ch 3 (3.1-3.4)

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CHAPTER 3ENERGY

Sub chapter covered3.1 Introduction3.2 Energy transfer by heat and work 3.3 Energy balance

3.4 Work boundary

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3.1 Intro

Energy exist in numerous forms.

– thermal, mechanical, chemical etc.

Their sum constitute Total Energy on aunit mass, e

m

E e (kJ/kg)

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energy

Macroscopic E Microscopic E

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Macroscopic E: form of energy arethose a system possesses as a wholewith respect to some outside reference

frame. eg: kinetic, potential energy.

Microscopic E: energy related to themolecular structure of a system and thedegree of molecular activity.Independent of outside reference frame.

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Sum of all microscopic energy forms calledinternal energy, U

Macroscopic energy of a system is relatedto motion and the influence of someexternal effect (gravity, magnetism,electricity & surface tension).

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Internal Energy

1) Translational energy

2) Rotational kinetic energy

3) Vibrational kinetic energy

4) Spin energy

5) Sensible energy

6) Latent energy

7) Chemical energy

8) Nuclear energy

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Kinetic Energy (KE)?

Potential Energy (PE)?

Total E of the system?

Flow Energy

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Kinetic Energy (KE): energy that asystem possesses as a result of its

motion relative to some reference frame.

)(2

2kJ

V m KE

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Potential Energy (PE): energy thata system possesses as a result of its

elevation in a gravitational field.

)(kJ mgz PE (kJ)

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Total E of the system (closedsystem):

)(2

2

kJ mgz V

mU PE KE U E

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FLOW ENERGY

Closed system: stationary system

Open system (control vol.): involved

fluid flow

Mass flow rate, : amount of massflowing through a cross section perunit

time.

m

)/( skg V m

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3.2 ENERGY TRANSFER

E transfer

By heat,

Q

By work,

W

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Mechanisms:

ConductionConvection

Radiation

Directional quantity

Qin Qout

E transfer by heat,

Q

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Other than E by heatForce acting through

distance

Directional quantity:

Win Wout

E transfer by work,W

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E transfer by work,W

Electrical work, We

Shaft work, Wsh

Spring work, Wspring

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3.3 ENERGY BALANCE

The conservation of E can expressed as:

E E E in out system

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1) Mechanisms of EnergyTransfer, E

inand E

out

Heat transfer, Q = 0, for adiabatic system

Work transfer, W = 0, if no work involved

Mass transfer, m = 0, for closed system

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2) Energy change of thesystem, ∆E system

E system = E final - E initial = E 2 - E 1

E = U + KE + PE

where U = m (u2

–u1 )

KE = ½ (m )(V 22 - V 1

2) PE = mg ( z 2 – z 1 )

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systemout massinmassout inout inout in E E E W W QQ E E

Balance EnergyOverall

)()()( ,,

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Discussion on Problem 2.10

Assignment on:Problem 2-49Problem 2-50

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CHAPTER 3

HEAT, WORK AND MASS Sub-chapter covered

3.4 Work boundary

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Boundary Work

• Boundary work occurs because the mass of the substancecontained within the system boundary

2

1

2

1

2

1

2

1 PdV Ads

A

F FdsW W bb

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The boundary work is equal to the area under theprocess curve plotted on the pressure-volume

diagram

Note from the figure:

P is the absolute pressure and is

always positive.

When dV is positive, Wb ispositive.

When dV is negative, Wb isnegative.

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Some Typical Processes

a) Constant volume

If the volume is heldconstant, dV = 0, and the boundary work equation becomes

0

2

1 PdV W b

b) Constant pressure

If the pressure is held constant,the boundary work equation becomes

12

2

1

2

1

V V P dV P PdV W b

P-V diagram for V = constant P-V diagram for P = constant

P

V

1

2

P

V

12

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c) Constant temperature, ideal gas

If the temperature of an ideal gas system is held constant, then

the equation of state provides the pressure-volume relation

V

mRT P

Then, the boundary work is

1

22

1

2

1ln

V

V mRT dV

V

mRT PdV W b

Note: The above equation is the result of applying the ideal gasassumption for the equation of state. For real gases undergoingan isothermal (constant temperature) process, the integral inthe boundary work equation would be done numerically.

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d) The polytropic process

The polytropic process is one in which the pressure-volume

relation is given as PV n = C (where n and C is constant)

The exponent n may have any value from minus infinity to plusinfinity depending on the process. Some of the more common

values are given below.Process Exponent n

Constant pressure 0

Constant volume

Isothermal & ideal gas 1

Adiabatic & ideal gas k = CP/C V

Here, k is the ratio of the specific heat at constant pressure C P to

specific heat at constant volume C V .

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The boundary work done during the polytropic process is

found by substituting the pressure-volume relation intothe boundary work equation

2

1

2

1 dV V

Const

PdV W nb

1,ln

1,1

1

2

1122

nV

V PV

nn

V P V P

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For an ideal gas undergoing a polytropic process, the boundary work

2

1

2

1dV

V

Const PdV W

nb

1,ln

1,1

1

2

12

nV V mRT

nn

T T mR

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Discussion

1. A frictionless piston-cylinder device initially contains 200L of saturated liquid refrigerant R134a. The piston is free to moveand its mass is such that it maintains a pressure of 800 kPa onthe refrigerant. The refrigerant is now heated until itstemperature rises to 50°C. Calculate the work done during this

process and show the process in P-v diagram

2. Air enters a nozzle steadily at 2.21 kg/m3 and 30 m/s and leaveat 0.762 kg/m3 and 180 m/s. If the inlet area of the nozzle is 80

cm2

, determinea) the mass flow rate through the nozzle b) the exit area of the nozzle

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Assignment 5:

Problem 4.8, 4.9, 4.12, 4.18

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To be continue…………………

ch 3 (3.1-3.4)

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