Chap 4 Thermodynamics

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GENERAL ENGINEERING & APPLIED SCIENCES THERMODYNAMICS CHAPTER 4

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THERMODYNAMICS

Thermodynamics is the branch of physics that deals with the conversions from one to another of various forms of energy and how these affect temperature, pressure, volume, mechanical action, and work. I. THERMODYNAMIC SYSTEM A thermodynamic system or simply a system refers to a definite quantity of matter most often contained within some closed surface chosen for study. A surrounding is the mass or region outside the system. A boundary is the real or imaginary surface that separates the system from its surroundings. It can be either fixed or movable KINDS OF THERMODYNAMIC SYSTEM

Closed system also known as Control mass is a system consisting of a fixed amount of mass, and no mass can cross its boundary. That is, no mass can enter or leave a closed system. However, energy in the form of heat or work, can cross the boundary.

Isolated system is a system in which neither mass nor energy is allowed to

cross the boundary.

Open system also known as Control volume is a system in which mass is allowed to cross the boundary.

PROERTIES OF A SYSTEM A property is any quantity, which serves to describe a system. It can be divided into two general types: Intensive property is one, which does not depend on the mass of the system

such as temperature, pressure, density, and velocity. Extensive property is one, which depends on the mass of the system such as

volume, momentum, and kinetic energy.


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GEAS GENERAL ENGINEERING & APPLIED SCIENCES GEAS GEAS

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STATE AND EQUILIBRIUM The state of system is its condition as described by giving values to

its properties at a particular instant. At a given state, all properties of a system have fixed values. If the value of even one property changes, the state of the system will change to a different one.

Equilibrium implies a state of balance. Under equilibrium state, there

are no unbalanced potentials or driving forces within the system. A system in equilibrium experiences no changes when it is isolated from its surroundings.

A system is in, Thermal equilibrium if the temperature is the same throughout the

entire system Mechanical equilibrium if there is no change in pressure at any point of

the system with time. Phase equilibrium if the system involves two phases, and the mass

of each phase reaches equilibrium level and stays there.

STATE VARIABLES

Temperature Temperature is a measure of the intensity of heat of a substance.

The Zeroth Law of Thermodynamics If two systems are in thermal equilibrium, they must be at the same temperature. If both systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.

TEMERATURE SCALES

☞ Celsius scale, ( oC) : (A. Celsius, 1701-1744) SI unit Freezing and Boiling points are assigned to 0 and 100oC, respectively.


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GENERAL ENGINEERING & APPLIED SCIENCES GEAS GEAS CHAPTER 4 - Thermodynamics

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☞ Fahrenheit scale, (oF): (G. Fahrenheit, 1686-1736)

English unit Freezing and Boiling points are assigned to 32 and 212oF, respectively.

THERMODYNAMIC TEMPERATURE SCALES

☞ Kelvin, (K): (Lord Kelvin, 1824-1907) SI unit

☞ Rankine, (R): (William Rankine, 1820-1872) English unit

CONVERSION FORMULAS:

( )5C F 32 K C 273

99F C 32 R F 4605

° = − ° = ° + °

° = + ° = ° + °

Celsius (formerly the centigrade)FahrenheitKelvinRankine

====

Where C

F

K

R

TEMPERATURE CHANGE

( )

5Δ Δ Δ Δ99Δ Δ Δ Δ5

K C C F

R F C

T T T T

T T F T T

= =

= ° =


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Density The mass density of a material is defined as the mass per unit volume of the material:

mmV

ρ =

The weight density of a material is defined as the weight per unit volume of the material:

wWV

ρ =

density massvolume weight

mWhere m

V W

ρ = =

= =

Specific Volume Specific volume is the volume per unit mass.

1V

mν = =

ρ

specific volume volumemass mass density

ν = == ρ =

Where V

m

Specific Gravity (relative density)

The specific gravity of a substance is the ratio of the density of the substance to the density of some standard substance. The standard is usually water (@ 4oC) for liquids and solids, while for gasses, it is usually air.

s tandard

sp gr ρ=ρ

Pressure Pressure is force per unit area.

( )2N/mFP ,A

=

2

force (N)area (m )

=

=

Where F

A

Note: 21Pa 1N/m=


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GAUGE PRESSURE

Gauge pressure is the amount by which the absolute pressure exceeds atmospheric pressure.

gauge abs atmP P P= − Where:

5

2

11 013 1014 77607601 013

gauge

abs

atm

P gauge pressure

P absolute pressureP atmospheric pressure

atm. Pa. lb / in (psi)

mm Hgtorr

. bar

=

=

=

=

= ×

====

Pascal’s Principle The pressure applied to a confined fluid increases the pressure throughout by the same amount.

