Constant Volume process , Constant Pressure Process,Constant temperature Process and reversible adiabatic process ~ MECHTECH GURU

### Constant Volume process , Constant Pressure Process,Constant temperature Process and reversible adiabatic process

Constant Volume process

Heating of gas enclosed in a rigid vessel:  dU = dQ or U2- U1 , Q = m Cv (T2 T1)
Shaft work done on a system at constant volume dU = dQ- dW = dQ – (dWpdv + dWs)

or dU = - dWs or -Ws = U2- U1

Constant volume process involving  electrical work:      - Ws = U2- U1

For an adiabatic process the work is done is independent of path.

Constant Pressure Process

1.        Reversible heating of a gas

2.        Phase Change at constant pressure(Rev.)

3.        Shaft work at constant pressure

4.        Electrical work at constant pressure

W = P (V2 –V1)

dU = dQ-dW = dQ- PdV = dQ- d(PV)

or, dQ = dU + d(PV) = d(U+ PV) = dH

Q = DH the heat interaction is equal to increase in enthalpy

Constant Temperature Process

dU = dQ-dW = dQ- PdV                                  for an ideal gas u= u(T) then dU = 0

dQ = PdV = RT (dv/v) Q = W = RT ln (v2/ v1)

dU = -dW or W = -DU

This equation is true for reversible as well as irreversible process.

Cv dT = -Pdv = -RT/v dv dT/T = -R/Cv dv/v

R/Cv = g - 1   ,dT/T = -(g-1) dv/v T2/T1 = (v1/v2) (g-1) Tv(g-1) = constant

Also Pv g = Constant using perfect gas relation
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