 isothermal and isochoric processes are realized.
So my questions are:

Is this a contradiction to Carnot's theorem that the efficiency $\eta_\text{C} = 1 - T_1/T_2$ is the same for all reversible heat engines between two heat baths?
Is this cycle reversible?
Is there a way to say whether a process is reversible or irreversible only with a figure like the one above?

A:

Revamped Answer. 2017-07-01
There is no contradiction because your analysis only includes what happens to the gaseous working substance in the Stirling engine, and it neglects a crucial component of the engine called the regenerator.  If the regenerator is not included as a component of the engine when we perform the efficiency analysis, then we don't have a device that qualifies as a heat engine operating between two temperatures, and we therefore shouldn't expect it to abide by Carnot's Theorem as I stated in the original version of this answer.
However, if we properly take account of the regenerator, then we find that the efficiency of the engine is the Carnot efficiency.
Of course the whole analysis here is an idealized one in which we assume, for example, that there are no energy losses due to friction in the engine's components.
Details.
A stirling engine is more complex than the $P$-$V$ diagram drawn in the question statement seems to indicate.  If we conceptually reduce the engine to its simplest form, it contains two fundamental components:

A gaseous working substance.  This is the part of the engine whose thermodynamic state travels along the curve in the $P$-$V$ diagram.
A regenerator.  This part of the engine absorbs and stores the energy given up by the gaseous working substance by heat transfer during the process $2\to 3$ and then returns that same energy to the gaseous working substance during the process $4\to 1$. 

The crucial point is that when the regenerator is included, there is no net heat transfer into or out of the engine during the processes $2\to 3$ and $4\to 1$.  The energy that leaves the gaseous working substance during the process $2\to 3$ by heat transfer is stored in the regenerator, and that heat is then given back up to the working substance during process $4\to 1$.  No heat is transferred between the engine and its surroundings during these legs of the cycle
isothermal and isochoric processes are realized. 
 So my questions are: 

 Is this a contradiction to Carnot's theorem that the efficiency $ \eta_\text{C } = 1 - T_1 / T_2 $ is the like for all reversible heating system engines between two heat bathtub? 
 Is this bicycle reversible? 
 Is there a way to say whether a summons is reversible or irreversible entirely with a figure like the one above? 

 angstrom: 

 Revamped Answer. 2017 - 07 - 01 
 There is no contradiction because your analysis entirely includes what happens to the gaseous work substance in the Stirling engine, and it neglects a crucial component of the engine call the regenerator.   If the regenerator is not included as a component of the engine when we do the efficiency analysis, then we don't have a device that stipulate as a heat locomotive operating between two temperature, and we therefore shouldn't expect it to abide by Carnot's Theorem as I express in the original version of this answer. 
 However, if we properly take account of the regenerator, then we find that the efficiency of the engine is the Carnot efficiency. 
 Of course the whole analysis here is an idealized one in which we assume, for example, that there are no energy losses due to friction in the engine's component. 
 Details. 
 A stirling engine is more complex than the $ P$-$V$ diagram drawn in the motion instruction seems to indicate.   If we conceptually reduce the locomotive to its simplest mannequin, it contains two fundamental component: 

 A gaseous working substance.   This is the part of the engine whose thermodynamic state travels along the bend in the $ P$-$V$ diagram. 
 A regenerator.   This part of the engine absorbs and stores the department of energy given up by the gaseous cultivate substance by heat transfer during the process $ 2\to 3 $ and then returns that like energy to the gaseous working substance during the process $ 4\to 1$. 

 The crucial point is that when the regenerator is included, there is no net estrus transfer into or out of the engine during the procedure $ 2\to 3 $ and $ 4\to 1$.   The energy that entrust the gaseous working kernel during the process $ 2\to 3 $ by heating system transfer is stored in the regenerator, and that heating system is then give back up to the working substance during process $ 4\to 1$.   No heat is transferred between the engine and its surroundings during these legs of the cycle
 islthermal and isochoric pvocesses are realized.
So my qusstions xre:

Is this a contradiction tl Xarnou'f theorem that the efficienby $\eta_\texr{C} = 1 - T_1/T_2$ is the same fov all vevervmble heat engings between tfo heat baths?
Iv ghns cycle reversible?
Is there a way to say whrtjer a process ys rtvewsibmv ir irreversible only with a fjgure lpke the one above?

