Basic Concepts & Terminologyteacher.buet.ac.bd/zahurul/ME6101/ME6101_Basics.pdf · The Path of a process is the succession of states through which the system passes. ... Basic Concepts

Basic Concepts & Terminology

Dr. Md. Zahurul Haq

ProfessorDepartment of Mechanical Engineering

Bangladesh University of Engineering & Technology (BUET)Dhaka-1000, Bangladesh

[email protected]://teacher.buet.ac.bd/zahurul/

ME 6101: Classical Thermodynamics

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Dr. Md. Zahurul Haq (BUET) Basic Concepts & Terminology ME 6101 (2017) 1 / 34

Thermodynamic System

T006

A thermodynamic System is simply any object, quantity of

matter, or region of space that is selected for thermodynamic

study. Everything that is not part of the system is referred to as

the Surroundings.Boundary or Control Surface (CS) separates the system fromits surroundings which

may be real or imaginary, at rest or in motion

may change its shape and size

neither contains matter nor occupies volume

has zero thickness and a property value at a point on the boundary

is shared by both the system and its surroundings.

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T009

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T061

A system defined to contain all of the air in a piston-cylinder device.

T062

A system defined to contain all of the air that is initially in a tank that

is being filled.c


Control Mass (CM) or Closed System

T007

CS

Heat√

Work√

Mass ×

CM SystemT744

In Control Mass (CM) or Closed system, the CS is closed to

mass flow, so that no mass can escape from or enter into the

system.

In CM system, heat & work may cross the CS.

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Control Volume (CV) or Open System

T008

T082

Mass passes through CS in Control

Volume (CV) or Open system.

c


Adiabatic System

T079 T083

In Adiabatic system, CS is impermeable to heat.

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Classification of Thermodynamic Systems

T001

Isolated system: a special case of CM system that does not interact in

any way with its surroundings.

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Macroscopic & Microscopic Views of Thermodynamics

Thermodynamic systems can be studied from two points of view:1 Microscopic approach or Statistical Thermodynamics

2 Macroscopic approach or Classical Thermodynamics

The microscopic approach recognizes that the system consists of

matter that is composed of countless, discrete molecules. Statistics

and probability theory are applied to deduce the macroscopic

behaviour or measurable quantities e.g. pressure, temperature etc.

In the macroscopic approach, the state of the system is described

by a relatively small set of characteristics that are called

Properties e.g. mass, temperature, pressure and volume.

Macroscopic approach works well when the system is sufficiently

large such that it contains many molecules. However, macroscopic

approach would not work well for a system that consists of a

rarefied gas (i.e., a vacuum with just a few molecules).

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State & Property

The description of the condition of a system at a given instant is

called its State.

A Property is a quantity whose numerical value depends on thestate but not on the history of the system. The origin ofproperties include those

1 directly measurable2 defined by laws of thermodynamics3 defined by mathematical combinations of other properties.

Two states are identical if, and only if, the properties of the two

states are identical.

Intensive properties are independent of the size or extent of the

system. Extensive properties depend on the size or extent of the

system. An extensive property is additive in the sense that its

value for the whole system is the sum of the values for its parts.

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E2, V2, T, P

E1, V1, T, PEsystem = E1 + E2

Vsystem = V1 + V2

Tsystem = T1 = T2

Psystem = P1 = P2

Extensive Properties

Intensive Properties

}

}

System boundary

T012

Property Extensive Intensive

Mass m ρ

Volume ~V v

KE1

2mV 2

1

2V 2

PE mgZ gZ

Total Energy E e

Internal Energy U u

Enthalpy H h

Entropy S s

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Process & Cycle

Any transformation of a system from one equilibrium state to

another is called Thermodynamic Process.

The Path of a process is the succession of states through which

the system passes.

A system process is said to go through a Thermodynamic Cycle

when the final state and the initial state of the process are same.

T044

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Thermodynamic Equilibrium

A system in Thermodynamic Equilibrium satisfies thefollowing stringent requirements:

1 Mechanical Equilibrium: no unbalance forces acting on any part

of the system or the system as a whole.2 Thermal Equilibrium: no temperature differences between parts

of the system or between the system and the surrounding.3 Chemical Equilibrium: no chemical reactions within the system

and no motion of any chemical species from one part to another

part of the system.

