chapter 2: energy and the 1st law of...

Chapter 2 Energy and the 1st Law of Thermodynamics

12/21/2014 7:39 PM

Dr. Mohammad Suliman Abuhaiba, PE 1

Homework Assignment # 2

Problems: 1, 7, 14, 20, 30, 36,

42, 49, 56

Design and open end

problem: 2.1D

Due Monday 22/12/2014

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Dr. Mohammad Suliman Abuhaiba, PE

2

Work and Kinetic Energy

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3

Potential Energy

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4

Conservation of Energy in Mechanics

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5

Broadening Our Understanding of Work

Thermodynamic definition of work: Work is done by a system on its

surroundings if the sole effect on

everything external to the system

could have been the raising of a

weight.

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Modeling Expansion or

Compression Work

dVp

V

V

2

1

Work is process (path)

dependent, and is NOT a

property of the system

Expansion / Compression

Work (Moving Boundary

Work)

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Sign Convention – Work

W > 0: Work done by system

W < 0: Work done on system

Power: Time rate of work

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Example 2.1

A gas in a piston–cylinder assembly

undergoes an expansion process for which

the relationship between pressure &

volume is given by p.Vn = Constant.

The initial pressure is 3 bar, the initial volume

is 0.1 m3, and the final volume is 0.2 m3.

Determine the work for the process, in kJ, if

a. n = 1.5

b. n = 1.0

c. n = 0

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9

Broadening Our

Understanding of Energy

Mechanical Energy: KE, PE, E

Work is done by energy transfer

Heat is another form of energy

Expand the conservation of energy

principle to accommodate thermal

systems.

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Broadening Our

Understanding of Energy In engineering TD change in total energy of a system

is made up of three macroscopic contributions:

1. change in kinetic energy, associated with motion

of system as a whole relative to an external

coordinate frame.

2. change in gravitational potential energy,

associated with position of system as a whole in

the earth’s gravitational field.

3. All other energy changes are lumped together in

the internal energy of the system. internal energy

is an extensive property of the system.

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Common Units: J(N·m) or kJ, ft·lbf, Btu

)(2

1 2

1

2

2 VVmKE

)( 12 zzgmPE

Kinetic Energy

Potential Energy

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Broadening Our


E:/library/ch02/pages/Pg36.html

E:/library/ch02/pages/Pg39.html

Total Energy: An extensive property of a

system

Kinetic Energy (Mechanical)

Potential Energy (Mechanical)

Internal Energy: U or u

• Represents all other forms of energy

• Includes all microscopic forms of energy

E KE PE U

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Broadening Our


Microscopic Interpretation of Internal Energy

Consider a system consisting of a gas contained

in a tank.

Think about the energy attributed to motions and

configurations of individual molecules, atoms,

and subatomic particles making up the matter in

the system

Gas molecules move about, encountering other

molecules or walls of container.

Part of internal energy of gas is translational

kinetic energy of molecules.

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Microscopic Interpretation of Internal Energy

kinetic energy due to rotation of molecules

relative to their centers of mass & kinetic energy

associated with vibrational motions within

molecules.

energy is stored in chemical bonds between

atoms that make up the molecules.

Energy storage on the atomic level includes

energy associated with electron orbital states,

nuclear spin, and binding forces in the nucleus.

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Sign Convention,

Notation, and Heat Transfer Rate

Q > 0: Heat transfer

into the system

Q < 0: Heat transfer

out of the system

Rate of heat

transfer:

Q

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Energy Transfer by Heat

Heat Transfer Modes

Conduction

Radiation

Emissivity, e, is a property of surface that

indicates how effectively the surface

radiates (0< e <1.0)

s = Stefan–Boltzmann constant

x

dTQ A

dx

4

beQ ATes

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Heat Transfer Modes

Convection ( )b fcQ hA T T

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1st Law of Thermodynamics

Consider a system of a

piston and cylinder with an

enclosed dilute gas

characterized by P,V,T & n.

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What happens to

the gas if the piston

is moved inwards?


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If the container is

insulated the

temperature will rise,

the atoms move faster

and the pressure rises.

Is there more internal

energy in the gas?


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External agent did

work in pushing the

piston inward.