Formula:

1 21 2

1 2

F FP PA A

OR= =

F1 F2


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HEAT and ENTROPY

HEAT, (Q)

Heat is a form of transferred energy that arises from the random motion of molecules. TRANSMISION OF HEAT There are three modes of transfer of heat:

Conduction in which heat transfer takes place from molecule to molecule through a body or through bodies in contact.

Convection in which the transfer is due to the motion of molecules of the medium.

Radiation in which the heat transfer takes place without any intervening medium.

Latent Heat is the amount of heat necessary to change the phase of the system without changing its temperature.

( )L fusion or vaporization

Q m H= ± Note: Use ( )+ → if heat is absorbed by the substance (substance melts) Use ( )− → if heat is released by the substance (substance freezes)

heat neededmasslatent heat (fusion or vaporization)

===

Where Q

m

H

Latent Heat of Fusion is the heat that is necessary to change a unit mass of a substance from solid to liquid state at its melting point. For ice at its melting point:

fH 80 cal / gm

144 BTU/ lb334 kJ / kg

=

==


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Latent Heat of Vaporization is the heat required to change a unit mass of a substance from liquid to vapor state. For water at its boiling point:

vH 540 cal / gm

970 BTU/ lb2257 kJ / kg

=

==

Sensible Heat is the amount heat necessary to change the temperature of

the system without changing its phase.

Sensible Heat Equation:

SQ mc T= Δ

heat neededspecific heat of the substancechange in temperature

==

Δ =

Where Q

c

T

Specific Heat is the amount of heat required to raise the temperature of 1

gm of the substance by 1oC. For water and ice:

1 cal/gm C

0.5 cal/gm Cw

i

cc

= ⋅ °

= ⋅ °

THE TOTAL HEAT entering a substance is the sum of the heat that changes the phase of the substance (latent heat) and the heat that changes the temperature of the substance (sensible heat). Total Heat Equation:

t L SQ Q Q= +

sensible heatlatent heat

s

l

Where Q

q

=

=


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ENTROPY, (S) Absolute entropy is a measure of the energy that is no longer available to perform useful work within the current environment. Other definition is that it is the measure of “randomness” or “ disorder” of the system. Entropy Equation:

K

QST

=

entropy, (J/K)heat, (J)temperature , (K)

===

Where S

Q

T

ENTHALPY AND

INTERNAL ENERGY

Internal Energy, (U) The internal energy (U) of a system is the total energy content of the system. It is the sum of the kinetic, potential, chemical, electrical, nuclear, and all other forms of energy possessed by the atoms and molecules of the system. ENTHALPY Enthalpy represents the total useful energy of a substance. Useful energy consists of two parts:

The internal energy, u Flow energy also known as flow work, pV

Enthalpy Equation:

H U pV= +

enthalpy internal energy pressure volume

====

Where H

U

p

V


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The First Law of Thermodynamics is a statement of the law of conservation of energy. It states that: If an amount of heat flows into a system, then this energy must appear as increased internal energy for the system and/or work done by the system on its surroundings

THE FIRST LAW OF

THERMODYNAMICS

The First Law Equation

Total Energy Entering=Total Energy Leaving

ΔQ=ΔU+ΔW

ΔΔΔ Δ

heat flow into a systemchange in internal energy of the systemp V (work done by the system)

===

Where Q

U

W

Note: The work done by a system ( ΔW ) is positive if the system thereby loses energy to its surroundings. When the surroundings do work on the system so as to give it energy, (ΔW ) is a negative quantity. ( )W p VΔ = Δ

The First Law Equation and Thermodynamic Processes

For isobaric process: (Constant pressure)

An isobaric process is a process carried out at constant pressure. First Law Equation for Isobaric Process:

( )Q U p VΔ = Δ + Δ

ΔΔ

Δ

heat flow into a systemchange in internal energy of the system

p pressureV= change in volume

Where Q

U

===


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For isovolumic process: (constant volume) An isovolumic process is a process carried out at constant volume. First Law Equation for Isovolumic Process:

Δ Δ Δ 0 Δ 0since Q U ( W , V )= → = =

ΔΔ

heat flow into a systemchange in internal energy of the system

Where Q

U

==

Note that for an isovolumic (also called isochoric or isometric) process, any heat flows into the system appears as increased internal energy of the system.

