NON FLOW PROCESSES IN FIRST LAW OF THERMODYNAMICS


Non flow processes is classified as



(1). Constant volume process – Isocharic  process
(2). Constant pressure process – Isobaric process.
(3)  Constant temperature process -  Isothermal process
(4). Reversible adiabatic process – Isentropic process
(5)). Polytropic process
(i). Constant Volume Process
                       
            V = C,           dV = 0

            dQ  = dU+PdV/J
dQ  = dU+PdV/J  but dV = 0
dQ = dU
Integrating we get

Q12 = (U2-U1)
  
we know that for constant volume process

Q12 = mCv(T2-T1)                         

Cv  - specific heat at constant volume = 0.713 KJ / Kg.K for air.

 Q12 =(U2-U1)   =  mCv(T2-T1)
For constant volume process Work done  = 0,Heat transfer  =  change in internal energy.


(ii). Constant pressure Process          
P = C
We know that
dQ  = dU+PdV/J
Integrating we get

Q12 = U2 –U1 + P [ V2 – V1] / 1000
      =  [U2 + P2 V2  / 1000 ]  - [ U1 + P1 V1 / 1000 ]        
Q12  = H2 – H1
H = U + PV / 1000
Enthalpy  = Internal energy  + Flow energy
But we know that for a constant pressure process 
Q12  = m Cp (T2-T1) 
Cp is specific heat at constant pressure. Cp =1KJ/Kg.K for air

Q12 = H2 – H1  = m Cp (T2-T1)
W = P (V2 –V1) / 1000
 [U2 – U1] = m Cv(T2-T1)
For constant pressure process heat transfer = change in enthalpy.

(iii). Relation between Cp, Cv  and R / J
From constant pressure process
Q12 = U2 –U1 + P [V2 – V1]
 m Cp (T2-T1) =   m Cv(T2-T1) + m R(T2 –T1)  / J
Cp  = Cv + R / J
Cp - Cv = R / J

(iv). Isothermal process,           

dT = 0 , T2 = T1           
we know that
P1V1/T1  =  P2V2/T2
P1V1   = P2V2   [ since  T2=T1]
PV = C
Hence isothermal process is also called as Hyperbolic process.
We know that
dQ  = dU+PdV/J
dQ  = m Cv dT2+PdV/J
dQ =PdV/J  [ since dT = 0]
Heat transfer  = Work done

Work done = 1∫2   P dV / J
PV = C
P = C / V
Substituting and integrating we get
W = P1V1 loge(V2/V1) / 1000
Q12 = W = P1V1 loge(V2/V1) / 1000
(v). Reversible Adiabatic Process

dQ = 0 ,  PVγ  = C
We know that
dQ  = dU+PdV/J
dU = -PdV/J  [ since dQ = 0 ]
change in internal energy  =  -  work done
change in internal energy  [ U2 – U1] = m Cv(T2-T1)
Workdone = 1∫2   P dV / J
We know that  PVγ  = C
P  =  C / Vγ
            Substituting and integrating we get
W = P1V1 – P2V2 / [γ – 1 ] x 1000

(vi). Relation between P ,V and T

P2/ P1 =  [V1 / V2 ] γ  
T2  / T1 =  [ P2/ P1 ] (γ -1 / γ)  
T2  / T1 = [V1 / V2 ] γ -1


(vii). Polytropic Process

            PVn  =  C
We know that                                                        
dQ  = dU+PdV/J
integrating we get
Q12       =  (U2-U1)  +   P1V1 – P2V2 / [n – 1 ]
=  m Cv(T2-T1) + mR(T1-T2)/ [n – 1 ]
            =  m Cv(T2-T1) - mR(T2-T1)/ [n – 1 ]
            = m Cv(T2-T1) – m Cv (γ  – 1) (T2-T1)/ [n – 1]
            =  [ n- γ  / n – 1] m Cv(T2-T1)
  Q12     = [ n- γ  / n – 1] ∆U
  W      =  P1V1 – P2V2 / [n – 1 ] x 1000
[ U2 – U1]        =  m Cv(T2-T1)

(viii). Relation between P ,V and T
P2/ P1 =  [V1 / V2 ] n  
T2  / T1 =  [ P2/ P1 ] (n -1 / n)  
T2  / T1 = [V1 / V2 ] n-

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