# Entropy and the Second Law of Thermodynamics Revision Notes

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13.10Entropy and the Second Law of Thermodynamics

In these revision notes for Entropy and the Second Law of Thermodynamics, we cover the following key points:

• Why the first law of thermodynamics is not sufficient in explaining all thermal-related phenomena?
• What are reversible and irreversible processes?
• What is entropy?
• What are the factors affecting the entropy of a thermodynamic system?
• What happens to the entropy in the universe during a thermal process?
• What does the Second Law of Thermodynamics say?
• What are some equivalent formulations of the Second Law of Thermodynamics?
• What is the operation principle of heat engines?
• How to calculate the efficiency of a heat engine?
• What are Carnot engines and what advantages do they offer compared to the traditional heat engines?
• Why Carnot engines have no practical applications in daily life?

## Entropy and the Second Law of Thermodynamics Revision Notes

Despite its importance in determining the values of heat, work and internal energy, the First law of Thermodynamics does not provide sufficient answers to everything that happens during a thermal process.

By definition, a reversible process is a thermodynamic process that can reverse without leaving any trace in the surroundings. A process can be either reversible or irreversible, i.e. a process that is not reversible, is irreversible. Slow expansion of compression of gases by supplying or taking of heat in small amounts can be considered as an action that produces reversible processes. We can also obtain slow compression by adding small weights on the piston.

In simple words, Entropy represents the degree of disorder in a thermodynamic system. Entropy is related to the temperature of system and the heat supplied to the system. Combining these two factors together, we obtain the equation of entropy S. It is

S = Q/t

where Q is the heat of system and T its temperature.

We are more interested in the change in entropy ΔS rather than in the actual entropy of a thermodynamic system. Therefore, we can write:

∆S = ∆Q/t

The unit of entropy is joule per kelvin [J/K].

The Second Law of Thermodynamics is one of the most important laws in physics. It says:

The total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible.

As a special case, we can say that the total entropy of a system remains constant only in ideal cases, i.e. when the process is completely reversible.

The Second Law of Thermodynamics is expressed in various forms that apparently seem as not related to each other but that are all equivalent. Some of them include:

Entropy of an isolated system either increases or at best, it remains constant during any change in the system.

It is impossible to convert entirely the heat energy supplied to a thermodynamic system into work. This means no heat engine can provide an efficiency of 100 percent, i.e. no perfect machine can exist.

It is impossible for heat to flow by itself from a colder object to a hotter one (Clausius Statement).

Heat engines are devices that operate by converting heat into mechanical energy, i.e. they produce motion from heat energy. Car motors, diesel engines, steam turbines and steam power plants are all examples of heat engines.

Heat engines operate by converting heat into mechanical energy, i.e. they produce motion from heat energy. Car motors, diesel engines, steam turbines and steam power plants are all examples of heat engines.

A heat engine uses a gas at high pressure to push against a piston. For this, it needs a source of thermal energy to heat up the gas inside the cylinder. These thermal energy sources originally are in another form, most commonly as chemical energy of fuels.

In simple terms, a heat engine absorbs heat energy from a source (called "hot reservoir") at high temperature, then it converts part of this energy into useful work and expels the rest outside the system (in the surroundings). Such a medium is at lower temperature than the system and is known as "cold reservoir" or "heat sink".

For continuous operation, a heat engine must operate in cycles, i.e. it must cool down to the initial temperature before starting the new cycle.

We can provide a more formal definition for entropy, which is based on the quantities involved in application of the Second Law of Thermodynamics in thermal engines:

Entropy is a thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.

From experiments, it is proven that the type of engine that produces the maximum efficiency is the "Carnot Engine", named after the famous French scientist Sadi Carnot. A Carnot engine produces a definite reversible cycle which has a maximum possible efficiency between two given heat reservoirs with different temperatures. In other words, a Carnot cycle is the most efficient cycle that can theoretically exist.

A Carnot cycle consists in two adiabatic and two isothermal processes. All these processes are reversible.

For the same difference in temperatures, the Carnot engine is the most efficient among all the other types of engines. However, a Carnot engine is more a theoretical model than a reality.

Thus, we can write

ereal < eCarnot

Two factors decrease the efficiency of a real engine. They are:

1. A real machine does not operate according a Carnot cycle
2. Friction between various parts of the engine decreases further the efficiency

The equation used to find the efficiency in a Carnot engine is

eCarnot = TH - TC/TH × 100%
= TH/TH - TC/TH × 100%
= 1 - TC/TH × 100%

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