For isothermal process: (constant temperature)

An isothermal process is a process carried out at constant temperature. First Law Equation for Isothermal Process:

Δ ΔQ W=

ΔΔΔ 0

heat flow into a systemwork done

since temperature is constant, )

Where Q

W

U

===

For ideal gas changing isothermally:

21 1

1

Δ Δ VQ W P V lnV

⎛ ⎞= = ⎜ ⎟

⎝ ⎠

For adiabatic process: (no heat flow)

An adiabatic process is a process in which no heat is transferred to or from the system.

0 Δ ΔU W= +

ΔΔΔ

0 (no heat flow into or from the systemwork donechange in internal energy

Where Q

W

U

===


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The second law of thermodynamics can be stated in three equivalent ways:

Heat energy flows spontaneously from hotter to a colder object, but not vice versa.

No heat engine that cycle continuously can change all its

input energy to useful work.

If a system undergoes spontaneous change, it will change in such a way that its entropy will increase or, at best, remain constant.

The THIRD law of thermodynamics states that The absolute entropy of a pure substances approaches zero as the absolute thermodynamic temperature approaches zero.

THE SECOND LAW OF

THERMODYNAMICS

THE THIRD LAW OF

THERMODYNAMICS

(Nernst Theorem)

.

Third Law equation:

lim sT 0K

0→

=


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PROCESSES

A process is any change that a system undergoes from one equilibrium state to another. A path refers to the series of states through which a system passes during a process.

☞ A reversible process is one that is performed in such a way that at the end of the process, both the system and the local surroundings can be restored to their initial states. A process that does not meet these requirements is said to be irreversible. A reversible process must be a quasiequilibrium process and is subject to the following restrictions:

No friction exists. Heat transfer is due only to an infinitesimal temperature difference Unrestrained expansion does not occur There is no mixing There is no turbulence There is no combustion or chemical reaction

TYPES OF PROCESSES

Isobaric process is process by which the state variable of a system is changed while the pressure is held constant.

ISOVOLUMIC PROCESS also known as isometric or isochoric process is a process

carried out at constant volume.

Adiabatic process is one in which no heat or other energy is transferred to or from the system. ☞ Isentropic process is an adiabatic process in which there is no change

in the system entropy.

☞ Throttling process is an adiabatic process in which there is no change in the system enthalpy but for which there is a significant pressure drop.

Isothermal process is a process carried out at constant temperature.


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POLYTROPIC PROCESS A polytropic process is one that obeys the polytropic equation of state ( ) ( )1 1 2 2

n np V p V=

pressurevolumepolytropic exponent

Where pVn

===

If:

01

Isobaric processIsothermal processIsentropic processIsometric process

n ;n ;n k ;n ;

==== ∞

The polytropic specific heat, c

n v

n

n kc cn 1

Q mc T

−⎛ ⎞= ⎜ ⎟−⎝ ⎠= Δ


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CYCLES

A cycle is a series of processes that eventually brings the system back to its original condition.

THERMAL EFFICIENCY (EFFICIENCY OF A HEAT ENGINE) The thermal efficiency of a power cycle is defined as the ratio of the useful work output to the supplied input energy.

thermalnet

input

Wnet work output

energy input Qη = =

In terms of heat variables:

thermalin out

in

Q Q

Q

−η =

THE CARNOT CYCLE The Carnot cycle is the most efficient power cycle . The efficiency of a

Carnot cycle is the maximum possible for any power cycle Efficiency Equation:

hgh low low

high high

T T T1T T−

η = = −

efficiency temperature in Kelvin

Where

T

η ==

Note that the efficiency is increased by rising the temperature THIGH at which heat is added or by lowering the temperature TLOW at which heat is rejected.


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REFRIGERATION

Refrigeration is the process of transferring heat from a low -temperature area to a high- temperature area. Since heat flows spontaneously only from high to low temperature areas according to the second law of thermodynamics, refrigeration needs an external energy source to force the heat transfer to occur. This energy source is a pump or compressor that does work in compressing the refrigerant. It is necessary to perform this work on the refrigerant in order to get it to discharge energy to the high-temperature area.

