Displacement work for different thermodynamic process :

When the force acts upon the system and it undergoes a change in its position , i.e., displacement occurs then displacement work is said to be done .

The displacement work for different processes :

(a) Isochoric Process :

The process for which the volume remains constant is Isochoric Process.

Volume = constant

Therefore , ∆W = 0. ( Because dV = 0 )

This process is a constant volume process , identified by rigid container.

(b) Isobaric Process :

The process for which the prsssure remains constant is Isobaric Process .

Pressure = P = constant

Therefore , ∆ W = P (V₂ – V₁ )

This process is a constant pressure process identified by pistons restricted movement .

(c) Isothermal process :

The thermodynamic process for which the temperature remains constant is isothermal process.

Temperature = T = constant

We know that ,

PV = mRT

P = mRT/V ; Assume , c = mRT

PV = c ; P’V’ = PV = c

{V₂ /V₁ = P₁ / P₂ }

∆W = P₁ V₁ ln (V₂ /V₁ )= mRT₁ ln (P₁ /P₂ )

Note : The above result is valid only for :

• Close system
• Reversible process
• Ideal gas

The Isothermal process is identified by phase change .

(d) Adiabatic Process :

The thermodynamic process for which the net heat transfer is zero , such process is Adiabatic Process.

This thermodynamic process is identified by insulated container.

for Adiabatic Process , PV^¥ = constant

Here ,

¥= Gamma = Adiabatic index

and it is valid only for :

1. Reversible process
2. Adiabatic Process

∆W = (P₁ V₁ – P₂ V₂ ) / ( ¥ – 1)

Note : The above result is valid only for :

1. Closed system
2. Reversible process
3. Adiabatic process

(e) Polytropic process :

This is the thermodynamics process which obeys the following relation :

PVⁿ = C

Here , P = pressure

V = volume

N = polytropic index

C = constant

Generally , 1 < N < ¥

∆ W = (P₁V₁ – P₂ V₂ ) / (N – 1)