Analysis of Second Law & Reversible Cyclic Machines P M V Subbarao Professor Mechanical Engineering Department Methods to Recognize Practicable Good Innovations…..

Kelvin Planks postulate “ It is impossible to construct a heat engine which produces no effect other than the extraction of heat from a single source and the production of an equivalent amount of work” Clausius postulate “ The Clausius statement: It is impossible to construct a heat pump produces no effect other than the transfer of heat from a cooler body to a hotter body. ” Statements of Second Law of Thermodynamics

Discussion of Statements of Second Law Both are negative statements. They cannot be proved. They will remain correct till they are disproved. Violation of Kelvin Planks statement leads to violation of Clasius statement and vice versa. Can a heat engine be reversed to work as heat pump or refrigerator? If yes, what will be the COP of this reversed engine? Can a reversed heat pump perform same as forward engine between same reservoirs?

Reversible Heat Pump First law: W LP = Q LP - Q HP Q HP Q LP W HP HTR (Sink) LTR (Source)  rev = Q HP /W HP W RHP Q RHP Q RLP First law: W RHP = Q RHP - Q RHP

Definition of Reversible Heat Pump A Reversed heat pump works as a Heat Engine. If A Heat Pump & Reversed heat pump are working between same reservoirs,

Consequences of Second Law The performance of a reversed heat pumps is same as a heat engine. The performance of reversed heat engine is same as a heat pump. Heat engine and Reversed heat pump follow Kelvin-Plank statement. Heat pump and Reversed heat engine follow Clausius statement. All reversible heat engines working between same reservoirs should equally perform. It is impossible to construct a reversible heat engine better than another reversible machine working between same reservoirs. All reversible heat pumps working between same reservoirs should equally perform. It is impossible to construct a reversible Heat pump better than another reversible machine working between same reservoirs.

A Compound Reversible Machine Q HP Q LP Q HE E  W net Q HE = Q HP Q LE LTR (Source) HTR (Sink) Q LE = Q LP Both Reversible Pump and Engine having same performance  rev = 1/  rev Perpetual Motion Machine III

Liberal Market & Innovation All innovations will perform equally, if each innovation is a reversible heat engine. All innovations will perform equally, if each innovation is a reversible heat pump. Innovation of reversible machines will lead to innovation of PMM –III. There is no scope for further innovation after first innovation. No need to have many ideas for a given need… What is this PMM-III?

Models for Reversible Machines A Blue Print for Construction of Reversible Machine!!!!

Famous Models for Reversible Machines The Stirling Cycle: Reverend Robert Stirling patented a hot air engine in 1816 called “The Economiser”. The Carnot Cycle :1824 : Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance which includes his description of the "Carnot cycle". The Regenerative Cycle

The Reversible Cycles : Carnot Cycle The first model (1824) for reversible machine is the Carnot cycle. This consists of two reversible isothermal processes and two reversible adiabatic processes. Hence Carnot Cycle is a Reversible Cycle. This mode can be used to construct either a heat engine or a heat pump.

pv Diagram : Gaseous (Single Phase) substance executing a Carnot Cycle 1 – 2 : Reversible Isothermal heat addition 2 – 3 : Reversible Adiabatic Expansion 3 – 4 : Reversible Isothermal Heat Rejection. 4 – 1 : Reversible Adiabatic Compression.

Carnot Gas Engine : Crank-Slider Mechanism

Boiler Condenser LTR Turbine HTR Compressor Carnot Engine using Phase Change Substance

pv Diagram

1 – 2 : Boiler: Isothermal Heating : T 2 = T 1 No work transfer, change in kinetic and potential energies are negligible  Q CV   ssuming a single fluid entering and leaving…

2-3 : Turbine :Reversible Adiabatic Process No heat transfer. Change in kinetic and potential energies are negligible 2 3 T

3 – 4 : Condenser : Isothermal Cooling : T 3 = T 4 No work transfer, change in kinetic and potential energies are negligible  Q CV   ssuming a single fluid entering and leaving…

Compressor : Reversible Adiabatic Compression Process SSSF: Conservation of mass First Law : No heat transfer, change in kinetic and potential energies are negligible  

Analysis of Cycle A Cycles is a Control Mass : Constant Mass Flow Rate First law:  q i =  w i q b +q c = w t +w c w net = q net = h 2 -h 1 + (h 4 -h 1 ) = T high (y 2 -y 1 ) + T low (y 4 -y 1 ) T high (y 2 -y 1 ) = T high  y boiler & T low (y 4 -y 1 ) = T low  y condenser w net = q net = h 2 -h 1 + (h 4 -h 1 ) = T high  y boiler + T low  y condenser q boiler = T high (y 2 -y 1 ) = T high  y boiler

Efficiency of the cycle = net work/heat input  y is a change in a variable of a working fluid. Different working fluid will have different values of  y at same Temperatures. However, the efficiencies of all reversible cycles operating between same reservoirs should have same efficiency!! The magnitude of  y should be same at hot and cold reservoir conditions.

Higher the temperature of heat addition, higher will be the efficiency. Lower the temperature of heat rejection, higher will be the efficiency. Efficiency of a Reversible Engine is independent of work fluid !!!!

The Original Problem To be solved by Carnot What is the maximum work possible from a kg of steam? Is this also independent of substance ?  y is a change in property of a working fluid and depends on substance!!! How to achieve required temperature with a given substance?

The Size of A Carnot Engine What decides the size (capital cost) of an engine? Work done per unit change in volume of a substance. Mean Effective Pressure. A mathematical model for an engine is said to be feasible iff both size and efficiency are reasonable !!!!

The Stirling engine and Stirling cycle

The Stirling Cycle

Ideal Regenerative Cycle      