Thermodynamics: Principles and Applications
Thermodynamics
Introduction: Thermodynamics is a branch of physics that studies the relationships between heat and work. Systems can be classified as open when mass exchange occurs, or closed when the average mass remains constant.
Extensive properties are mass-dependent, while intensive properties are not. Important concepts include thermodynamic variables (pressure, volume, and temperature), which define the thermodynamic state of a system, and functions of state (enthalpy, internal energy, etc.).
A thermodynamic system can be represented by P, V, and T. These variables do not change if the system is in equilibrium, but they will change if the system undergoes a process. These transformations can be represented in a Clapeyron diagram, with P and V as the coordinate axes. Specific types of processes include:
- Isochoric: V = constant
- Isobaric: P = constant
- Isothermal: Constant temperature
Thermodynamic Processes
Processes can be classified as:
- Reversible: The process can return to its initial state.
- Irreversible: Once initiated, the process cannot be interrupted.
Another classification of transformations:
- Cyclic: The initial and final points are the same.
- Open: The beginning and ending points are different.
Work
Work refers to the work done by a force, which is the dot product of the force and the displacement. dW = FdL = PdV. The total work corresponds to the sum of the elemental work. dW = PdV (area in Clapeyron diagrams). Work is positive when the system expands and negative when it contracts. In a Clapeyron diagram, negative work is clockwise, and positive work is counterclockwise.
Heat
A system that is not isolated can exchange energy with its surroundings in the form of heat. A system absorbs heat (+) when dQ > 0 and emits heat (-) when dQ < 0.
First Law of Thermodynamics
Energy is neither created nor destroyed, but transformed. dQ1 – dW1 = dQ2 – dW2. In any thermodynamic transformation, the heat absorbed by a system is spent on doing work and increasing its internal energy. dQ = dW + dU. These quantities are measured in Joules (J) in the SI system, and in ergs in the CGS system.
Second Law of Thermodynamics
A heat engine working in cycles cannot perform work in contact with a single heat reservoir. To perform work, it needs to be in contact with two reservoirs at different temperatures: a hot source and a cold sink.
Efficiency: η = (1 – dQ2/dQ1) = (dQ1 – dQ2) / dQ1 (dQ1 is from the hot source). The efficiency of a thermal engine is always less than unity. To express this principle mathematically, one must understand the concept of entropy. Any thermodynamic transformation has a unique meaning, and the value of entropy increases (ΔS > 0).
Carnot Engine
The Carnot engine is a theoretical engine. Its cycle consists of two isotherms and two adiabatic processes (reversible). Its efficiency is η = (1 – dQ2/dQ1) = (T1 – T2) / T1 (depending on temperature). The work is positive, and the area of the cycle represents the work done. An engine doing the opposite has a coefficient of performance E = dQ2 / dW.
Thermodynamic or Kelvin Scale
The Kelvin scale is a thermodynamic scale (independent of the substance) based on the Carnot cycle.
- 1st postulate: Te – Tf = 100, which corresponds to an efficiency of η100 = (dQe – dQf) / dQe
- 2nd postulate: Te – T = x, with efficiency η = (dQe – dQ) / dQe
Establishing a relationship between efficiency and temperature: [(Te – Tf) / (Te – T)] = [(dQe – dQf) / (dQe – dQ)]