# 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
= U
2 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