The Second Law of Thermodynamics

Considering you have read the article of the first law of thermodynamics, you saw that the heat can be converted into work and vice versa. There are different statements of the second law of thermodynamics. We start with also known as engine statement (or Kelvin-Plank form) of the second law of thermodynamics. In terms of the conversion of heat into mechanical energy (Kelvin-Plank form) the second law of thermodynamics limits the conversion of heat into mechanical energy. It's a simple but powerful statement of the law of nature about the limitation that no heat engine is capable of converting all heat provided completely into mechanical energy.

The heat supplied to a thermodynamic system is also used to increase the internal energy of the system. The internal energy of the system does not depend on the path of the thermodynamic system but depends on the current state of the system. Take some pieces of paper in your hand and throw them in any direction. They are not ordered in a particular place on the floor instead scattered everywhere which represents the randomness or disorder of the event. All thermodynamic processes always have a tendency towards randomness or disorder of the system. We'll define the term entropy based on the randomness or disorder of a system and define the second law in terms of entropy later. Different statements of the second law ultimately mean the same thing.

Engine Statement of the Second Law of Thermodynamics

To begin we define the engine statement of the second law of thermodynamics based on its limitation to convert heat into mechanical work. It states that no heat engine can convert the absorbed heat from a hot reservoir completely into mechanical work and come back to the original state in which it began. This statement is also called Kelvin-Plank statement of the second law of thermodynamics.

Figure 1 The energy flow diagram showing the energy flow in a heat engine.

The Figure 1 shows an energy flow diagram where the engine takes heat $Q_\text{h}$ from the hot reservoir at temperature $T_\text{h}$ and converts some amount of the absorbed heat into work $W$ and some amount of the absorbed heat $Q_\text{c}$ is thrown to the cold reservoir. It means, the total heat $Q_\text{h}$ absorbed is the sum of the work done by the system and the heat thrown to the cold reservoir that is

\[{Q_h} = W - {Q_c} = W + \left| {{Q_{\rm{c}}}} \right| \tag{1} \label{1}\]

Note that the heat thrown to the cold reservoir flows out of the system of the engine and it is negative. Therefore, $Q_\text{c}$ is already negative and negative sign with $Q_\text{c}$ is used to correct the above expression or you can add the absolute value of $Q_\text{c}$ to work done. The ratio of work done by the engine $W$ to the heat absorbed $Q_\text{h}$ is called the efficiency of the engine denoted by $e$. The efficiency $e$ is always less than unity. From Equation \eqref{1}, $W = {Q_h} + {Q_c}$ and the efficiency is

\[e = \frac{W}{{{Q_{\rm{h}}}}} = \frac{{{Q_h} + {Q_c}}}{{{Q_h}}} = 1 + \frac{{{Q_c}}}{{{Q_h}}} \tag{2} \label{2}\]

Thermodynamics
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