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Second Law of Thermodynamics
The Second Law of Thermodynamics states that thermodynamic processes occur spontaneously only in one direction, from a state of higher energy to lower energy. It introduces the concept of irreversibility and helps predict the direction of natural processes. This law, combined with the First Law, is needed to determine the final equilibrium state of a system.
Clausius Statement of the 2nd Law
It is impossible to construct a system that allows heat to flow from a cooler body to a hotter body without external work. This means heat naturally flows from high to low temperature unless work is applied.
Kelvin-Planck Statement of the 2nd Law
It is impossible for any cyclic process to convert heat energy entirely into work without losses. In other words, no heat engine operating between a heat source and sink can be 100% efficient.
Reversible Process
A theoretical process that can be reversed without leaving any change in the system or surroundings. It represents an idealized limit, as actual processes are always accompanied by irreversibilities like friction or heat transfer across a finite temperature difference.
Irreversible Process
A real-life process where energy is lost due to factors like friction, unrestrained expansion, chemical reactions, or mixing. Such processes cannot return both the system and surroundings to their original states.
Thermal Reservoir
A hypothetical large system that maintains a constant temperature even as it absorbs or rejects heat. Examples include the ocean, atmosphere, or a large furnace.
Thermal Efficiency (η)
A measure of how efficiently a heat engine converts heat into work. For a cyclic process: η = 1 - (Q_C/Q_H), where Q_H is heat added from the hot reservoir, and Q_C is heat rejected to the cold reservoir. Efficiency is always less than 100%.
Coefficient of Performance (COP)
For refrigeration cycles, the COP measures how effectively heat is removed: COP_refrigeration = Q_C/W_cycle, where Q_C is the heat extracted from the cold space. For heat pumps, the COP measures heating performance: COP_heat pump = Q_H/W_cycle, where Q_H is the heat delivered to the hot space.
Carnot Cycle
An ideal thermodynamic cycle composed of two reversible isothermal processes (constant temperature) and two reversible adiabatic processes (no heat transfer). Its efficiency depends only on the absolute temperatures of the hot (T_H) and cold (T_C) reservoirs: η = 1 - (T_C/T_H). This cycle sets the theoretical upper limit of efficiency for any heat engine.
Clausius Inequality
For any cyclic process, the integral of δQ/T over the cycle is less than or equal to zero: ∮(δQ/T) ≤ 0. Equality holds for reversible cycles, while irreversibilities make it less than zero. It explains why entropy increases in real processes.
Maximum Efficiency
For a reversible heat engine operating between two reservoirs, the maximum efficiency is η_max = 1 - (T_C/T_H), where T_H is the absolute temperature of the hot reservoir, and T_C is the absolute temperature of the cold reservoir. Efficiency increases with a larger temperature difference.
Irreversibilities
These are energy losses due to non-idealities in a process. Examples include: 1) Friction, which converts useful mechanical energy into heat, 2) Heat transfer across a temperature gradient, causing energy dissipation, 3) Unrestrained expansion of gases, leading to loss of work potential, 4) Chemical reactions that generate heat and disorder, 5) Mixing of substances at different states or compositions.