A mixture of substances is in chemical equilibrium if there is no

tendency for a net chemical reaction to occur.

In the absence of gravitational effects, mechanical equilibrium

implies equality of forces throughout.

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T077

T076

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A system is said to be in Stable/Equilibrium State when no

finite change of state can occur unless there is an interaction

between the system and its environment which leaves a finite

alteration in the state of the environment.

During a Quasi-static Process, the system is at all times

infinitesimally near a state of thermodynamic equilibrium; this

implies that the process should be carried out infinitely slowly to

allow the system to settle to a stable state at the end of each

infinitesimal step in the process.

Theoretical calculations must relate to Stable states, since it is

only for these we have thermodynamic data.

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Categories of Thermodynamics Quantities

1 State functions: all properties are state functions.

2 Process or Path functions: quantities whose values depend on

the path of the process.

T038

∫2

1dy = y2 − y1 = ∆y ⇒

∮dy = 0

State function

∫2

1δZ ≡ Z12 6= ∆Z

T013

Path function

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Zero’th Law of Thermodynamics

Zero’th Law of Thermodynamics

Two systems with thermal equilibrium with a third are in thermal

equilibrium with each other.

A

B C

Thermal Equilibirum

Thermal Equilibirum

0th Law

T745 T002

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Conservation of Mass

Mass Continuity Equation

T444

T443

⇒ mcv (t) + mi = mcv (t + ∆t) + me

⇒ mcv (t + ∆t) − mcv (t) = mi − me

⇒ mcv (t+∆t)−mcv (t)∆t

= mi−me

∆t

if ∆t → 0 : ⇛ dmcv

dt= _mi − _me

dmcv

dt=

∑i _mi −

∑e _me

_m = ρAV = AV

v(for 1D flow)

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⊲ [Moran Ex. 4.1]: Feed-water heater at steady-state. Determine _m2 & V2.

Assume, v2 ≃ vf (T2).

T125

dmcv

dt=

∑i _mi −

∑e _me

⇒ dmcv/dt = 0

⇒∑

i _mi = _m1 + _m2

⇒∑

e _me = _m3

_m = ρAV

⇒ _m3 = ρ3(AV)3

⇒ ρ2 = ρ(T = T2,P = P2) ρ3 = ρ(x = 0.0,P = P3)

=⇒ _m2 = 14.15 kg/s, V2 = 5.7 m/s ⊳.

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Mass Balance: Transient Flow

dmcv

dt=

∑

i

_mi −∑

e

_me ⇛ dmcv = dmi − dme

⇒∫t

0

(

dmcv

dt

)

dt =∫t

0 (∑

i _mi ) dt −∫t

0 (∑

e _me )dt

⇒ ∆mcv = mcv (t) − mcv (0) =∑

i

(∫t

0 _midt)

−∑

e

(∫t

0 _medt)

∆mcv = mcv (t) − mcv (0) =∑

i

mi −∑

e

me

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Work & Heat

Work in Mechanics

m m

−F F −F F ∆F

s

ΣFH = 0 ΣFH =∆F : acceleration

Ï if ∆F → 0 : quasi-static processTikZ001

The product, W = Fs of force F and displacement s is defined as

the work done by the force F and against the force −F .

The scalar quantity, work, is defined as the scalar product of force

and displacement:

W = F · s

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Work & Heat

Mechanical Work & Power

Mechanical work (Wmech) is defined as the product of the force

F and a displacement ∆s when both are measured in the same

direction (collinear).

The amount of work δWmech done in moving through a

differential distance ~ds against an external force ~Fext is:

⇒ δWmech = ~Fext . ~ds

⇒ Wmech =∫~S2

~S1

~Fext . ~ds

T746

Power ( _W ) is the time rate at which work is done on or by asystem.⇒ δW ≡ _Wdt

⇒ _Wmech = ~Fext . ~V

⇒ Wmech =∫t2

t1

_Wdt =∫t2

t1~Fext . ~Vdt

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Work & Heat

Acceleration & Gravitational Work

Acceleration work (Wacc) is the work done on the system to

change its velocity.

