Lecture 6 30572g

Thermodynamics I Lecture 6: Work and Heat Prof: Dr. P.Q. Gauthier

Work 

Work is usually defined as a force F acting through a displacement x, the displacement being in the direction of the force. That is: 2

W   Fdx 1

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Work 

In thermodynamics, work is defined as an energy interaction between a system and its surroundings. 

A rising piston ,



a rotating shaft

an electric wire crossing the system boundaries are all associated with work interactions 



Work has energy units: kJ, kJ/kg



Power has Energy per seconds units: kJ/s =Watts

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Work 

Work is a directional quantity. 

Work done on a system is negative,



Work done by the system is positive



System possess energy, but not work,



Work is associated with a process, not a state 

Unlike properties, work has no meaning at a state

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Work 

Work is a path function

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Mechanical Forms of Work 

If F is constant

W F*s



If F is not constant

W

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

2

1

kJ

Fds

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Mechanical Forms of Work 

Moving Boundary work: This type of work is associated with the expansion or compression of a gas in a piston-cylinder device. This is the primary form of work involved in automobile engines

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Quasi-equilibrium process 

Quasi-equilibrium process is a process during which the system remains in equilibrium at all times

Figure:

A

differential

gas

does

amount

a of

work δWb as it force the piston

to

move

by

a

differential amount ds

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Quasi-equilibrium process 

Boundary work in differential form

Wb  Fds  PAds  PdV 

The total work done during the entire process 12 is 2

2

1

1

Wb   Wb   PdV To integrate P=f(V) should be available

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Quasi-equilibrium process



Figure: The area under the process curve on a P-V diagram represents the boundary work

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Boundary Work during a Constant Volume Process 

Example 1: A rigid tank contains air at 500 kPa and 150˚C. As a result of heat transfer to the surroundings, the temperature and pressure inside the tank drop to 65˚C and 400 kPa, respectively. Determine the boundary work done during this process

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Boundary Work during a Constant Volume Process

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Solution

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Boundary Work for a ConstantPressure Process 

Example 2: A frictionless piston-cylinder device contains 10lbm of steam at 60 psia and 320˚F. Heat is now transferred to the steam until the temperature reaches 400˚F. If the piston is not attached to a shaft and its mass is constant, determine the work done by the steam during this process

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Example 2

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Solution

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Solution

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Polytropic Process 

During expansion and compression processes of real gases, n

pressure and volume are often related by PV = C, where n and C are constants. A process of this kind is called a polytropic process

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Boundary Work during Isothermal Process 

Example: A piston cylinder device initially contains 0.4 m 3 of air at 100 kPa and 80°C. The air is now compressed to 0.1 m 3 in such a way that the temperature inside the cylinder remains constant. Determine the work done during this process

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Polytropic Process

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Solution

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Polytropic Process



Figure: Schematic of P-v diagram for a polytropic process

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Polytropic Process 

Wb for a polytropic process

Wb 



2

1

PdV 



2

1

n 1 n 1 2 V  V C n 2 1 dV  C V dV  C 1 n  1 Vn

n 1 n CV21n  CV11n P2V2nV21n  PV V P2V2  PV 1 1 1 1 1    1 n 1 n 1 n

For an ideal gas PV=nRT, thus P2V2  PV mR(T2  T1 ) 1 1 Wb   for n  1 1 n 1 n Thermodynamics I

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Problem 

Argon is compressed in a polytropic process with n= 1.2 from 120 kPa and 30C to 1200 kPa in a piston cylinder device. Determine the work produced and heat transferred during this compression process, in kJ/kg

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Solution

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Solution

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