S:

Revamped Answer. 2017-07-01
There is jo clntradiction becaude your anaoysif only includds what hakpzns to the faseous working substance in thd Stixling enging, znf it neglectw a cgucial componcmt of dhe engone called the rejeneeator.  If the regeneretor is not included as a com[ouent of the engine whwn we pgrfork thd efwicjeicy analydis, then we dkn't have a eevice that qualifits ww a heat engihe opewaeing between two temperatures, and we thtrefode shouldn't expect it ti abide by Carnot's Thgorem as I stated in the original version of this answer.
Howaver, mf we pvopefoy take account of the regenerator, then we find fhst the efficiencn of the engine is tje Sarnot efficigncy.
Of ekudse the whole analjsis hete is qn idealieed ome in which we assume, for ezample, that nherw are no energy lodses due to frivtion in the engine's componeuts.
Detzils.
A stirllng engins is more complex thsn the $P$-$V$ diagram drawn in tre questiin scatement seeks to yndicate.  Lf we conceptually reducf the etgine to ihs simplest form, it contains two fundamental vokpotents:

A gcseous working subseance.  This is the paxt of ghe engine whose vhermodynamis state travend along the rurve in ehe $P$-$V$ duagram.
A fegenerator.  Tnis part of the engune absorbs and stprer the energy givzu op by the gaseois dorhijg sttstance by haat gravxfer auring uke irozess $2\to 3$ and then returnv thzt same energy to yhc gaseous working substance duting the process $4\tl 1$. 

Thx crucmal poont is that when the regenerator js includfd, bhere is no nqt hcat jransfer inco or out of the engine during the procewses $2\to 3$ and $4\to 1$.  Rhe energy that learex the gaseons worhing subsdance during the proxess $2\to 3$ by heat uransfer is stored in tge reganerahor, and that heat is then given back up to the working substance during peocess $4\to 1$.  No heaf is tranvfzrrzd betwqen vhx engine and its xurroundings during these legs uf the cfcje
isothermal and isochoric processes are realized. So are: this a to Carnot's theorem 1 T_1/T_2$ is the for all reversible engines between two heat baths? Is cycle reversible? Is there a way to say whether a process is reversible irreversible only with a figure like the one above? A: Revamped Answer. 2017-07-01 is contradiction your only includes what happens to the gaseous working substance in the Stirling engine, and it neglects crucial component of the engine called the regenerator. the regenerator is not as a component of the when perform the analysis, we have a device qualifies as a heat engine operating between two temperatures, and we therefore shouldn't expect it to abide Carnot's Theorem stated in original of answer. However, if take account of the regenerator, then the efficiency of the engine is the Carnot Of course whole analysis here is an idealized in which we assume, for example, that there no energy losses due to friction in the engine's components. Details. A stirling engine is than the $P$-$V$ diagram in the question seems indicate. we reduce the to its simplest form, it contains two fundamental components: A gaseous substance. This is the part of the engine whose thermodynamic along curve in the diagram. A regenerator. This of engine absorbs and stores given by substance heat during the process $2\to and then returns that same to the gaseous working 1$. The crucial point is that when the is included, there is no net heat into or out of the engine during the processes $2\to 3$ and 1$. The leaves the gaseous working substance during the process 3$ by heat transfer stored in the regenerator, and that heat is then back to the substance during process 1$. No heat transferred between the its surroundings these of
 isothermal and isochoric proCesses are rEalizEd.
SO my QuEstiOns aRe:

Is this a contrADictIon to Carnot's theorem thaT the eFfICienCY $\eTa_\texT{C} = 1 - T_1/T_2$ is tHE sAME foR aLl RevErSIbLe heaT enGines beTween two heAt bAtHs?
Is this cyclE ReVersible?
Is TheRe a way to say wHetHer a prOcEss IS reveRsiBle or IrreveRSible oNly with a fIgURe like THe one abOVE?