⇒ Wacc =∫t2t1

m d ~Vdt

· ( ~Vdt) =∫ ~V2

~V1m ~V · d ~V

⇒ Wacc,12 =mV 2

22 −

mV 21

2 = ∆KE

mV 2/2 ≡ translational kinetic energy KE.

Gravitational work (Wgrav ) is the work done against gravity to

change the elevation of a system.

⇒ Wgrav =∫t2t1−m~g · ~Vdt =

∫z2z1

mg dz

⇒ Wgrav ,12 = mgz2 − mgz1 = ∆PE

mgz ≡ gravitational potential energy PE.

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Work & Heat

Shaft Work

Differential amount of shaft work (δWshaft) done on the system

by the external force F moving through a differential distance

ds = rdθ can be written as:

⇒ δWshaft = Fds =(

τr

)

(rdθ) = τdθ

⇒ _Wshaft =δWshaft

dt= τω

τ ≡ applied torque, τ = Fr

ω ≡ rotational speed, ω = dθ/dt

T747

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Work & Heat

Thermodynamic Work & Heat

Work

is an energy transfer across the system boundary in an organized from

such that its sole effect could be the raising of a weight.

Heat

is energy in transition from one body or system to another solely

because of a temperature difference between the systems.

m + ve

W + ve Q + veT748

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Work & Heat

T010

The magnitudes of heat and work depend on the arbitrary selection of

boundaries between interacting systems.c


Work & Heat

Comparison of Heat & Work

T023

An example of the difference between heat and work.

Heat and work are both transient phenomena. Systems never

possess heat or work. These two are the only mechanisms by

which energy can be transferred across the boundary of a closed

system.

Both heat and work are boundary phenomena. Both are observed

only at the boundary of the system, and both represent energy

crossing the boundary.

Both heat and work are path functions and inexact differentials.

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Work

General Work Expressions

Thermodynamic work is generalized to include all forms of work,

and a generalized force Fk and generalized displacement dδk can

be identified:

Wk =

∫Fkdδk

A general system could have many possible work modes, so a

general work expression is:

W = Ws + Wb + Wf + · · · =∑

Wk

Ws ≡ shaft work: rotary useful work

Wb ≡ boundary work: due to expansion/compression of system

Wf ≡ flow work: interaction required for the mass to cross CS

We ≡ electrical work

· · ·

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Work

Wb

Vi

Ve

Ws

P

P

Psi

se

TikZ002

T462

Flow work, Wf is associated with mass crossing the CS.Wf ,i = +(PAi )Si = PVi

Wf ,e = −(PAe )Se = −PVe

⇒ Wf = Wf ,i +Wf ,e = P(Vi −Ve )

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Work

Boundary Work, Wb

P

P

d x

d A

TikZ004

Force acting on an element dA of CS = PdA

Work performed as dA recedes a distance dx =~Fext . ~ds = −(PdA)dx

Work done = δWb = −∫ ∫

A

PdAdx = −P∫ ∫

A

dAdx = −PdV

δWb = −PdV ⇛ Wb = −∫2

1 PdV for reversible process

dV is the change in volume represented by the volume enclosed between the

full and the broken curves in figure.c


Work

Compression & Expansion Work

T460

δWb = ~Fext .d~s = Fextds (for compression)

= Fext

(

−dV

A

)

=Fext

A(−dV )

= −PdV

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Work

i

f

a

b

V

P

2P0

P0

V0 2V0

TikZ005

Wi→f =

Wif = −32PoVo

Wia + Waf = −2PoVo + 0 = −2PoVo

Wib + Wbf = 0 − PoVo = −PoVo

Work done by a system depends not only on the initial and final states

but also on the intermediate states =⇒ path function.

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Work

T066

P = f (V ): not specified.

T067

P = Patm

W12 = −

∫ 2

1PdV = −Patm(V2 − V1)

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Work

Process involving a change in volume with W = 0

T022

Work can only be identified at the system boundary.

If the gas & the vacuum space is considered as system: no work is

done as no work can be identified at the system boundary.

If the gas is the system: there is a change in volume, but no

resistance at the system boundary as the volume increases, and so

no work is done in the process of filling the vacuum.

c


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Basic Concepts & Terminologyteacher.buet.ac.bd/zahurul/ME6101/ME6101_Basics.pdf · The Path of a process is the succession of states through which the system passes. ... Basic Concepts