Now,

1.27

where η_carnot is the Carnot efficiency of an engine operating between two fixed temperatures. Efficiency of any thermodynamic cycle cannot be more than the Carnot cycle efficiency.

1.28

Hence,

1.29

Thermodynamics Processes

Second law of thermodynamics enables us to divide all the processes into two classes:

1. Reversible or ideal process
2. Irreversible or natural process

A process is reversible if, after the process has been completed, means can be found to restore the system and its elements of its and the surroundings to their respective initial states. Some of the reversible processes are:

Frictionless motion of solids Slow frictionless adiabatic expansion/compression of a gas Slow isothermal compression/expansion of a gas Electrolysis of water Flow of electric current through inductors and capacitors

 Any process, which is not reversible, is irreversible. All natural (spontaneous) processes are irreversible. Some of the irreversible processes are:

Irreversibility due to finite temperature differences between combustion gas and working fluids in a boiler Internal irreversibilities in pipe fittings, bends etc- viscous dissipation Unrestrained expansion-Joule Thomson effect Mixing of two different fluid streams Magnetization of materials exhibiting hysteresis Joulean heat production due to flow of current through a electric conductor

Various processes can be expressed mathematically. The first as well as the second law can be combined together to analysis a thermodynamic system/process. Such mathematical relationships are elaborately discussed in Module 1 - Lecture 6.