Internal Energy ($U$ or $E$)
The Energy Content of a System | Thermodynamics
1. Definition & Components
Internal Energy ($U$): The sum of all possible forms of energy present within a system is called its Internal Energy.
It is the storehouse of energy. It includes:
- Translational kinetic energy of molecules.
- Rotational and Vibrational energies.
- Electronic energy (movement of electrons).
- Nuclear energy.
- Potential energy due to intermolecular forces.
Note: The absolute value of $U$ cannot be calculated because it involves unknown quantities like nuclear energy. We only measure the Change in Internal Energy ($\Delta U$).
2. Important Characteristics
- State Function: $\Delta U$ depends only on the initial and final states, not on the path taken. $\Delta U = U_{final} - U_{initial}$.
- Extensive Property: It depends on the quantity of matter (mass/moles) in the system.
- Cyclic Process: For a cyclic process (returns to initial state), $\Delta U = 0$.
3. For Ideal Gases
In an ideal gas, there are no intermolecular forces, so Potential Energy is zero. The internal energy is purely Kinetic Energy.
Joule's Law: The Internal Energy of an ideal gas is a function of Temperature only.
$$ U = f(T) $$
$$ \Delta U = n C_v \Delta T $$
- If $T$ is constant (Isothermal), $\Delta U = 0$ (for ideal gas).
- $C_v$ = Molar heat capacity at constant volume.
4. Relation with First Law
The First Law of Thermodynamics relates Internal Energy, Heat ($q$), and Work ($w$).
$$ \Delta U = q + w $$
Sign Convention (IUPAC):
- $q > 0$: Heat absorbed by system.
- $q < 0$: Heat released by system.
- $w > 0$: Work done on the system (Compression).
- $w < 0$: Work done by the system (Expansion).
5. Calculation in Specific Processes
- Isochoric Process ($V = \text{const}$): Work $w = -P\Delta V = 0$. Therefore, $\Delta U = q_v$ (Heat exchanged at constant volume).
- Adiabatic Process ($q = 0$): $\Delta U = w_{ad}$ (Work done changes internal energy).
- Chemical Reaction: $\Delta U = \Delta H - \Delta n_g RT$.
Practice Quiz
Test your knowledge on Internal Energy.
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