LECTURE 8

First Law Analysis to Non-flow Processes

Constant Volume process:

1. Heating of gas enclosed in a rigid vessel:

dU = dQ or U₂- U₁ , Q = m C_v (T₂ – T₁)

2. Shaft work done on a system at constant volume

dU = dQ- dW = dQ – (dW_pdv + dW_s)

or dU = - dW_s or -W_s = U₂- U₁

3. Constant volume process involving electrical work:

- W_s = 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.

C_v dT = -Pdv = -RT/v dv

dT/T = -R/C_v dv/v

R/C_v = 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