Thermodynamics Notes - Laws, Equations, and Applications

Thermodynamics is the branch of physics that deals with heat, work, and the energy transformations between them. It forms the foundation of understanding energy systems, from engines to refrigerators, and even the universe's fundamental processes.

This article provides detailed notes on thermodynamics, including its laws, key concepts, equations, and applications.

What is Thermodynamics?

Definition: Thermodynamics studies the relationships between heat, work, and energy in physical and chemical systems.

Key Concept: Energy can be transformed from one form to another, but the total energy of an isolated system remains constant.

Basic Terms in Thermodynamics

1. System and Surroundings

• System: The part of the universe under study (e.g., a gas in a cylinder).
• Surroundings: Everything outside the system.

2. Types of Systems

• Open System: Exchanges both matter and energy with its surroundings.
• Closed System: Exchanges only energy, not matter, with its surroundings.
• Isolated System: Exchanges neither matter nor energy with its surroundings.

3. State Variables

Properties that describe the state of a system.

• Examples: Pressure ($P$), Volume ($V$), Temperature ($T$), Internal Energy ($U$).

4. Thermodynamic Processes

Processes that change the state of a system.

• Isothermal: Constant temperature ($\mathrm{\Delta }T=0$).
• Adiabatic: No heat exchange ($Q=0$).
• Isobaric: Constant pressure ($\mathrm{\Delta }P=0$).
• Isochoric: Constant volume ($\mathrm{\Delta }V=0$).

Laws of Thermodynamics

Zeroth Law of Thermodynamics

Statement: If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

Significance: Forms the basis for defining temperature.

First Law of Thermodynamics

Statement: Energy cannot be created or destroyed; it can only change forms.

Mathematical Expression: $$\mathrm{\Delta }U=Q-W$$ Where:

• $\mathrm{\Delta }U$: Change in internal energy.
• $Q$: Heat added to the system.
• $W$: Work done by the system.

Applications:

• Understanding heat engines.
• Analyzing energy conservation in systems.

Second Law of Thermodynamics

Statement: Heat cannot spontaneously flow from a colder body to a hotter body without external work being done.

Key Concepts:

• Entropy ($S$): A measure of the disorder or randomness of a system.
• Heat engines and refrigerators operate within the constraints of this law.

Entropy Change: $$\mathrm{\Delta }S=\frac{Q_{\text{rev}}}{T}$$

Third Law of Thermodynamics

• Statement: As the temperature of a system approaches absolute zero ($0 \, \text{K}$), the entropy of the system approaches a constant minimum value.
• Implication: Absolute zero is unattainable in practice.

Key Thermodynamic Equations

Work Done by a Gas

Isothermal Process:

$$W = nRT \ln\left(\frac{V_f}{V_i}\right)$$

Adiabatic Process:

$$W = \frac{P_iV_i - P_fV_f}{\gamma - 1}$$

Isobaric Process:

$$W = P \Delta V$$

Isochoric Process:

$$W = 0$$

Heat Capacities

Molar Heat Capacity at Constant Volume ($C_V$):

$$C_V = \frac{f}{2}R$$

Where $f$: Degrees of freedom.

Molar Heat Capacity at Constant Pressure ($C_P$):

$$C_P = \frac{f + 2}{2}R$$

Relation Between $C_P$ and $C_V$:

$$C_P - C_V = R$$

Thermodynamic Cycles

Thermodynamic cycles describe processes in engines, refrigerators, and other systems.

1. Carnot Cycle

• Definition: A theoretical cycle that represents the most efficient heat engine.
• Efficiency: $$\eta = 1 - \frac{T_c}{T_h}$$Where $T_h$: Temperature of the hot reservoir, $T_c$: Temperature of the cold reservoir.

2. Otto Cycle

• Used in internal combustion engines.
• Efficiency: $$\eta = 1 - \frac{1}{r^{\gamma - 1}}$$Where $r$: Compression ratio.

3. Refrigerator and Heat Pump

• Coefficient of Performance (COP): $$\text{COP (refrigerator)} = \frac{Q_c}{W}$$$$\text{COP (heat pump)} = \frac{Q_h}{W}$$

Applications of Thermodynamics

Heat Engines:

• Power generation in thermal power plants.
• Working of car engines and jet turbines.

Refrigeration and Air Conditioning:

Cooling systems rely on thermodynamic cycles.

Chemical Reactions:

Enthalpy and entropy changes explain reaction feasibility.

Energy Systems:

Solar panels, fuel cells, and batteries use thermodynamic principles.

Biological Systems:

Metabolic processes are governed by energy transformations.

Problem-Solving Tips

Identify the Process:

Determine if the process is isothermal, adiabatic, isobaric, or isochoric.

Use the Correct Equation:

Apply formulas specific to the process type.

Pay Attention to Units:

• Ensure consistency in units for $P$, $V$, $T$, and $R$.

Understand Energy Conservation:

• Use $\mathrm{\Delta }U=Q-W$ for the first law.

Calculate Efficiency:

Use efficiency formulas for engines and refrigerators.

FAQs About Thermodynamics

What is the significance of entropy?

Entropy measures the disorder of a system and determines the feasibility of processes. Higher entropy indicates greater disorder.

Why is the Carnot cycle ideal?

The Carnot cycle is reversible and represents the maximum efficiency achievable by a heat engine.

How does thermodynamics relate to real-world systems?

Thermodynamics explains energy transformations in engines, refrigerators, power plants, and biological systems.

Can we achieve absolute zero temperature?

No, absolute zero cannot be achieved due to the third law of thermodynamics.

Thermodynamics provides a framework for understanding energy transfer, work, and heat in physical systems. From the laws of thermodynamics to specific processes and cycles, mastering these concepts is essential for solving problems in engineering, physics, and beyond. These comprehensive notes serve as a valuable resource for academic and practical applications of thermodynamics.

Explore related topics:

• Thermal Physics
• Kinetic Theory of Gases
• Calorimetry