W = Fd = (PA)x

W = PV

x


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Work done on the

gas equals the

change in the gases

internal energy,

W = U

x


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Let’s change the situation:

Keep the piston fixed at its original location.

Place the cylinder on a hot plate.

What happens to gas?


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Heat flows into the gas.

Atoms move faster, internal

energy increases.

Q = heat in Joules

U = change in internal

energy in Joules.

Q = U


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What if we added

heat and pushed

the piston in at the

same time?

F


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Work is done on the

gas, heat is added to

the gas and the

internal energy of the

gas increases!

Q = W + U

F


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For the gases perspective:

heat added is positive, heat

removed is negative.

Work done on gas is positive, work

done by the gas is negative.

Temperature increase means internal

energy change is positive.


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Conservation of Energy: 1st Law

of Thermodynamics

KE PE U Q W

Change in amount

of energy contained

within the system

during some time

interval =

Net amount of

energy transferred

in across the

system boundary

by heat transfer

during the time

interval

-

Net amount of

energy transferred

out across the

system boundary

by work during the

time interval

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Alternative Forms of the Energy

Balance

Differential Form:

dE Q W

dEQ W

dt

Time Rate Form:

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Example 2.2 Cooling a Gas in a Piston–Cylinder

Four kilograms of a certain gas is contained within

a piston–cylinder assembly. The gas undergoes a

process for which the pressure–volume relationship

is pV1.5 = constant . The initial pressure is 3 bar, the

initial volume is 0.1 m3, and the final volume is 0.2

m3. The change in specific internal energy of the

gas in the process is u2 - u1 = - 4.6 kJ/kg. There are

no significant changes in kinetic or potential

energy. Determine the net heat transfer for the

process, in kJ.

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Example 2.3 Considering Alternative Systems

Air is contained in a vertical piston–cylinder assembly fitted with

an electrical resistor. The atmosphere exerts a pressure of 1 bar

on the top of the piston, which has a mass of 45 kg and a face

area of .09 m2. Electric current passes through the resistor, and the volume of the air slowly increases by .045 m3 while its

pressure remains constant. The mass of the air is 0.27 kg, and its

specific internal energy increases by 42 kJ/kg. The air and piston

are at rest initially and finally. The piston–cylinder material is a ceramic composite and thus a good insulator. Friction between

the piston and cylinder wall can be ignored, and the local

acceleration of gravity is g 9.81 m/s2. Determine the heat

transfer from the resistor to the air, in kJ, for a system consisting of

a. the air alone

b. the air and the piston

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Example 2.4 Gearbox at Steady State During steady-state operation, a gearbox receives

60 kW through the input shaft and delivers power

through the output shaft. For the gearbox as the

system, the rate of energy transfer by convection is

where h = 0.171 kW/m2 K is the heat transfer

coefficient, A =1.0 m2 is outer surface area of

gearbox, Tb = 300 K is the temperature at the outer

surface, and Tf = 293 K is the temperature of the

surrounding air away from the immediate vicinity of

the gearbox. For the gearbox, evaluate the heat

transfer rate and power delivered through the

output shaft, each in kW.

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Example 2.5 Silicon Chip at Steady State

A silicon chip measuring 5 mm on a side and 1

mm in thickness is embedded in a ceramic

substrate. At steady state, the chip has an

electrical power input of 0.225 W. The top

surface of the chip is exposed to a coolant whose temperature is 20°C. The heat transfer

coefficient for convection between the chip

and the coolant is 150 W/m2 K. If heat transfer

by conduction between the chip and the

substrate is negligible, determine the surface temperature of the chip, in °C.

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Example 2.6 Transient Operation of a Motor

The rate of heat transfer between a certain

electric motor and its surroundings varies with time

as , where t is in seconds and is

in kW. The shaft of the motor rotates at a constant

speed of 100 rad/s and applies a constant torque

of 18 N.m to an external load. The motor draws a

constant electric power input equal to 2.0 kW. For

the motor, plot , each in kW, and the

change in energy E, in kJ, as functions of time from

t = 0 to t = 120 s. Discuss.

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Cycle Analysis

Power Cycles

Refrigeration & Heat

Pump Cycles

cycle cycle cycleE Q W cycle cycleQ W

cycle

in

W

Q

in

cycle

Q

W

out

cycle

Q

W

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