COEFFICIENT OF PERFORMANCE, (COP) The Coefficient of Performance (COP) is defined as the ratio of the useful energy transfer to the work input.

in in

in out in

Q QCOPW Q Q

= =−

ENERGY EFFICIENCY RATIO, (EER) The Energy Efficiency Ratio (EER) is defined as the useful energy transfer in BTU/hr divided by the input power in watts.

in

in

QEERP

=

energy efficiency ratioenergy input in BTU/hrpower input in watts

in

in

Where eer

Q

P

==

=


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THE GAS LAWS

IDEAL GAS LAW

The absolute pressure P of n kilomoles of gas contained in a volume V is related to the absolute temperature T by

PV nRT=

universal gas constantabsolute pressureabsolute temperaturenumber of moles

= m/M

====

Where R

P

T

n

Values of R in different units:

f

8.314 J/mol K=1.986 BTU/mol R=1545 ft-lb /mol R

= ⋅⋅ °⋅ °

R

SPECIAL CASES OF THE IDEAL GAS LAW

• Boyle’s Law (n, T constant): constantPV = At constant temperature and number moles, the volume gas varies inversely with the pressure. In other words, an increase in pressure is accompanied by a decrease in volume and vice versa. 1 1 2 2PV PV=

Charles’ Law (n, P constant): constantVT=

At constant pressure and number of moles, the volume of an ideally behaving gas is directly proportional to the Kelvin temperature. In other words, gas volume increases when the temperature is raised.

1 2

1 2

V VT T

=


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• Gay – Lussac’s Law (n, V constant): constantPT=

1 2

1 2

P PT T

=

• The Combined Gas Law

1 1 2 2

1 2

p V p VT T

=

STANDARD CONDITIONS (S.T.P.):

5

T 273.15 K 0 Cp 1.013 10 Pa 1 atm= = °

= × =

Note: Under standard conditions, 1 kmol of ideal gas occupies a volume of 22.4 m3.

DALTON’S LAW OF PARTIAL PRESSURE The total pressure of a mixture of ideal, nonreactive gasses is the sum of the partial pressures of the component gases.

t 1 2 3 nP p p p ... P= + + + +

t

1 2 3 n

Where P total pressure of the mixturep , p , p ,...,p partial pressure of component gases

=

=

AVOGADRO’S LAW At equal volume, under the same pressure and temperature conditions, gases contain the same number of molecules.

1 1 1

2 2 2

m M Rm M R

= =

massmolecular weightgas constant

Where mMR

===


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TEST – 4

1. A “closed system” is also known as A. control mass* B. isolated system C. control volume D. control boundary 2. A “closed system” wherein even energy is not allowed to cross the

boundary is called an A. control volume B. isolated system* C. control mass D. control boundary 3. An “open system” is also known as

A. control volume* B. control boundary C. control mass D. isolated system

4. The boundary of a control volume system is called a A. control surface* B. control point C. control area D. control line

5. Mass per unit volume is A. weight B. pressure

C. density* D. specific gravity


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6. The ratio of the density of a substance to the density of some standard substance at a specified temperature is called A. specific gravity * B. relative weight C. elasticity D. specific density

7. The reciprocal of density (i.e. volume per unit mass) is called

A. specific gravity B. specific volume* C. bulk modulus D. specific weight

8. Properties that are independent of the size of the system, such as temperature, pressure, and density are called

A. intensive properties*

B. extrinsive properties C. extensive porperties D. extrinsic properties 9. Properties that are dependent on the size or extent of the system such

as mass, volume, and total energy are called

A. intensive properties B. intrinsic properties C. extensive properties* D. chemical properties 10. The area under the process curve on a T-S diagram represents

A. heat transfer* B. temperature change C. work D. entropy

11. An isentropic process on a T-s diagram is easily recognized as a

A. horizontal line segment B. vertical line segment* C. oblique line segment D. parabola


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12. The h-s diagram is also called a A. Argand diagram B. Euler diagram C. Mollier diagram* D. Grolier diagram

13. A pure substance at absolute zero temperature is in perfect order, and its entropy is zero. This is best known as A. The first law of thermodynamics B. The second law of thermodynamics C. The third law of thermodynamics* D. The Zeroth law of thermodynamics

14. The condition in which the temperature is the same throughout the

entire system is called:

A. thermal equilibrium* B. phase equilibrium C. mechanical equilibrium D. chemical equilibrium 15. The condition in which there is no change in pressure at any point of the

system with time.

A. thermal equilibrium B. phase equilibrium C. mechanical equilibrium* D. chemical equilibrium 16. The condition in which the mass of each phase reaches an equilibrium

level and stays there.

