CARNOT AND REVERSED CARNOT CYCLE CLASS NOTES FOR MECHANICAL ENGINEERING

CARNOT AND REVERSED

CARNOT CYCLES CLASS NOTES

FOR MECHANICAL

ENGINEERING

This cycle consists of reversible

processes. All processes in nature

are irreversible. Carnot cycle

is not achievable. It is a power

producing cycle. Reversed Carnot cycle is a

power consuming cycle. Carnot cycle has

alternately isentropic and isothermal

processes.

  1. Introduction

Carnot cycle is a theoretical thermodynamic cycle (heat engine cycle). It is an ideal thermodynamic cycle consisting of four reversible processes. This is the most efficient cycle for converting thermal energy into work. It creates cooling in the reversed form. It works as a refrigerator in summer. This works as a heat pump in winter. Nicolas Leonard Saudi Carnot found it in 1824.

A system passes through a series of different states.  It comes to its initial state. It becomes a thermodynamic cycle. A cycle if produces work, it acts as a power cycle. Carnot cycle is only theoretical. It is not achievable in actual practice. All processes are reversible.

  1. Carnot Cycle Processes

(a)  Isothermal Reversible expansion at high temperature, TH (isothermal heat addition)
(b) Reversible adiabatic ( Isentropic) expansion to obtain work
(c)Isothermal Reversible  compression at low temperature, TL (isothermal heat rejected).
(d) Reversible adiabatic (Isentropic) compression requiring work input

  1. Carnot Cycle on Temperature Entropy Chart

     Best understanding of this cycle is on a temperature entropy chart. It will consist of two horizontal lines. One corresponds to  constant high temperature. Other corresponds to constant low temperature.  There are two vertical lines of constant entropy. Compare all other cycles with Carnot cycle on this chart.

  2. Carnot cycle efficiency

η = (TH — TL) / TH
A steam engine (heat engine) working on Rankine cycle is the close to Carnot cycle. There is little irreversibility in it.

  1. Application of Second Law of Thermodynamics to Carnot Cycle

Second law of thermodynamics (Planck statement) puts a limit on a heat engine to convert heat into work. It puts a limit on the efficiency of the heat engine. To achieve the highest efficiency, the processes must be reversible. All processes in nature are ir-reversible.  This cycle is far away from reality. Carnot Cycle is just a theoretical cycle. It is not achievable fully in actual practice. It has complete reversible processes. These are not achievable.

REVERSED CARNOT CYCLE

Reverse Carnot cycle is reverse of Carnot Cycle. It is also an ideal cycle. This cycle consists of four processes in the sequence i.e. isothermal, isentropic, isothermal and isentropic.  An isothermal process has to be very very slow. An isentropic process has to be very very fast. So the sequence of processes will be very slow, very fast, very slow and very fast. This alternate combination in actual practice is not possible. Carnot cycle is a heat engine cycle (power producing cycle). Reversed Carnot cycle is a refrigeration cycle (power consuming cycle). In any refrigeration cycle

input is Work/motion/electricity

output is cooling in summer OR Output is heating in winter

Efficiency of Reversed Carnot Cycle

=Cooling effect/ Work Input

= TL /(Th-TL)

Efficiency is greater than 1. Hence, in a Reversed Carnot Cycle, we do not talk of efficiency . We talk about coefficient of performance (COP).

COP   = COOLING EFFECT/WORK INPUT and COP >1

 LIMITATIONS OF REVERSED CARNOT CYCLE

Isothermal process is possible if it is very slow and

isentropic process is possible if it very fast.

This alternate combination of very fast, very slow, very fast and very slow is not possible. It is non achievable in actual practice. Thus, these are the limitations of this cycle.

 COEFFICIENT OF PERFORMANCE OF A REVERSED CARNOT CYCLE

COP reverse  Carnot  is a measure of refrigeration efficiency of a refrigeration system working on reverse Carnot cycle.

Coefficient of performance = cooling effect/work input= output/input and COP >1

It depends on two key absolute temperatures only. Evaporator (Low) absolute temperature Te (or TL) and condenser (high) absolute temperature T( or TH)

Theoretical COP = COP Reverse Carnot   =  Te / (Tc – Te)= TL/(TH –TL)

This COP Reverse Carnot is independent of the followings.

(i) The type of compressor/condenser/expansion device/evaporator used

(ii) Properties of the working fluid.

  REVERSE CARNOT CYCLE IN ACTUAL PRACTICE

The alternatives for this are

(i) Use two isothermal phase change processes

(ii) Also, use two high speed devices like a compressor and a turbine to achieve two isentropic processes

The four processes are in the following sequence in a Refrigeration or Air conditioning machine.

Iso-thermal phase change process                        (evaporation)

High speed compressor                                        (Compression)

Again Iso-thermal phase change process            (condensation)

High speed turbine for expansion                       (Expansion)

Refrigerator and heat pump work on reverse Carnot Cycle

ηheat engine = (TH—TL)/TL           TL =  evaporation temperature(low)

Refrigerator COP= /(TH–TL)   TH=condensation temperature (high)

Heat Pump COP  =T/(TH–TL)

COP (heat Pump)= COP(cooling machine) + 1

No machine can work on reverse Carnot cycle. A machine can work on modified cycle only.

VARIOUS MACHINES WORKING ON MODIFIED REVERSE CARNOT CYCLE

EXAMPLES OF COOLING MACHINES

Fridge

Water Cooler

Window Air Conditioner

Split Air Conditioner

Cold storage plant

Ice Plant

Air conditioning plant in a theater, Hospital, library, computer center, Mall, Multistory residential complex

Heat pumps  are machines which heat the room (hall) in winter.

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