What is Work Done For Different Thermodynamics Processes?

The primary or sole purpose of thermodynamics is to convert the unorganized form of energy (Heat) into organized form of energy ( work ). In thermodynamics, we always look to gain maximum work.

Work is not a property of the system. It is path function an inexact differentiates. Work is defined by the system if system changes then nature of work also changes ( for example below figure). Here in below picture system is showed by a dotted line.

If work is done by the system, then it is taken positive, but if work is done on the system by some external means then work is considered harmful.

In the thermodynamic displacement ds occurs due to force F  then u can give the equation of work as follow:

DW = F.ds , but as u know that  PRESSURE = FORCE / AREA

SO , dW=P.A.ds

dW=P.dV ( A.ds = dV )

or we can write above equation like,

W = ∫P.dV . This is an equation of Work which is used in thermodynamics. But this equation is only valid for the closed system and reversible process.

·         Now in this very post we will learn about work done by ideal gas in different processes like  isobaric process, isochoric process, isothermal process, adiabatic process & polytropic process

1.      ISOBARIC PROCESS:

Isobaric processes are constant pressure process. So for isobaric process P=C.

Apply work done equation for this process

W = ₁∫²P.dV ( for process 1-2 ) . here P is constant.

 So we can write W = P₁∫²dV

 W = P [V ]₁² 

 W = P (V₂ –V₁ ). This is an equation of work done for an isobaric process.

2.     ISOCHORIC PROCESS:

  Isochoric processes are constant volume process. So for isochoric process V=C.

Apply work done equation for this process

W = ₁∫²P.dV ( for process 1-2 ) . here V is constant.

So dV = 0 and W=0.

For isochoric process work done is zero.

3.      ISOTHERMAL PROCESS.

For the isothermal process, as we know the temperature is constant. So, we can write PV=C (from ideal

gas equation PV= mRT ). We can also write like this    P = C/V.

Apply work done equation for this process

W = ₁∫²P.dV ( for process 1-2 ) .  here P = C/V

 So we can write W = ₁∫²  (C/V)dV

W = C ₁∫²  (1/V)dV  Þ W = C [ln (V) ]₁²

W = C ln(  V₂ / V₁)

But C =  PV, so we write that

W = P₁V₁ln(  V₂ / V₁) or W= mRT ln(  V₂ / V₁) or W=P₁V₁ln( P₁/ P₂) or W=mRT ln( P₁/ P₂)

These are equation of workdone for isothermal process.

4.      ADIABATIC PROCESS:

As we all know that, condition for adiabatic process can be written as PV^ɣ=C. We can also 

write like this    P = C/V^ɣ.

Apply work done equation for this process

W = ₁∫²P.dV ( for process 1-2 ) .  here P = C/V^ɣ

 So we can write W = ₁∫²  (C/V^ɣ)dV

W = C ₁∫²  (1/V^ɣ)dV  Þ W = C [V^1-ɣ/1-ɣ ]₁²

By using formula PV^ɣ=C. we can write above equation as 

W = (P₁V₁ – P₂V₂)/ (ɣ-1)

Above equation of workdone is for adiabatic process. Above equation can also be 

written as

W = mR ( T₁ – T₂ )/ (ɣ-1)

5.     POLY-TROPIC PROCESS :

                         As we all know that, condition for polytropic process can be written as

PVⁿ=C. We can also write like this    P = C/Vⁿ.

Apply work done equation for this process

W = ₁∫²P.dV ( for process 1-2 ) .  here P = C/Vⁿ

 So we can write W = ₁∫²  (C/Vⁿ)dV

W = C ₁∫²  (1/Vⁿ)dV  Þ W = C [V^1-n/1-n ]₁²

By using formula PVⁿ=C. we can write above equation as 

W = (P₁V₁ – P₂V₂)/ (n-1)

Above equation of workdone is for polytropic process. Above equation can also be written as

W = mR ( T₁ – T₂ )/ (n-1)