A. phase equilibrium* B. chemical equilibrium C. thermal equilibrium D. mechanical equilibrium


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17. A condition in which the chemical composition of the system does not change with time.

A. phase equilibrium

B. chemical equilibrium* C. thermal equilibrium D. mechanical equilibrium 18. Any change that a system undergoes from equilibrium state to another is

called a

A. process* B. conversion C. state D. cycle

19. A series of states through which a system passes during a process is called the ______________of the process.

A. path*

B. condition C. state D. course 20. A process during which, the temperature T remains constant is called

A. isothermal process* B. isometric process C. isobaric process D. isochoric process 21. A process during which, the pressure P remains constant is called

A. isothermal process B. isobaric process* C. isovolumic process D. isometric process 22. A process during which, the specific volume V remains constant is called A. isometric B. isochoric C. isovolumic D. all of the above*


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23. Who coined the term energy in1807?

A. William Thomson B. Thomas Young* C. Lord Kelvin D. Rudolph Clausius 24. The energy that a system possesses as a result of its motion relative to

some reference frame is called

A. kinetic energy* B. spin energy C. potential energy D. elastic energy 25. The energy that a system possesses as a result of its elevation in a

gravitational field is called

A. kinetic energy B. gravitational energy C. potential energy* D. mechanical energy 26. Who wrote the first thermodynamic textbook in 1859?

A. Lord Kelvin B. William Rankine* C. Thomas Young D. Rudolph Clausius 27. It states that if two bodies are in thermal equilibrium with a third body,

they are also in thermal equilibrium with each other.

A. first law of thermodynamics B. zeroth law of thermodynamics * C. third law of thermodynamics D. second law of thermodynamics 28. Pressure below atmospheric pressure are called

A. absolute pressure B. vacuum pressure* C. standard pressure D. reference pressure


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29. The pressure applied to a confined fluid increases the pressure throughout by the same amount. This is best known as

A. Pascal’s principle *

B. Archimedes principle C. Torricelli’s principle D. Amagat’s law 30. A device used to measure small and moderate pressure differences is

called A. hygrometer B. manometer* C. nozzle D. diffuser

31. Atmospheric pressure is measured by a device called

A. barometer* B. manometer C. thermometer D. goniometer

32. The pressure relative to absolute vacuum is called

A. standard pressure B. absolute pressure* C. vacuum pressure D. atmospheric pressure

33. The difference between the absolute pressure and the local atmospheric

pressure is called the

A. relative pressure B. gauge pressure* C. vacuum pressure D. standard pressure

34. A liquid that is about to vaporize is called

A. saturated vapor B. plasma C. superheated vapor D. saturated liquid*


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35. A vapor that is about to condense is called

A. saturated vapor* B. plasma C. super heated vapor D. saturated liquid

36. At a given pressure, the temperature at which pure substance changes

phase is called

A. critical temperature B. saturation temperature* C. triple point D. kindling temperature

37. At a given temperature, the pressure at which a pure substance changes

phase is called

A. critical pressure B. saturation pressure* C. absolute pressure D. vacuum pressure

38. The amount of energy absorbed during melting and is equivalent to the

amount of energy released during freezing is called

A. latent heat of vaporization B. melting energy C. latent heat of fusion* D. specific heat

39. The amount of energy absorbed during vaporization and is equivalent to

the amount of energy released during condensation is called

A. latent heat of vaporization* B. melting energy C. latent heat of fusion D. specific heat

40. A process during which there is no heat transfer is called

A. isentropic process B. isothermal process C. adiabatic process* D. isometric process


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41. A process during which the entropy remains constant is called

A. isentropic process* B. isothermal process C. adiabatic process D. isometric process

42. The transfer of energy from the more energetic particles of a substance

to the adjacent less energetic ones as a result of interaction between particles is called

A. convection B. conduction* C. radiation D. emission

43. The transfer of energy between a solid surface and the adjacent fluid that

is in motion, and it involves the combined effects of conduction and fluid motion is called

A. convection* B. conduction C. radiation D. emission

44. The transfer of energy due to the emission of electromagnetic waves (or

photons) is called

A. convection B. conduction C. radiation* D. emission

45. The area under the process curve on a P-V diagram represents the

boundary

A. temperature B. pressure C. energy D. work*


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46. During actual expansion and compression process of gases, pressure and volume are often related by PVn=C, where n and C are constants. A process of this kind is called

