Modes of Work Transfer

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

Development of Power for Different Needs!!!

Negative Work

• When a system does positive work, its surroundings do an equal quantity of negative work.

• Conversely, when surroundings do positive work, the system does and equal quantity of negative work.

Types of Work Transfers

• Moving Boundary work (displacement work)• Electrical work• Shaft work• Flowing fluid work

Moving Boundary work (displacement work)

• Boundary work occurs when a change in the system causes a force to act on the boundary and make it move.

Simple Processes for Displacement Work : Control Mass

Control Mass : Constant Volume & Pressure Processes

2v

a

bv

RTp

Isothermal Process by A Control Mass

Isothermal Process of Real Gases in a Control Mass

• Van der Waals EOS

2v

a

bv

RTp

RTbvv

ap

2

c

c

p

TRa

64

27 22

c

c

p

RTb

8

27

Displacement Work done by Superheated Steam During An Isothermal Process

Specif ic

Temp Volume Pressure

C m3/kg MPa

600 0.02491 15

600 0.02683 14

600 0.02905 13

600 0.03164 12

600 0.0347 11

600 0.03837 10

600 0.04285 9

600 0.04845 8

600 0.05565 7

600 0.06525 6

600 0.07869 5

600 0.09885 4

600 0.1324 3

600 0.1996 2

600 0.4011 1

Isothermal Expansion of Steam

0

2

4

6

8

10

12

14

16

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Specifi c Volume m3 / kg

Generalized Process in A Control Mass

• p = p0 + k (V-V0)

• p2 = p02 + k (V-V0)2

• Polytropic Nature of Fluid Process:

pVn = Constant– n: Polytropic constant.

– n=0 : Constant Pressure Process.

– n=: Constant Volume Process.

The Polytropic Process by A Control Mass

• One in which the pressure-volume relation is given as PVn=constant

• “n” may have any value from minus to plus infinity.• Work transfer during a polytropic process.

• For a vapour under going a polytropic process.

2v

a

bv

RTp