A:

revaMped Answer. 2017-07-01
There is NO cONtradiction becAuse yoUr ANaLYSis OnlY includes wHaT happENs to the GAsEOUS woRKing substance In the StirliNG enGine, anD iT neGLects a CruciAl COmpOnent of the eNginE called thE regenERator.  If THe regenErator Is nOt iNcluDEd As A coMpONenT Of The ENgiNe when we PeRfOrm thE effICIENcy aNalYsis, Then wE don't have a devIce That QUalIfies As a heAt enGiNe opeRating BetweEn Two temperatures, And wE thereforE shOuLdn'T eXpect IT to abiDe bY CaRnot's ThEorem as i StaTeD IN ThE original version of ThIS AnSwer.
HoweVer, if wE PrOpERly take aCcOunT of tHE RegenEratOR, tHen we finD that tHE eFfIciency Of The engInE is The carnoT EffiCiency.
of course The whOLe analysis here IS an idealized oNE iN WHiCH we aSsuMe, for examplE, thaT TherE are NO eNerGY lossEs due To FRiCTion in the engine's comPoNents.
DEtailS.
A stirling engIne is more cOMPLex than tHe $P$-$V$ DIaGRam drawn in the qUestiOn statemenT Seems to iNdicaTe.  If we coNceptuallY REduce the EngIne To iTs sIMPlEst form, it contAINs twO fUndamenTal ComponeNts:

a gaSeoUs wOrKing substAnce.  This Is ThE pArT of The enGIne whose ThErmOdYnaMic stATe travEls alOng tHe CuRVe iN the $P$-$V$ dIAgRAM.
A reGeNeRatoR.  ThIs Part oF the ENgiNe absorBs and storEs tHE eneRgY gIven up bY the gaseous woRkIng substanCe By hEat traNSFer durinG the process $2\to 3$ and then retURns that SamE enerGy to The gaseouS woRking sUbsTAnce duRing thE procEsS $4\to 1$. 

tHE crucIAL pOinT iS that when tHE RegEneraToR is iNcluded, There is no net heat trANsfEr into or out of The EngiNE DuRinG ThE ProCeSSes $2\TO 3$ And $4\to 1$.  The energy tHat leaves tHe GAsEous workinG SubStAnce durIng the pRocesS $2\To 3$ by heaT transfer Is stored iN tHe reGENerAtor, and thaT heat is tHen given bACk up tO ThE workIng SubstaNcE duRing pRocess $4\TO 1$.  No Heat iS transFeRred beTween ThE engine aNd its surroundings during These lEgs of The Cycle
 isothermal and isochoricprocessesare r eal ize d. 
Somy q uestions are:Is t his a contradiction to  Carn ot ' s th e or em th at thee ff i c ien cy  $ \et a_ \ te xt{C}  =1 - T_1 /T_2$ is t hesa me for all r e ve rsible hea t e ngines betwe entwo he at  ba t hs?
I s t his c ycle r e versib le?
Is th er e  a way to sayw h et hera process is reve r si b le or irrevers ible o nl y  w i t h a  fi gure liketh e one above?A: R eva m ped Answer. 2 017-07-01
T h ere  is no  c ont r adicti on be ca u seyour analys is o nly inclu des wh a t happe n s to th e gase ous  wo rkin g  s ub sta nc e  in th e S t irl ing engi ne ,and i t ne g l e c ts a  cr ucia l com ponent of the  en gine cal led t he re gene ra tor. If th e reg en erator is not i nclu ded as acom po nen tof th e  engin e w hen  we per form th e  ef fi c i e nc y analysis, then w ed o n' t have a  devic e  t ha t  qualifi es  as  a h e a t eng ineo pe rating b etween tw otempera tu res, a nd  we  th erefo r e sh ouldn' t expect  it t o  abide by Carn o t's Theorem a s  I s ta t ed i n t he original  ver s ionof t h is  an s wer.Howev er ,  i f  we properly take a cc ount o f the  regenerator,  then we f i n d  that th e ef f ic i ency of the en gineis the Car n ot effic iency .
Of cou rse the w h o le analy sis  he reisa n  i dealized onei n  whi ch  we ass ume , for e xam ple , t hat  t here areno energ ylo ss es  du e tof rictionin  th eeng ine's compon ents. 
Det ai ls . 
Astirlin g  e n g ineis  m orecom pl ex th an t h e $ P$-$V$diagram d raw n  inth equestio n statement s ee ms to indi ca te.   If w e conceptu ally reduce the enginet o its s imp lestform , it cont ain s twofun d amenta l comp onent s: 

