Carnot cycle concept.

CARNOT CYCLE complete concept and questions:
[This concept is useful in GATE, UPSC IES and for INTERVIEW also]
* Carnot cycle consists of  isothermal heat addition and isothermal rejection & isentropic compression and isentropic expansion processes. 

*Efficiency of carnot cycle is ={1-(T1÷T2)}×100
(Here temperature T1, T2 should be in Kelvins. )
* CARNOT cycle efficiency is the maximum efficiency that can be achieved by any engine.
* Carnot cycle is a theoretical cycle only.

Let me explain some example problems:

Q1)  What is the carnot cycle efficiency if it works between 27°c and 327°c? 

Efficiency of carnot cycle ={1-(T1÷T2)}×100
                                 ={1-((27+273)÷(327+273))}×100
                                 ={1-(300÷600)}×100
                                 =50%

Q2) An inventor said he developed an engine which works between temperature limits of 27°c and 327°c and rejects 20% of absorbed heat. Which kind of engine is this? 

Efficiency = (work output /Heat input )×100
                   =[(Qadd-Qrej)/Qadd]×100
                   =[(Q-0.2×Q)/Q]×100
                   =80%

BUT MAXIMUM POSSIBLE EFFICIENCY BETWEEN GIVEN TEMPERATURE LIMITS
 IS 
CARNOT EFFICIENCY = [1-(T1/T2)]×100
                                        = 50%

 So the engine developed by the inventor is impossible.
IMPORTANT POINTS REGARDING CARNOT efficiency:
(very important for competitive exams)

1)actual efficiency < carnot efficiency               
                                   (irreversible engine)
2)actual efficiency = carnot efficiency 
                                   (Reversible engine)
3)actual efficiency >carnot efficiency 
                                   (Impossible engine )

Important facts of CARNOT CYCLE :

*isothermal heat addition and rejection processes are very slow processes. 
*Isentropic compression and expansion processes are very fast processes. 

   SO COMBINATION OF VERY FAST  AND VERY SLOW PROCESSES IS IMPOSSIBLE hence Carnot cycle is impossible. 

    But we can make isothermal process very fast
by working in TWO PHASE REGION. where heat addition will not cause raise in temperature, since in two phase region latent heat is added. 

   However impact force from liquid particles of liquid vapour mixture causes erosion of turbine and compressor blades. So again CARNOT cycle can't  be implemented. 

Date:1/11/2019(update)

Different ways of finding efficiency:
Finding efficiency is very important for GATE AND IES. So here we discussed various ways to calculate efficiency. 

According to the given data efficiency is calculated. 
Example:
1) If Lower and Upper Temperatures (T1, T2) are given then Efficiency =[1-(T1/T2)]×100%
2)if heat input(Q) and work output (W) are given then efficiency = (W/Q)×100%
3) If Heat added(Qadd)and heat rejected(Qrej) are given then efficiency
                                      =[(Qadd-Qrej)/Qadd]×100%
4) if COP of refrigerator is given then efficiency =(1/(1+COPref))×100%
5) If COP of Heat pump is given then efficiency =(1/COP)×100%
(Above efficiency calculation is only for carnot cycle. and efficiency calculation for finite temperature is the toughest, so we will update it very soon  )

[It is the complete knowledge for all competitive exam questions on carnot cycle]

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By RAJKUMAR CLASSES