure or volume. This is because the only form of internal energy in an ideal gas is the translational kinetic energy of its molecules.
In this case, the total internal energy is given by the expression:
\[ U = n C_v T \]
where:
- \( n \) is the number of moles of the gas.
- \( C_v \) is the heat capacity at constant volume.
- \( T \) is the temperature in kelvin.
For a monatomic ideal gas , where the only forms of energy are translational, the following is true:
\[ U = \frac{3}{2} n RT \]
where R is the gas constant.
If the gas is diatomic or polyatomic, there are additional contributions from molecular rotation and vibration, which makes its internal energy higher.
How internal energy is measured
The total internal energy of a system cannot be measured directly, since it includes all the energy of the particles at the microscopic level. However, we can measure its variation ( \( \Delta U \)), which is what is really relevant in thermodynamic processes.
To determine a change in internal energy, one can measure:
- The heat transferred (Q) and the work done (W) in a process.
- Temperature changes , using calorimeters that allow determining the heat absorbed or released.
- Chemical reactions and changes of state , since during these processes the internal energy varies.
For example, in an exothermic chemical reaction, the internal energy decreases because part of it is released as heat. In an endothermic reaction, the opposite occurs: the system absorbs energy from the surroundings and its internal energy increases.
The change in internal energy of a thermodynamic system
Changes in physical state (fusion, evaporation, sublimation, etc.) involve variations in internal energy. During these processes:
- The temperature remains constant , but the internal energy changes due to the alteration in intermolecular forces.
- In evaporation , the molecules absorb heat to overcome the cohesive forces of the liquid and pass to the gaseous state.
- In condensation , the opposite occurs: molecules release energy when they change from gas to liquid.