A g aseou s wo rki ng  substance .  Th is is  t he p art ofthe engine whose t h erm odynamic stat e t rave l s  a lon g  t h e c ur v e i n the $P$-$V$ dia gram.
A re ge n er ator.  Thi s  pa rt  of the  engine  abso r bs andstores th e energygi venu p  by  the gaseo us worki ng substa n ce by he at tr ans fer du ri ngthe p rocess $2\ to 3$  and t he n retu rns t ha t same e nergy to the gaseous wo rkingsubst anc e duringthe pro cess $4\t o 1$ . 

The cr uci alpoint  is thatwhen th e r e gener ator is includ e d,  th e r eis no net h e a t  tr ansfe r i n to oroutof the engine dur i ng the process es $ 2 \ to3$a nd $ 4\ to 1$.  The en erg yt h at leave sthe gaseous  working  s u bstan ce dur ing th e proce s s  $ 2 \to 3$  byhea t transfe r i ss tored i nth e  regen erat or , andthat h e at i s then given backup to t he wo r kin g sub st ance du r ingprocess $4 \to 1$.  No  heatis t ransf erred b et ween t heen gine and i t s surroun dings  during  t hese  le gs ofthec y cle
 isothermal_and isochoric_processes are realized.
So my_questions are:

Is_this_a contradiction_to_Carnot's theorem that_the efficiency $\eta_\text{C}_= 1 - T_1/T_2$_is the same_for_all reversible heat engines between two heat baths?
Is this cycle reversible?
Is there a way_to_say whether_a_process_is reversible or irreversible only_with a figure like the_one above?

A:

Revamped_Answer. 2017-07-01
There is no contradiction because your analysis_only_includes what happens_to the gaseous working substance in the Stirling engine,_and it neglects a crucial component_of the engine_called_the_regenerator.  If the_regenerator is not included as a_component of the engine when we_perform the efficiency analysis, then we don't_have a device that qualifies as_a heat engine operating between_two temperatures,_and we therefore shouldn't expect_it to abide_by Carnot's_Theorem as I_stated in the original version of_this answer.
However, if_we properly take account of the_regenerator,_then we find_that_the_efficiency of_the engine is_the_Carnot efficiency.
Of_course_the whole analysis here is an_idealized_one in which we assume, for example,_that there are no_energy_losses due to friction_in the engine's components.
Details.
A stirling_engine is more complex than the_$P$-$V$ diagram_drawn in_the question statement seems to indicate.  If we conceptually reduce_the engine to its simplest form,_it contains two fundamental_components:

A gaseous_working_substance.  This_is_the part_of the engine whose thermodynamic state travels_along the_curve in the $P$-$V$ diagram.
A regenerator._ This part of_the_engine absorbs and stores the energy_given up by the gaseous working_substance by heat transfer during_the_process_$2\to 3$ and then returns_that same energy to the gaseous_working substance during_the process $4\to 1$. 

The crucial point_is_that when the regenerator is included,_there_is no net heat transfer into_or_out_of the engine during the_processes $2\to 3$ and $4\to 1$._ The energy that leaves the gaseous working substance_during the process_$2\to 3$ by heat transfer_is_stored_in the regenerator, and that heat is then given back_up to_the working substance_during process $4\to 1$.  No heat is transferred between_the engine and its surroundings during these_legs of the cycle