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)
Reversible Adiabatic Process
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
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