A. isentropic process B. isochoric process C. polytropic process* D. adiabatic process

47. The idealized surface that emits radiation at a maximum rate is called a

A. blackbody* B. emitter

C. absorber D. radiator

48. In what form can energy cross the boundaries of a closed system? A. sound

B. heat* C. magnetic waves

D. light 49. A device that increases the velocity of a fluid at the expense of pressure

is called

A. nozzle* B. diffuser C. pressure exchanger D. manometer

50. A device that increases the pressure of a fluid by slowing it down is

called

A. nozzle B. diffuser* C. pressure exchanger D. manometer


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GG

1. H

m S

2. D

et

S

3. A

se

S

GEAGEAS

Heat of 2 x 104 melt. Calculate

Solution:

QST

2 10S273

S 73.26

ΔΔ =

×Δ =

Δ =

Determine the exhaust tempethe engine is 62

Solution:

max

max

max

1

1

0.5

= −

= −

=

η

η

η

A heat engine tsource in each efficiency of thi

Solution:

H

W 4Q 1233%

η = =

η =

SoIn

GEAS S

J is added to a the change in

40 J3K

J6 K

maximum possrature of 120°C20°C.

( )( )

cool

hot

TT

120 273 K620 273 K

56

+

+

takes 1200 J ofcycle and does engine?

400J 100%200J

×

olven The

181

ENERAL ENGINEE CHAP

a block of ice aentropy.

sible efficiency C, and the temp

f heat from thes 400 J of work

ed Prermod

ERING & APPLIED PTER 4 - Therm

L

at 0°C causing

of an automobperature of the

e high – temperk in each cycle

robledynam

SCIENCES odynamics

Loading Next Page

part of it to

bile engine with burning gas in

rature heat e. What is the

ems mics

h n


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4. A heat engine takes 1200 J of heat from the high – temperature heat source in each cycle and does 400 J of work in each cycle. How much heat is released into the environment in each cycle?

Solution:

H C

C H

W Q QQ Q W

1200J 400J800J

= −

= −

= −=

5. A steam turbine takes in steam at a temperature of 400OC and release

steam to the condenser at a temperature of 120OC. Calculate the Carnot efficiency for this engine.

Solution:

( ) ( )( )

H C

H

T T 100%T

400 273 120 273100%

400 273673K 393K 100%

673K41.6%

−η = ×

+ − += ×

+

−= ×

=

6. The tire of an automobile which has a volume of 0.65 m3 is inflated to a

gage pressure 250 kPa. Determine the mass of air in the tire if the temperature is 20°C.

Solution:

( ) ( )( )

32

PVmRT

kJ N-mR(air) 0.287 287kg-K kg-KN250000 101325 0.65m

mmN-m287 293Kkg-K

m 2.72 kg

=

= =

+=

⎛ ⎞⎜ ⎟⎝ ⎠

=


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7. A steam turbine takes in 500 kJ of heat in each cycle. If the efficiency of this turbine is 41.6 %, what is the maximum amount of work that could be generated by the turbine in each cycle?

Solution:

( )

H

H

WQ

W Q0.416 500 kJ208 kJ

η =

= η

=

=

8. Calculate the increase in internal energy, if a 0.95-lbm object is travelling

at a rate of 250 ft/s to enter a viscous liquid and essentially brought to rest before it strikes the bottom. Consider the object and liquid as the system, and assume the change in potential energy is negligible.

Solution:

1 2

2 21 1 2 2

2

2 22 1 1 2

E E1 1mV U mV U2 2V 0

1 1U U U mV mV2 2

=

+ = +

=

− = Δ = −

1U 0.95 lbm2

Δ =1slug

32.2 lbm×

2ft250s

U 922 ft-lbf

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

Δ = 9. What is the coefficient of performance of a carnot refrigerator which

delivers heat to a reservoir at 32°C and removes heat from a reservoir at -10°C?

Solution:

cold hot

coldhot cold

10 273 263 K, 32 273 305 KT TTCOP

T T263COP

305 263COP 6.3

= − + = = + =

=−

=−

=


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10. Determine the difference in weight of air when the temperature is 93°F during summer and winter when the temperature is 10°F in a room which measures 30x100x20 ft. The pressure is 14 psia.

