Thermodynamic - Work Done is Path Dependend

 Thermodynamic - Work Done is Path Dependend

 

Thermodynamic - Work Done

 

- Definition:

  In Thermodynamics, Work Done Refers To The Energy Transfer

  That Occurs When A Force Acts On A System, Causing It To

  Undergo A Displacement. It Is A Form Of Energy Transfer That

  Can Change The State And Properties Of A Thermodynamic

  System.

- The Sign Of Work Done Is Important In Thermodynamics. If

  Work Is Done On The System (Energy Being Transferred Into

  The System), It Is Considered Positive.

- If Work Is Done By The System (Energy Being Transferred Out

  Of The System), It Is Considered Negative.

- Units Of Work:

  Work Is Typically Expressed In Units Of Energy, Such As Joules

  (J) In The International System Of Units (SI). Other Common

  Units Include Foot-Pounds (Ft-Lb) And Calorie (Cal).

- Types Of Work Done: In Thermodynamics,Some Common Types

  Include Expansion Work, Compression Work, Electrical Work,

  And Shaft Work. Each Type Of Work Has Its Own Specific

  Formula And Considerations.

- Applications:

  Understanding Work Done In Thermodynamics Is Crucial In

  Various Real-Life Applications, Such As The Design Of Engines,

  Power Plants, Refrigeration Systems, And Energy Conversion

  Devices.

 

  Thermodynamic - Work Done Is Path Dependend

 

- One Crucial Aspect Of Work In Thermodynamics Is That It Is

  Path Dependent.

- This Means That The Amount Of Work Done Depends On The

  Specific Path Taken During The Process.

- Different Paths Can Lead To Different Amounts Of Work, Even If

  The Initial And Final States Of The System Are The Same.

 

- Prove That Work Done Is Path Dependend

 

Ans :

 

- Work Done Along Path

  A-D-C

- Work Done Formula

  δw=Pdv

- W1 = P1(V2-V1)+ 0....(1)  (In Eq.(1) 0 Means Volume Constant)

- Work Done Alongpath A-B-C

- W2 = 0 + P2(V2-V1)

  W2 = P2(V2-V1)....(2)

- Work Done Along A → C

  W3 = 1/2 (V2-V1)(P1-P2) + P2(V2-V1)

     = 1/2 P1(V2-V1)- 1/2 P2(V2-V1) + P2(V2-V1)

     = 1/2 P1(V2-V1) + 1/2 P2(V2-V1)

- W3 = 1/2 (P1+P2) (V2-V1)....(3)

- From Equation (1),(2),(3)

  W1≠W2≠W3

- It Means Work Done Depend On Path

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