**Constant Volume
process**

_{2}- U

_{1}, Q = m C

_{v}(T

_{2}– T

_{1})

Shaft work done on a system at constant volume dU = dQ- dW = dQ – (dW

_{pdv}+ dW

_{s})

or dU = - dW_{s}
or -W_{s} = U_{2}- U_{1}

Constant volume process
involving electrical work: - W_{s}
= U_{2}- U_{1}

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 (V_{2}
–V_{1})

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 (v_{2}/
v_{1})

**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 T_{2}/T_{1}
= (v_{1}/v_{2}) ^{(}^{g-1)} Tv^{(}^{g-1)} =
constant

^{g}= Constant using perfect gas relation

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