Solution:

( )

( ) ( )

( )

( ) ( )

23

2

summer

23

2

winter

PVmRT

ft-lbfR(air) 53.3 lbm-R

12inlb14 30 100 20 ft1ftin

m 4103.8-lbmft-lbf53.3 93 460 Rlbm-R

12inlb14 30 100 20 ft1ftin

m 4828.5-lbmft-lbf53.3 10 460 Rlbm-R

m W

=

=

⎛ ⎞⎛ ⎞⎜ ⎟× × ×⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠= =+

⎛ ⎞⎛ ⎞⎜ ⎟× × ×⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠= =+

Δ = Δ = 4828.5-lbm 4103.8-lbmW 724.7 lbf

−Δ =

11. The initial temperature of the pressurized can which contains air at a

gage pressure of 38psi, is 75°F. What will be the temperature when the gage pressure reaches 205 psi, the can will burst?

Solution:

( ) ( )( ) ( )

( ) ( )

1 2

1 2

2 12

1

2

2

2

P PT T

P TTP

205 14.7 144 75 460T

38 14.7 144

T 2230 R 460T 1770 F

=

=

+ +=

+

= −

= °


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12. Calculate the work done (ft-lbf) in converting water having 0.0256 ft3 volume into steam of volume 2.25 ft3 at constant pressure of 305 lb/in2.

Solution:

( )2

32

3

W P V

lb 12inW 305 2.25 0.0256 ft1ftin

W 97.7 10 ft-lbf

= Δ

⎛ ⎞⎛ ⎞⎜ ⎟= × −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

= ×

13. Determine the compression ratio of an Otto cycle with an efficiency of

55% and r = 1.5.

Solution:

r 11

2

1.5 11

2

12

Otto cycle:11

VV

10.55 1V

V

V 5 compression ratioV

−

−

= −⎛ ⎞⎜ ⎟⎝ ⎠

= −⎛ ⎞⎜ ⎟⎝ ⎠

⎛ ⎞ = ⇒⎜ ⎟⎝ ⎠

η

14. A Carnot engine takes in 110 calories of heat with high-temperature

reservoir at 130°C in each cycle, and gives up 78 calories to the low-temperature reservoir. What is the temperature of the latter reservoir?

Solution:

( )

1 1

2 2

22 1

1

2

Q TQ T

QT TQ

78T 150 273 300 K 27 C110

=

=

⎛ ⎞= + = = °⎜ ⎟⎝ ⎠


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15. A vertical, frictionless piston cylinder device containing gas, has a mass of 10 kg with a cross-sectional area of 10 cm2 and is pulled with a force of 100N, calculate the pressure inside if the atmospheric pressure is 101 kPa.

Solution:

( )

( )

atm

atm

atm

atm

232

2

3

PA F mg P A

P P A mg F

mg FP PA

mg FP PA

m10kg 9.8 100NsP 101 10 Pa

1m10 cm100cm

P 99 10 PaP 99 kPa

+ = +

− = −

−− =

−= +

⎛ ⎞× −⎜ ⎟⎝ ⎠= × +⎛ ⎞⎛ ⎞⎜ ⎟× ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

= ×=

16. Determine the mass of air when the pressure is 20 psi and the

temperature is 80°F in a closed chamber with dimensions of 30ft x 20 ft x 15 ft. Assume air to be an ideal gas. R(air) = 53.3 ft-lb/lbm-R.

Solution:

( )

( )

23

2

PVmRT

lb 12in20 30 20 15 ft1ftin

mft-lb53.3 80 460 R

lbm-Rm 901 lbm

=

⎛ ⎞⎛ ⎞⎜ ⎟× × ×⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠=⎛ ⎞ +⎜ ⎟⎝ ⎠

=


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17. What is the absolute pressure for a system if the gauge pressure is 1 MPa and the barometric pressure (atmospheric pressure) is 103 kPa.

Solution:

abs atm gage3 6

abs

abs

P P P

P 103 10 Pa 1 10 PaP 1.103 MPa

= +

= × + ×

=

18. If gallium liquid is employed in a barometer instead of mercury at 35°C.

Determine the height of a column of gallium sustained in the barometer at 1 atm pressure. Note that the density of liquid gallium is 6.09 g/cm3 at 35°C, and the density of mercury is 13.6 g/cm3.

