Chap 4 Thermodynamics

CHAPTER

4

THERMODYNAMICS

GENERAL ENGINEERING & APPLIED SCIENCES

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



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. system. However, energy in the form of heat or work, can cross the boundary.



is a system in which neither mass nor energy is allowed to cross the boundary.



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


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.

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.

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 ☞

o

Celsius scale, ( C) :

(A. Celsius, 1701-1744)

 SI unit  Freezing and Boiling points are assigned to 0 and 100oC,

respectively.


GEAS


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.

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.

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 ☞

o

Celsius scale, ( C) :

(A. Celsius, 1701-1744)

 SI unit  Freezing and Boiling points are assigned to 0 and 100oC,

respectively.


GEAS GEA

CHAPTER 4 -

Thermodynamics

GENERAL ENGINEERING & APPLIED SCIENCES ☞

o

Fahrenheit scale, ( F):

(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: 5

°C = (F − 32° )

K = °C + 273°

°F = C + 32°

R = °F + 460°

9 9 5

Where



Celsius us (for (forme merly rly the centi centigr grade ade)) = Celsi F = Fahrenheit K = Kelvin R = Rankine C

TEMPERATURE CHANGE ΔTK

= ΔTC

ΔTC

=

ΔTR

= ΔT ( °F )

ΔTF

=

5 9 9 5

ΔTF ΔTC


GEAS 


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

ρm =

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

ρw =

Where



ρm = density V = volume

m = mass W

= weight

Specific Volume Specific volume is the volume per unit mass.

ν= Where



V

V m

1

=

ρ

ν = specific volume m = mass

= volume ρ = mass density V

Specific Gravity

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 o usually water (@ 4 C) for liquids and solids, while for gasses, it is usually air. sp gr = 

ρ ρstandard

Pressure Pressure is force per unit area. F P = , N/m 2 A

(

Where

)

= force (N) 2 A = area (m ) F

1 Pa = 1 N/ m2


GEAS GEA

CHAPTER 4 -

Thermodynamics


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

Pgauge

= Pabs − Patm

Where:

Pgauge Pabs Patm

= gauge pressure = absolute pressure = atmospheric pressure = 1 atm = 1.013 × 10 Pa = 14.7 lb / in (psi) = 760 mm Hg = 760 torr = 1.013 bar 5

2

The pressure applied to a confined fluid increases the pressure throughout by the same amount.

F1

F2

Formula:

P1

= P2

OR

F1 A1

=

F2 A2


GEAS


HEAT and ENTROPY HEAT, (Q)

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  Convection  Radiation



in which heat transfer takes place from molecule to molecule through a body or through bodies in contact. in which the transfer is due to the motion of molecules of the medium. 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. QL

= ± m (H) fusion or vaporization

Use ( + ) → if heat is absorbed by the substance (substance melts) Use ( − ) → if heat is released by the substance (substance freezes) Where

= heat needed m = mass H = latent heat (fusion or vaporization) Q

Latent Heat o f 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:

Hf = 80 cal / gm

= 144 BTU/ lb = 334 kJ/kg


GEAS GEA

CHAPTER 4 -

Thermodynamics


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

Hv



= 540 cal / gm = 970 BTU/ lb = 2257 kJ/kg

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

QS Where

= mcΔT

= heat needed c = specific heat of the substance ΔT = change in temperature Q

Specific Heat is the amount of heat required to raise the temperature of 1 o gm of the substance by 1 C.

For water and ice: c w = 1 cal/gm ⋅ C ° ci

= 0.5 cal/gm ⋅ C °

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:

Qt

Where

Qs ql

= QL + QS

= sensible heat = latent heat


GEAS


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:

S

Where

=

Q TK

= entropy, (J/K) Q = heat, (J) T = temperature , (K) S

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 Where

= enthalpy U = internal energy p = pressure V = volume H


GEAS GEA

CHAPTER 4 -

Thermodynamics


THE FIRST LAW OF THERMODYNAMICS

The 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 Equation Total Energy Entering=Total Energy Leaving Δ Q= Δ U+ Δ W

Where

= heat flow into a system ΔU = change in internal energy of the system ΔW = pΔV (work done by the system) ΔQ

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. Δ W = p ( ΔV )  

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:

