The second law of thermodynamics

The second law of thermodynamics states that processes occur in a certain direction, not in any direction. A process does not occur unless it satisfies both the first and the second laws of thermodynamics. Bodies that can absorb or reject finite amounts of heat isothermally are called thermal energy reservoirs of heat reservoirs.

Work can be converted to heat directly, but heat can be converted to work only by some devices called heat engines. The thermal efficiency of a heat engine is defined as

${\eta }_{th}=\frac{W_{net,out}}{Q_H}=1-\frac{Q_L}{Q_H}$

where $W_{net,out}$ is the net work output of the heat engine, $Q_H$

is the amount of heat supplied to the engine, and $Q_L$is the amount of heat rejected by the engine.

Refrigerators and heat pumps are devices that absorb heat from low-temperature media an reject it to higher-temperature ones. The performance of a refrigerator or a heat pump is expressed in terms of the coefficient of performance, which is defined as

$$\begin{gathered} CO{P}_R=\frac{Q_L}{W_{net, in}}=\frac{1}{Q_H/Q_L-1} \\ CO{P}_{HP}=\frac{Q_H}{W_{net, in}}=\frac{1}{1-Q_L/Q_H} \end{gathered}$$

The Kelvin-Planck statement of the second law of thermodynamics states that no heat engine can produce a net amount of work while exchanging heat with a single reservoir only. The Clausius statement of the second law states that no device can transfer heat from a cooler body to a warmer one without leaving an effect on the surroundings.

A process is said to be reversible if both the system and the surroundings can be restored to their original conditions. Any other process is irreversible. The effects such as friction, nonquasi-equilibrium expansion or compression, and heat transfer through a finite temperature difference render a process irreversible and are called irreversibilities.

The Carnot cycle is a reversible cycle that is composed of four reversible processes, two isothermal and two adiabatic. The Carnot principles state that the thermal efficiencies of all reversible heat engines operating between the same two reservoirs. These statements form the basis for establishing a thermodynamic temperature scale related to the heat transfer between a reversible device and the high- and low-temperature reservoirs by

${\left(\frac{Q_H}{Q_L}\right)}_{rev}=\frac{T_H}{T_L}$

Therefore, the $Q_H/Q_L$ratio can be replaced by $T_H/T_L$for

reversible devices, where $T_H and T_L$are the absolute temperature of the high- and low-temperature reservoir, respectively.

A heat engine that operates on the reversible Carnot cycle is called a Carnot heat engine, as well as all other reversible heat engine, is given by

${\eta }_{th,rev}=1-\frac{T_L}{T_H}$

This is the maximum efficiency a heat engine operating between two reservoirs at temperature $T_H and T_L can have.$

The COPs of reversible refrigerators and heat pumps are given in a similar manners as 

$CO{P}_{R,rev}=\frac{1}{T_H/T_L-1}$

and

$CO{P}_{HP,rev}=\frac{1}{1-T_L/T_H}$

Again, these are the highest COPs a refrigerator or a heat pump operating between the temperature limits of $T_H and T_L can have.$