# The Second Law of Thermodynamics

The second law of thermodynamics tells us that the total heat absorbed can not be completely converted to mechanical work. It means there is always some heat that is wasted (in practical sense) or transferred to the surroundings (in Physical sense).

It imposes a limitation in the nature we are all familiar with. Although there are different forms of the same statement, they ultimately conclude to the one limitation of nature that in any cyclic process, the conversion of work to energy and the reverse can not be done with 100% efficiency.

In 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 work.

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.

THE SECOND LAW OF THERMODYNAMICS: No heat engine can convert all the absorbed heat from a hot reservoir completely into mechanical work.

This statement is also called Kelvin-Plank statement of the second law of thermodynamics.

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

$e = \frac{W}{{{Q_{\rm{h}}}}} = \frac{{{Q_h} + {Q_c}}}{{{Q_h}}} = 1 + \frac{Q_c}{Q_h} = 1 - \frac{|Q_c|}{Q_h} \tag{2} \label{2}$

The above equation shows that the efficiency of any heat engine can never be equal to 1. Because efficiency 1 means 100% efficient engine which can never happen in the nature. The heat $Q_c$ is transferred to the surroundings such as increasing the air temperature.