# Kelvin-Plank Statement of Second Law of Thermodynamics

6.3.1 Statement

Kelvin-Plank states, “It is impossible to construct an engine working in a cycle whose sole effect is the conversion of all the heat energy supplied to it by a source into an equivalent amount of work”.

6.3.2 Explanation

Heat Q1 is given to the system, the system does some work WE. To bring back to original position of the piston W c work is done on the system as a result Q2 amount of heat is rejected from the system.

Thus                                        Q net= Q1-Q2

W net= WE-We

Σ Q cycle = Σ W cycle

From first law, cycle or O net = W m.

Q1 – Q2 = WE-WC

Fig. 6.4 shows a heat engine cycle

Process 1 – 2 = Q1 heat is added from furnace to boiler

Process 2-3 = WT work is done by Turbine.

Process 3- 4 = Q2 heat is rejected to sea, river or atmosphere.

Process 4 – 1 = W p work is done on the pump.

Thus the cycle completes.

Q1 – Q2 = W r – WP.

6.3.3 Heat Engine

Heat engine is a device which works in a complete cycle and converts heat to work. Thus

(W r – W p) (Ref Fig. 6.4) and Q1 are of primary interest for heat engine. The efficiency of heat engine is defined as

= W net /Q1 = WT – WP / Q1 = Q1 – Q2 / Q1 = 1-Q2 / Q1

This efficiency is termed as thermal efficiency of a heat engine cycle.

6.3.4 Thermal and Mechanical Energy Reservoirs

A thermal energy reservoir (TER) is a body with a very large heat capacity to which, and from which, heat can be transferred without any change in its temperature  thermodynamic property). Higher temperature body is written as TERH and lower temperature body is written as TERL. If heat is transferred from it, then it is known as heat source or simply source. If heat is transferred to it, then it is considered as a heat sink or simply sink. Heat reservoirs are characterised by its temperature. A mechanical energy reservoir (MER) is a large body enclosed by an adiabatic impermeable wall capable of storing work as potential energy (such as wound spring) or K.E. (such as rotating flywheel). An MER performs quasi statically.

Fig. 6.5 shows a cyclic heat engine (C.H.E). It takes Q1 heat from the source and rejects Q2 heat to the sink. It also performs work W net.

C.H.E. = Cyclic heat engine.

6.3.5 Perpetual Motion Machine of the Second Kind ( PMM 2)

PMM 2 is a machine which takes heat from a single source and converts to equal amount of work as its sole effect. PMM 2 is impossible according to Kelvin-Plank’s statement of the second law of thermodynamics.