ऊष्मागतिकी के नियम

• Thermodynamics is the study of energy, its transformations, and its relation to matter.
• It is governed by a set of fundamental laws that describe the behavior of energy and matter at a macroscopic level.
• These laws are universal and apply to all physical systems.

Zeroth Law of Thermodynamics

• If two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.
• If A is in thermal equilibrium with C, and B is also in thermal equilibrium with C, then A is in thermal equilibrium with B.
• This law allows for the definition of temperature as a fundamental property that determines whether systems are in thermal equilibrium.
• Thermal equilibrium implies no net heat flow between the systems.

First Law of Thermodynamics

• The first law of thermodynamics is the application of the conservation of energy principle to thermodynamic systems.
• Energy can neither be created nor destroyed, only altered in form.
• The change in internal energy of a system is equal to the net heat added to the system minus the net work done by the system. Mathematically, ΔU = Q - W.
• ΔU represents the change in internal energy of the system.
• Q represents the heat added to the system (positive) or removed from the system (negative).
• W represents the work done by the system (positive) or on the system (negative).
• The first law introduces the concept of internal energy (U), which is the energy associated with the microscopic components of a system.
• Internal energy is a state function, meaning its value depends only on the current state of the system, not on how that state was reached.

Second Law of Thermodynamics

• The second law of thermodynamics introduces the concept of entropy (S) and dictates the direction of natural processes.
• It states that the total entropy of an isolated system can only increase over time or remain constant in ideal cases.
• Entropy is a measure of the disorder or randomness of a system.
• Processes that increase entropy are spontaneous, meaning they occur naturally without external intervention.
• The second law can be stated in several equivalent ways:
  • Heat cannot spontaneously flow from a colder body to a hotter body without external work being performed on the system.
  • It is impossible to convert heat completely into work in a cyclic process without transferring some energy to a colder reservoir (Kelvin-Planck statement).
  • The entropy of an isolated system will increase to a maximum value (entropy increases in irreversible processes).
• The change in entropy (ΔS) for a reversible process is given by ΔS = Q/T, where Q is the heat transferred and T is the absolute temperature.

Third Law of Thermodynamics

• The third law of thermodynamics states that the entropy of a perfect crystal at absolute zero temperature (0 K) is zero.
• As the temperature approaches absolute zero, the entropy of a system approaches a minimum or zero value.
• This law provides a reference point for determining the absolute entropy of a substance.
• It implies that it is impossible to reach absolute zero in a finite number of steps.

Thermodynamic Processes

• Thermodynamic processes describe how a system changes from one state to another.
• Several common types of processes are:
  • Isothermal process: Occurs at constant temperature (T = constant).
  • Isobaric process: Occurs at constant pressure (P = constant).
  • Isochoric process: Occurs at constant volume (V = constant). Also known as isovolumetric.
  • Adiabatic process: Occurs without heat transfer (Q = 0).

Isothermal Process

• Temperature remains constant during the process.
• Involves heat transfer to maintain constant temperature.
• For an ideal gas, the work done during an isothermal process is W = nRT ln(V₂/V₁), where n is the number of moles, R is the ideal gas constant, T is the absolute temperature, and V₁ and V₂ are the initial and final volumes, respectively.

Isobaric Process

• Pressure remains constant during the process.
• Work done during an isobaric process is W = P(V₂ - V₁).
• Heat transfer results in a change in internal energy and work done.

Isochoric Process (Isovolumetric)

• Volume remains constant during the process.
• Since there is no change in volume, no work is done by or on the system (W = 0).
• All heat transfer goes into changing the internal energy of the system (ΔU = Q).

Adiabatic Process

• No heat is transferred into or out of the system (Q = 0).
• Changes in internal energy are due solely to work done.
• Adiabatic processes are characterized by the equation PV^γ = constant, where γ (gamma) is the adiabatic index (ratio of specific heats, Cp/Cv).
• Work done during an adiabatic process is W = (P₂V₂ - P₁V₁) / (1 - γ).

Heat Engines

• A heat engine is a device that converts thermal energy into mechanical work.
• It operates in a cyclic process, taking heat from a hot reservoir, converting part of it into work, and rejecting the remaining heat to a cold reservoir.
• The efficiency (η) of a heat engine is defined as the ratio of the work done to the heat input: η = W/Q_H = 1 - (Q_C/Q_H), where Q_H is the heat from the hot reservoir and Q_C is the heat rejected to the cold reservoir.
• The Carnot engine is a theoretical heat engine that operates on the Carnot cycle, which consists of two isothermal processes and two adiabatic processes.
• The Carnot engine has the maximum possible efficiency for any heat engine operating between two given temperatures: η_Carnot = 1 - (T_C/T_H), where T_H and T_C are the absolute temperatures of the hot and cold reservoirs, respectively.

Refrigerators and Heat Pumps

• Refrigerators and heat pumps are devices that transfer heat from a cold reservoir to a hot reservoir, requiring external work to be done.
• They operate in a cycle, using a refrigerant to absorb heat from the cold reservoir and release heat to the hot reservoir.
• The performance of a refrigerator is measured by its coefficient of performance (COP), defined as the ratio of the heat removed from the cold reservoir to the work input: COP_refrigerator = Q_C/W.
• The performance of a heat pump is also measured by its coefficient of performance (COP), defined as the ratio of the heat delivered to the hot reservoir to the work input: COP_heat_pump = Q_H/W.
• For an ideal refrigerator or heat pump operating on the Carnot cycle, COP_refrigerator = T_C / (T_H - T_C) and COP_heat_pump = T_H / (T_H - T_C).

Entropy and Irreversibility

• Irreversible processes are processes that cannot be reversed without leaving a change in the surroundings.
• Examples include friction, heat transfer across a finite temperature difference, and mixing of gases.
• Irreversible processes always increase the total entropy of the system and its surroundings.
• The increase in entropy is a measure of the energy that is no longer available to do work.
• For any real process, the total entropy change (ΔS_total) is always greater than or equal to zero: ΔS_total ≥ 0.
• Reversible processes are idealizations that occur infinitely slowly and without any dissipative effects (e.g., friction).
• In a reversible process, the total entropy change is zero: ΔS_total = 0.