Thermodynamics 3 ( Work and Heat)

7/28/2019 Thermodynamics 3 ( Work and Heat)

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Battery motor system with a fan

Figure-1

.

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Baked Potato

Figure-2

Surrounding

T1

System

(baked potato)

T2

T2 > T1

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Observation:

In both figures 1 & 2, there is an energy transfer between the system and surrounding.

In figure 1, the system comprising of battery and motor is raising the weight. This is ,ineffect , a force acting through a distance. Therefore work is done on the surrounding by

the system.

In figure 2, the system comprising of a baked potato will eventually get cooled to the

surrounding temperature due to heat energy from the baked potato to the surrounding.

Energy transfer across the boundary is taking place in two distinct forms- heat and work.

Heat is defined as the form of energy that is transferred between two systems ( or a

system and its surroundings) by virtue of a temperature difference.

Work is said to be done by a system if the sole effect on things external to the system

can be reduced to the raising of a weight. The weight may not be actually be raised but

the net effect external to the system would be the raising of weight.

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Weight is replaced by a fan

Figure-3

The weight is raised with the pulley driven by a motor.

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Sign convention

System Work

Surrounding

Work is positive

Heat is negative

System Work

Surrounding

Work is Negative

Heat is positive

Heat

Heat

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Boundary work/P dV work

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Cylinder

P1=P-dP,

V1=V+dV

P2=P1-dP,

V2=V1+dV

Sand grains

P, V

Stops

GasPiston

Pn,Vn

W = Force X distance= (Pressure x area) x distance

= P ( A Z )

= P dV

For a process 1-2 ,

W1-2 = PdV

It is assumed the system moves

through equilibrium states ( 1,2,

..n)and there is no friction between the

piston and cylinder.

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n

Vn

Representation of expansion work in PV plot.

The area under the process curve on a P-

V diagram is equal, in magnitude, to the

work done during a quasi-equilibrium

process of a closed system.

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Work is a path function

Choose the correct answer:

a)b)

c)

d)

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Pdv work in various quasi static processes

a) Process in which pressure is constant ( isobaric process)

W1-2= PdV = P(V2-V1)

b) Process in which volume is constant( isochoric process)

W1-2= PdV =0

c) Process in which PV = C

W1-2 = PV l n ( V2/V1)

d) Process in which PV n = C (poly tropic constant)

Work done W1-2 = (P2V2-P1V1)/(1-n) n 1

When the gas is considered as ideal gas, the above equation become

Work done W1-2 = mR(T2-T1)/(1-n)

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Boundary work or P dV at constant pressure (isobaric process )

Steam

M= 5 kg

P1= 400 kPa, T1= 200 Deg C

T2= 250 Deg C

Heat

A frictionless pistoncylinder device contains 5 kg of steam at 400 kPa

and 200 deg C. Heat is now transferred to the steam until the temperature

reaches 250 deg C. If the piston is not attached to a shaft and its mass is constant,

determine the work done by the steam during this process. Represent the process

in the P-V diagram and discuss

Sp. Vol v1= 0.5343 m3/kg

Sp. Vol v2 = 0.5952 m3/kg

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Boundary work for a constant volume process (isochoric process)

Air

P1= 500 kPa

T1= 150 Deg C

P2= 400 KPa

T2= 65 Deg C

Heat

A rigid tank

A rigid tank contains air at 500

kPa and 150C. As a result of

heat transfer

to the surroundings, the

temperature and pressure

inside the tank drop to

65C and 400 kPa, respectively.

Determine the boundary work

done during

this process.

Class activity: To represent the process in the P-V diagram and discuss

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Isothermal compression of an ideal gas

Air is compressed at T0=80 deg C

V1=0.4 m3

P1= 100 kPa

V2= 0.1 m3

A pistoncylinder device initially contains 0.4 m3 of air at

100 k Pa and 80C. The air is now compressed to 0.1 m3 insuch a way that the temperature inside the cylinder

remains constant. Determine the work done during this

process.

For ideal gas at constant temperature,PV=mRT0

Workdone = PVln ( V2/V

1)

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Thermodynamics 3 ( Work and Heat)

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