Wednesday, 6 July 2016

DISPLACEMENT WORK OR PdV WORK IN THERMODYNAMICS

DISPLACEMENT WORK OR PdV WORK IN THERMODYNAMICS

We were discussing various basic concepts of thermodynamics such as thermodynamic state, path, process and cycles in our previous post. We have also discussed the concept and method of calculation of work energy transfer and heat energy transfer as well as sign convention for heat transfer and work transfer in thermodynamics in our recent post.

Today we will see here the various forms of work transfer in the post, we will discuss following types of work transfer as mentioned here
  1. Displacement work or PdV work
  2. Flow work
  3. Shaft work
  4. Paddle wheel work
We will discuss each and every type of work transfer in detail. Let us first start to discuss the displacement work or PdV work.

Let us consider the following arrangement of cylinder and piston. Cylinder contained with gas and displayed here the two equilibrium state of the system by state 1 and state 2. At state 1, gas will be at high pressure and will have lower volume and state of the system is displayed here by the co-ordinate P1V1.

Let piston moves to its final position which is displayed here as state 2. Gas will be at lower pressure and will have higher volume as compared to state 1. Condition of the system at state 2 is displayed here by the co-ordinate P2V2.

Let us consider one intermediate point with pressure p and volume v during travelling of piston from state 1 to state 2. We must note it here that this intermediate point must also be equilibrium state as thermodynamic properties such as pressure p and volume v are only significant for equilibrium states.
Let area of the piston is A and piston moves by infinitesimal distance dS due to the pressure force of the gas acting over the piston. 

What will be the pressure force acting over the piston? Pressure force exerted by gas over the piston will be calculated as F= P. A

Let us concentrate the infinitesimal amount of work carried out by gas over the piston in order to move the piston by infinitesimal distance i.e. dl and it will be calculated as mentioned here 

dW= F. dS = P. A.dS
dW= P. (A. dS) = P.dV

Because (A. dS) will the infinitesimal displacement volume i.e. dV

Magnitude of the work done by gas over the piston will be calculated by determining the area under the curve or path 1-2. This derivation of work done by gas over the piston is only valid for quasi static process or quasi equilibrium process and therefore path 1-2 must be quasi static path.


We will see another topic i.e. “Work energy transfer in thermodynamics: Paddle wheel work” in our next post.
Do you have suggestions? Please write in comment box

Reference:

Engineering thermodynamics by P.K. Nag
Engineering thermodynamics by R. K. Rajput
Image courtesy: Google

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