ΔQ = ΔU + p ( ΔV ) Where

= heat flow into a system ΔU = change in internal energy of the system p = pressure

ΔQ

ΔV=

change in volume


GEAS 


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

Where

= ΔU

→ (ΔW = 0,

since ΔV

= 0)

= heat flow into a system ΔU = change in internal energy of the system

ΔQ

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: ΔQ

Where

= ΔW

= heat flow into a system ΔW = work done ΔU = 0, since temperature is constant ) ΔQ

For ideal gas changing isothermally: ΔQ

⎛V ⎞ = ΔW = P V ln ⎜ ⎟ ⎝V ⎠ 2

1

1

1



For adiabatic process: (no heat flow) An adiabatic process is a process in which no heat is transferred to or from the system. 0

Where

= ΔU + ΔW

= 0 (no heat flow into or from the system ΔW = work done ΔU = change in internal energy ΔQ


GEAS GEA

CHAPTER 4 -

Thermodynamics


THE SECOND LAW OF THERMODYNAMICS

The ways:

can be stated in three equivalent



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 (Nernst Theorem)

.

The

states that

The absolute entropy of a pure substances approaches zero as the absolute thermodynamic temperature approaches zero.



Third Law equation: lims

=0

T →0K


GEAS


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 

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



also known as isometric or isochoric process is a process carried out at constant volume.



i s 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.

is a process carried out at constant temperature.


GEAS GEA

CHAPTER 4 -

Thermodynamics


POLYTROPIC PROCESS

A polytropic process is one that obeys the polytropic equation of state

n

n

p1 ( V1 ) = p2 ( V2 ) Where

p = pressure

= volume n = polytropic exponent

V

If: n=0;

Isobaric process

n =1 ;

Isothermal process

n=k ;

Isentropic process

n = ∞;

Isometric process

The polytropic specific heat, c

⎛n−k ⎞ = cv ⎜ ⎟ ⎝ n −1 ⎠ Q = mc nΔT cn


GEAS


CYCLES

A 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.

ηthermal =

net work output energy input

=

Wnet Q input

In terms of heat variables:

ηthermal =



Q in

− Q out Q in

THE CARNOT CYCLE The Carnot cycle is the most efficient power cycle . The efficiency of a Carnot cycle is the maximum possible for an y power cycle Efficiency Equation:

η= Where

Thgh − Tlow Thigh

= 1−

Tlow Thigh

η = efficiency T = temperature in Kelvin

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.


GEAS GEA

CHAPTER 4 -

Thermodynamics


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. COP

=

Qin Win

=

Qin Qout

− Qin

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. EER

Where

eer Q in Pin

=

Qin Pin

= energy efficiency ratio = energy input in BTU/hr = power input in watts


GEAS


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 Where

= nRT

R = universal gas constant

= absolute pressure T = absolute temperature n = number of moles P

= m/M

R = 8.314 J/mol ⋅ K

=1.986 BTU/mol ⋅°R =1545 ft-lb f /mol ⋅°R

SPECIAL CASES OF THE IDEAL GAS LAW

•

Boyle’s L aw (n, T const ant): PV = constant 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. PV = PV 1 1 2 2

Charles’ Law (n, P constant):

V

= constant

T 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.

V1 T1

=

V 2 T 2


GEAS GEA

CHAPTER 4 -

Thermodynamics


•

Gay – Lussac’s Law (n, V constant): P1 T1

•

=

P T

= constant

P2 T 2

The Combined Gas Law p1V1 T1

=

p2 V2 T2

STANDARD CONDITIONS (S.T.P.):

= 273.15 K = 0 °C p = 1.013 × 10 5 Pa = 1 atm

T

Under standard conditions, 1 kmol of ideal gas occupies a volume of 22.4 m 3. 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.

Pt = p1 + p2 + p3 + ... + Pn

= total pressure of the mixture p1, p2 , p3 ,..., pn = partial pressure of component gases W here

Pt

AVOGADRO’S LAW

m1 m2

Where

=

M1 M2

=

R1 R2

m = mass M = molecular weight R = gas constant


GEAS


TEST – 4

1.

A “closed system” is also known as A. B. C. D.

2.

A “closed system” wherein even energy is not allowed to cross the boundary is called an A. B. C. D.

3.

control volume* control boundary control mass isolated system

The boundary of a control volume system is called a A. B. C. D.

