chapter 2: energy and the 1st law of thermodynamics

Chapter 2Energy and the 1st Law of Thermodynamics

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Dr. Mohammad Abuhaiba1

Work and Kinetic Energy

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Dr. Mohammad Abuhaiba

2

Potential Energy

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Conservation of Energy in Mechanics

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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 the system

W < 0: Work done on the system

Power: Time rate of work

W

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Example 2.1Evaluating Expansion Work

A gas in a piston–cylinder assembly undergoes an

expansion process for which the relationship

between pressure and volume is given by

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, and

c. n 0.

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Further Examples of Work

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Rotating Shaft

Electric Power

Broadening Our

Understanding of Energy

Mechanical Energy: KE, PE, E

Work is done by energy transfer.

Heat is another form of energy.

Need to expand the conservation of

energy principle to accommodate

thermal systems.

Broadening Our

Understanding of EnergyIn engineering TD the change in total energy of a

system is considered to be 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 the 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.

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.

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 an example

system of a piston and

cylinder with an enclosed

dilute gas characterized by

P,V,T & n.

What happens to

the gas if the piston

is moved inwards?


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?


External agent did

work in pushing the

piston inward.

W = Fd =(PA)x

W = PV

x


Work done on the

gas equals the

change in the gases

internal energy,

W = U

x


Let’s change the situation:

Keep the piston fixed at its original location.

Place the cylinder on a hot plate.

What happens to gas?


Heat flows into the gas.

Atoms move faster, internal

energy increases.

Q = heat in Joules

U = change in internal

energy in Joules.

Q = U


What if we added

heat and pushed

the piston in at the

same time?

F


Work is done on the gas,

heat is added to the gas

and the internal energy of

the gas increases!

Q = W + U

F


Some conventions:

For the gases perspective:

heat added is positive, heat removed is

negative.

Work done on the gas is positive, work

done by the gas is negative.

Temperature increase means internal

energy change is positive.


Conservation of Energy: The 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 . 2Cooling 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

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 . 3Considering 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 . 4Gearbox 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 the outer surface area of the gearbox, Tb = 300 K (27C) is the

temperature at the outer surface, and Tf = 293 K (20C) is the

temperature of the surrounding air away from the immediate

vicinity of the gearbox. For the gearbox, evaluate the heat

transfer rate and the power delivered through the output shaft,

each in kW.

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Example 2 . 5Silicon 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 20C. 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 . 6Transient 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 (about 955 RPM)

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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Homework Assignment # 2

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

42, 49, 56

Design and open end

problem: 2.1D

Due Wednesday 22/2/2012

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chapter 2: energy and the 1st law of thermodynamics

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