*THERMODYNAMIC CYCLES

THERMODYNAMIC CYCLES

(WITH SEQUENCE OF THERMODYNAMIC PROCESSES)

 A Thermodynamic Cycle consists of thermodynamic processes in series such that system returns to its initial starting point.

(a)    POWER CYCLES (HEAT ENGINE CYCLES) WITH EXTERNAL COMBUSTION

Cycle Process 1—2(compression) Process 2—3(heat addition) Process 3—4(Expansion) Process 4—1(Heat rejection) Remarks
CARNOT CYCLE ISENTROPIC ISOTHERMAL ISENTROPIC ISOTHERMAL IDEAL HEAT ENGINE CYCLE
BELL COLEMAN CYCLE ADIABATIC ISOBARIC ADIABATIC ISOBARIC REVERSED BRAYTON CYCLE
ERICSSON  CYCLE ISOTHERMAL ISOBARIC ISOTHERMAL ISOBARIC  
RANKINE CYCLE ADIABATIC ISOBARIC ADIABATIC ISOBARIC USED IN STEAM ENGINES
STIRRLING CYCLE ISOTHERMAL ISOCHORIC ISOTHERMAL ISOCHORIC USED IN STIRLING ENGINE

 

(b)   POWER CYCLES (HEAT ENGINE CYCLES) WITH INTERNAL COMBUSTION

BRAYTON CYCLE ADIABATIC ISOBARIC ADIABATIC ISOBARIC USED IN JET ENGINES 
DIESEL CYCLE ADIABATIC ISOBARIC ADIABATIC ISOCHORIC USED IN DIESEL ENGINES
OTTO CYCLE ADIABATIC ISOCHORIC ADIABATIC ISOCHORIC USED IN PETROL AND GAS ENGINES

 

© POWER CONSUMPTION CYCLES (REFRIGERATION AND AIR CONDITIONING CYCLES)

CYCLE COMPRESSION HEAT REJECTION EXPANSIN HEAT ABSORPTION REMARKS

 

VAPOR COMPRESSION REFRIGERATION CYCLE ADIABATIC ISOBARIC(ISOTHERMAL) ISENTHALPIC ISOBARIC(ISOTHERMAL) REVERSED RANKINE CYCLE
VAPOR ABSORPTION REFRIGERATION CYCLE ADIABATIC ISOBARIC (ISOTHERMAL) ISENTHALPIC ISOBARIC(ISOTHERMAL) REVERSED RANKINE CYCLE
GAS REFRIGERATION CYCLE ADIABATIC ISOBARIC (NON-ISOTHERMAL) ADIABATIC ISOBARIC(NON -ISOTHERMAL) REVERSED BRAYTON CYCLE

 

 

Clausius Inequality

A cycle with one or more irreversible processes will have efficiency less than that of Carnot cycle working between the same temperature limits. This may be due to lesser heat input at high temperature or more heat rejection at lower temperature. Mathematically it can be expressed as Clausius inequality as given below:

∮dQ/T≤0

But ds = dQ/T

The equal sign is applicable only to the ideal cycle (Carnot cycle). In this, integral is equal to net change in entropy in one complete cycle. Therefore change of entropy is zero in the most efficient cycle. This inequality is applicable to all heat engines in actual practice.

Prove of Clausius Inequality Theorem

∮dQ/T ≤0

Proof

For an heat engine
η  = ((Heat supplied at high temp–Heat rejected at low temp))/(Heat supplied at high temp)

= (QH — QL) / QH

For a reversible cycle

η = (TH — TL) / TH

∴  (QH — QL) / QH  = (TH — TL) / TH

1– QL/QH = 1 — TL/ TH

 

 QL/QH = TL/ TH

QL/ TL = QH/ TH

Clausius theorem in the integrated form around a reversible cycle becomes

∮dQ/T=0

For a real cycle with an irreversible process, its efficiency will be less than that of a reversible cycle. Therefore the equality sign comes into existance and it becomes Clausius inequality.

∮dQ/T< 0