5.

control volume isolated system* control mass control boundary

An “open system” is also known as A. B. C. D.

4.

control mass* isolated system control volume control boundary

control surface* control point control area control line

Mass per unit volume is A. B. C. D.

weight pressure density* specific gravity


GEAS GEA

CHAPTER 4 -

Thermodynamics


6.

The ratio of the density of a substance to the density of some standard substance at a specified temperature is called A. B. C. D.

7.

The reciprocal of density (i.e. volume per unit mass) is called A. B. C. D.

8.

specific gravity specific volume* bulk modulus specific weight

Properties that are independent of the size of the system, such as temperature, pressure, and density are called A. B. C. D.

9.

specific gravity * relative weight elasticity specific density

intensive properties* extrinsive properties extensive porperties extrinsic properties

Properties that are dependent on the size or extent of the system such as mass, volume, and total energy are called A. B. C. D.

intensive properties intrinsic properties extensive properties* chemical properties

10. The area under the process curve on a T-S diagram represents A. B. C. D.

heat transfer* temperature change work 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


GEAS


12. The h-s diagram is also called a A. B. C. D.

Argand diagram Euler diagram Mollier diagram* 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. B. C. D.

The first law of thermodynamics The second law of thermodynamics The third law of thermodynamics* The Zeroth law of thermodynamics

14. The condition in which the temperature is the same throughout the entire system is called: A. B. C. D.

thermal equilibrium* phase equilibrium mechanical equilibrium chemical equilibrium

15. The condition in which there is no change in pressure at any point of the system with time. A. B. C. D.

thermal equilibrium phase equilibrium mechanical equilibrium* chemical equilibrium

16. The condition in which the mass of each phase reaches an equilibrium level and stays there. A. B. C. D.

phase equilibrium* chemical equilibrium thermal equilibrium mechanical equilibrium


GEAS GEA

CHAPTER 4 -

Thermodynamics


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

phase equilibrium chemical equilibrium* thermal equilibrium mechanical equilibrium

18. Any change that a system undergoes from equilibrium state to another is called a A. B. C. D.

process* conversion state 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. B. C. D.

isothermal process* isometric process isobaric process isochoric process

21. A process during which, the pressure P remains constant is called A. B. C. D.

isothermal process isobaric process* isovolumic process isometric process

22. A process during which, the specific volume V remains constant is called A. B. C. D.

isometric isochoric isovolumic all of the above* 175 Loading Next Page

GEAS


23. Who coined the term energy in1807? A. B. C. D.

William Thomson Thomas Young* Lord Kelvin Rudolph Clausius

24. The energy that a system possesses as a result of its motion relative to some reference frame is called A. B. C. D.

kinetic energy* spin energy potential energy elastic energy

25. The energy that a system possesses as a result of its elevation in a gravitational field is called A. B. C. D.

kinetic energy gravitational energy potential energy* mechanical energy

26. Who wrote the first thermodynamic textbook in 1859? A. B. C. D.

Lord Kelvin William Rankine* Thomas Young 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. B. C. D.

first law of thermodynamics zeroth law of thermodynamics * third law of thermodynamics second law of thermodynamics

28. Pressure below atmospheric pressure are called A. absolute pressure B. vacuum pressure* C. standard pressure D. reference pressure


GEAS GEA

CHAPTER 4 -

Thermodynamics


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

Pascal’s principle * Archimedes principle Torricelli’s principle 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. B. C. D.

standard pressure absolute pressure* vacuum pressure atmospheric pressure

33. The difference between the absolute pressure and the local atmospheric pressure is called the A. B. C. D.

relative pressure gauge pressure* vacuum pressure standard pressure

34. A liquid that is about to vaporize is called A. saturated vapor B. plasma C. superheated vapor D. saturated liquid*


GEAS


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. B. C. D.

critical temperature saturation temperature* triple point kindling temperature

37. At a given temperature, the pressure at which a pure substance changes phase is called A. B. C. D.

critical pressure saturation pressure* absolute pressure vacuum pressure

38. The amount of energy absorbed during melting and is equivalent to the amount of energy released during freezing is called A. B. C. D.

latent heat of vaporization melting energy latent heat of fusion* specific heat

39. The amount of energy absorbed during vaporization and is equivalent to the amount of energy released during condensation is called A. B. C. D.

latent heat of vaporization* melting energy latent heat of fusion 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


GEAS GEA

CHAPTER 4 -

Thermodynamics


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

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

convection conduction* radiation 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. B. C. D.

convection* conduction radiation emission

44. The transfer of energy due to the emission of electromagnetic waves (or photons) is called A. B. C. D.

convection conduction radiation* emission

45. The area under the process curve on a P-V diagram represents the boundary A. B. C. D.

temperature pressure energy work*


GEAS


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. B. C. D.