Solution:

( )Ga gρ ( ) ( ) ( )Ga Hgh g= ρ ( ) ( )( ) ( )

( )

Hg

Hg HgGa

Ga

Hg

Hg 3

3Ga

3

h

hh

1 atm pressure h 760 mmHg 76 cmHg

g13.6cmg13.6 76 cmHg

cmh 169.7 cmGa 1697 mmGag6.09

cm

=

= = =

=

⎛ ⎞⎜ ⎟⎝ ⎠= = =

⎛ ⎞⎜ ⎟⎝ ⎠

ρ

ρ

ρ

19. A piston weighing 5.2 kg has a cross-sectional area of 400 mm2. What is

the pressure exerted by the piston on the gas in the chamber? Solution:

( ) ( )2

22

FPA

5.2kg 9.8m smgP

A 1m400mm1000mm

P 127 kPa

=

==⎛ ⎞⎛ ⎞⎜ ⎟× ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

=


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20. The volume of the container is 0.5 m3 which holds oxygen at 70°C and 30 bars. How much oxygen in the container if the atmospheric pressure is 1.013 bar?

Solution:

( )

( ) ( )

( )( )

2

2 3

PVmRT

R 8.314 J mol-KRMolar mass O 1kg2 16g

1000gN101325

m30 1.013 bar 0.5m1barm 8.8kg8.314 J mol-K 70 273 K

1kg2 16g1000g

=

= =⎛ ⎞

×⎜ ⎟⎝ ⎠

+ ×= =

+⎛ ⎞

×⎜ ⎟⎝ ⎠

21. A cylinder containing 75 lbm of carbon dioxide, the pressure is 25psig at

240°F. Find the volume of the cylinder. R(carbon dioxide) = 35.13 ft-lbf/lbm-R.

Solution:

( ) ( )

( )2

2

3

mRTVP

ft-lb75lbm 35.13 240 460 Rlbm-RV

lb 12in14.7 251ftin

V 322.6 ft

=

⎛ ⎞ +⎜ ⎟⎝ ⎠=

⎛ ⎞+ × ⎜ ⎟⎝ ⎠

=


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22. What is the specific volume of Argon gas in a vessel having a pressure of 150 kPa at 20°C. Ar = 39.9amu.

Solution:

( )

( )

3

3

3

3

PV mRTJ8.314 R mol-KR(Argon) gMolar mass 39.9 mol

J JR(Argon) 0.208 0.208 10g-K kg-K

V RTSpecific Volumem P

J0.208 10 20 273 Kkg-K

Specific Volume150 10 Pa

mSpecific Volume 0.407kg

−

=

= =

= = ×

= =

⎛ ⎞× +⎜ ⎟

⎝ ⎠=×

=


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23. A container having a volume of 70.85L contains oxygen gas at a pressure 861.6kPa when the temperature is 24°C. Oxygen leaks from the drum until the pressure drops to 689.3 kPa, while the temperature remains constant. How much oxygen leaked out of the container?

Solution:

( ) ( )( )

( ) ( )

1 1 1

1 11

1

1

1

2 2 2

2 22

2

2

Initial : P 861.6kPa,V 70.85L, T 24P VnRT

L-kPaR 8.314mol-K

861.6kPa 70.85Ln

L-kPa8.314 24 273 Kmol-K

n 24.72 molsFinal:P 689.3kPa,V 70.85L, T 24

P VnRT

689.3kPa 70.85Ln

L-kPa8.314mol-K

= = =

=

=

=⎛ ⎞ +⎜ ⎟⎝ ⎠

=

= = =

=

=⎛⎜⎝

( )

( )

2

leaked 1 2

leaked

leaked 2

leaked 2 2

24 273 K

n 19.78 molsAmount of oxygen leaked out:n n n 24.72 mols 19.78 molsn 4.94 mols

2 16gm O 4.94 mols

1molm O 158g O

⎞ +⎟⎠

=

= − = −

=

= ×

=


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24. The initial volume of the air inside a chamber is 0.028 m3 at a pressure of 10.3 MPa. It is heated and the volume is changed to 0.227 m3. Consider the expansion process is quasi-static and given by the relation PV1.4 = C, find the total work done.

Solution:

( ) ( )

21 2

11.4

1.4

1.4 1.41 1 2 2

1.4 1.4

21 2

12

1 2 1.412

1 2 1.410.227 0.227

1.41 2 1 11.4 1.40.028 0.028

0.2271.461 2 1.40.028

1 2

W PdV

PV CCP

V

P V P VP

V V

W PdV

CW dVV

dVWV

dV dVW C P VV V

dVW 10.3 10 Pa 0.028V

W 408.832 kJ

−

−

−

−

−

−

−

=

=

=

= =

=

=

=

= =

= ×

=

∫

∫∫∫∫ ∫

∫

Chap 4 Thermodynamics

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Transcript of Chap 4 Thermodynamics