in the carnote cycle , in the P-V ploti want to know how i can calculate the work doneusing...

Question

in the carnote cycle , in the P-V ploti want to know how i can calculate the work doneusing integration w= limit integration between v3 and v1 ( P.dV )is P a constant ?i don't think so, should i put Pressure limits ?please help menote : in the problemV1 = 0.4 cubic metre "max volume"V3 = 20.38*10^-3 cubic metre "min volume"P1 = 10^5 bascalP2 = 1.2*10^5 bascalthanks in advance :)

David · Accepted Answer

CARNOT CYCLE 
First of all we should understand what is carnot cycle  
In following P-V diagram we will come to know about carnot cycle
So we may see that there are four process and details of these process are as 
mentioned below  
Process 1-2  
 This is isothermal compression process from 1 to 2  
 During this process Q out heat will be rejected 
 Work done for this process
W12 = ∫    
  
  

3 
4 
1 
2 
Isothermal  
Isothermal  
V 
P 
Adiabatic  
Adiabatic  
Qin 
Q out 
In isothermal process Temperature T is constant  
We may put the value of P 
P = n RT/V 
W12 =   n RT  ∫     
  
  
 
After integration we will have  
W12 = n RT log [V2/V1] 
W12 = P1V1 log [V2/V1]
Where, 
n= No. of mol of gas  
R= gas constant
Process 2-3  
 This step is adiabatic compression process from 2 to 3 
 Heat transfer for this process Q= 0 
 Work done for this process
W23 = ∫    
  
  
 
As we have stated that this process is adiabatic process  
So,

in the carnote cycle , in the P-V plot i want to know how i can calculate the work doneusing integration w= limit integration between v3 and v1 ( P.dV ) is P a constant ? i don't think so, should i...

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