Thermodynamics: Entropy (Class 11 & 12)

NCERT References:

• Class 11: Chapter 12 - Thermodynamics
• Class 12: Chapter 2 - Thermodynamics

Detailed Notes

Thermodynamic Definition of Entropy:

• Entropy (S) is a measure of the randomness or disorder in a thermodynamic system.
• Mathematically, entropy is defined as the change in thermal energy (Q) divided by the absolute temperature (T): $$S = \frac{\Delta Q}{T} \ \ \ \text{(reversible process)}$$
• Entropy has units of joules per kelvin (J/K).

Entropy Change for Various Processes:

• Isothermal Processes: In an isothermal process, the temperature remains constant.

$$S_2 - S_1 = \frac{Q}{T}$$

• Adiabatic Processes: In an adiabatic process, no heat is exchanged with the surroundings.

$$S_2 - S_1 = 0$$

• Isobaric Processes: In an isobaric process, the pressure remains constant.

$$S_2 - S_1 = C_p\ln\frac{T_2}{T_1} - R\ln\frac{V_2}{V_1}$$

• Isochoric Processes: In an isochoric process, the volume remains constant.

$$S_2 - S_1 = C_v\ln\frac{T_2}{T_1}$$

Entropy and Spontaneity:

• Spontaneous processes are those that occur naturally without external intervention.
• Entropy change is directly related to spontaneity. In a spontaneous process, entropy increases.
• The greater the increase in entropy, the more spontaneous the process.

Entropy, Heat, and Temperature:

• Entropy is closely linked to heat and temperature.
• Heat transfer increases the entropy of a system, while work done on the system decreases its entropy.
• At absolute zero (0 Kelvin), the entropy of a pure crystalline substance is zero.

Entropy Generation in Irreversible Processes:

• Real processes are irreversible, meaning there is always some entropy generation.
• Irreversible entropy generation is due to factors such as friction, internal resistance, and mixing of substances.

Second Law of Thermodynamics and Entropy:

• The second law of thermodynamics states that in any closed system, entropy can never decrease over time.
• This means that all natural processes tend to increase the overall entropy of the universe.

The T-S Diagram:

• A temperature-entropy (T-S) diagram is a graphical representation of the changes in temperature and entropy of a system during a thermodynamic process.
• T-S diagrams provide valuable insights into heat transfers, work done, and the spontaneity of processes.

Understanding T-S Diagrams:

• The T-S diagram is constructed with temperature (T) on the y-axis and entropy (S) on the x-axis.
• Each point on the diagram represents the thermodynamic state of the system.

Construction and Interpretation of T-S Diagrams for Different Processes:

• For different thermodynamic processes, the T-S diagram shows specific trends and shapes.
• Isothermal processes appear as horizontal lines, while adiabatic processes are represented by vertical lines.

Areas under the T-S Curve:

• The area under the T-S curve represents the heat transfer (Q) for a reversible process.
• Heat absorbed by the system is represented by a positive area, while heat released is represented by a negative area.

Heat and Work Transfers in T-S Diagrams:

• In a T-S diagram, the work done by the system is represented by the area enclosed by the curve and the horizontal axis.
• Heat transfer is represented by the area between the curve and the vertical axis.

Carnot Cycle and Reversibility on T-S Diagram:

• The Carnot cycle is a theoretical cycle that represents the most efficient way to convert heat into work.
• On a T-S diagram, the Carnot cycle is a rectangle, representing a reversible process.

T-S Diagrams of Various Processes (Isobaric, Isochoric, Isothermal, Adiabatic, etc.):

• T-S diagrams can be constructed for various thermodynamic processes to visualize and analyze their characteristics.
• Each type of process has a specific shape and trend on the T-S diagram.

Applications of T-S Diagrams:

• T-S diagrams find extensive applications in understanding thermodynamic systems and processes.
• They are used to analyze heat transfers, work done, efficiency, and spontaneity.

Analyzing Thermodynamic Systems Using T-S Diagrams:

• T-S diagrams help in analyzing the thermodynamic behavior of systems and their changes during processes.
• By studying the shape, slope, and area under the curve, valuable information can be obtained.

Calculating Entropy Changes and Heat Transfers:

• T-S diagrams provide a graphical method to calculate entropy changes and heat transfers for various processes.
• The area under the curve represents heat transfer, and the change in entropy can be determined from the x-axis.

Efficiency Analysis and Interpretation:

• T-S diagrams can be used to analyze the efficiency of thermodynamic cycles, such as the Carnot cycle.
• By comparing the areas representing heat transfers and work done, the efficiency can be determined.

Refrigeration Cycle on a T-S Diagram:

• T-S diagrams are often used to analyze and optimize refrigeration cycles.
• The shape and areas of the curves provide insights into the heat transfer processes involved.

Heat Pump and T-S Diagram Analysis:

• T-S diagrams are also useful in analyzing and visualizing heat pump cycles.
• By studying the heat transfer processes, the efficiency and performance of heat pumps can be evaluated.