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

sound heat* magnetic waves light

49. A device that increases the velocity of a fluid at the expense of pressure is called A. B. C. D.

nozzle* diffuser pressure exchanger 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


EA EA S

CHAPTER 4 -

Thermodynamics

GE NERAL ENGINEE RING & APPLIED SCIENCES

S lv d P obl ms

I Th rmo yna ics 1.

4

eat of 2 x 10 J is added to block of ice t 0°C causing part of it to elt. Calculate the change in entropy. olution: ΔS = ΔS =

ΔQ

T 2 × 10 4 J

27 K ΔS = 73.26 J

2.

K

etermine the maximum pos ible efficiency of an automo ile engine wit xhaust tempe rature of 120° , and the tem erature of the burning gas in the engine is 6 0°C. olution:

3.

η max

T = 1 − cool Thot

η max

= 1−

η max

= 0.56

(120 + 273 ) K ( 620 + 273 ) K

heat engine t akes 1200 J o f heat from the high – tempe ature heat ource in each cycle and doe s 400 J of wor in each cycle . What is the fficiency of thi s engine? olution: η=

W QH

=

00 J 1 00 J

× 100%

η = 33%

181 oading Next Page

GEAS 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:

= QH − QC QC = QH − W = 1200 J − 400 J = 800J W

O

5. A steam turbine takes in steam at a temperature of 400 C and release O steam to the condenser at a temperature of 120 C. Calculate the Carnot efficiency for this engine. Solution:

η= = =

TH

− TC TH

× 100%

( 400 + 273 ) − (120 + 273 ) × 100% ( 400 + 273 ) 673K − 393K 673K

× 100%

= 41.6%

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:

m=

PV RT

R(air) = 0.287 kJ

kg-K

= 287 N-m kg-K

( 250000 + 101325 ) m=

N m2

(0.65m 3 )

⎛ 287 N-m ⎞ 293K ) ⎜ kg-K ⎟⎠ ( ⎝

m = 2.72 kg


GEAS GEA

CHAPTER 4 -

Thermodynamics


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 c ycle? Solution:

η= W

8.

W QH

= ηQH = 0.416 ( 500 kJ) = 208 kJ

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:

E1 = E2 1

mV12

2 V2

1

+ U1 = mV22 + U2 2

=0

U2 − U1 = ΔU =

1 2

mV12 −

1 2

mV22

1⎛ 1slug ΔU = ⎜⎜ 0.95 lbm × 2⎝ 32.2lbm ΔU = 922 ft-lbf

9.

2 ⎞⎛ ft ⎞ ⎟⎟ ⎜ 250 ⎟ s⎠ ⎠⎝

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:

Tcold

= −10 + 273 = 263 K, Thot = 32 + 273 = 305 K

COP = COP =

Tcold Thot

− Tcold

263

305 − 263 COP = 6.3


GEAS


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:

m=

PV RT

R(air ) = 53.3 ft-lbf lbm-R 2⎞ ⎛ ⎜ 14 lb 2 × ⎛⎜ 12in ⎞⎟ ⎟ ( 30 × 100 × 20) ft3 ⎜ in ⎝ 1ft ⎠ ⎟ ⎠ msummer = ⎝ = 4103.8-lbm ft-lbf (53.3 lbm-R ) (93 + 460) R 2⎞ ⎛ ⎜ 14 lb 2 × ⎛⎜ 12in ⎞⎟ ⎟ ( 30 × 100 × 20 ) ft3 ⎜ in ⎝ 1ft ⎠ ⎟ ⎠ mwinter = ⎝ = 4828.5-lbm ft-lbf 53.3 10 460 R + ( ) ( lbm-R )

Δm = ΔW = 4828.5-lbm − 4103.8-lbm ΔW = 724.7 lbf 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:

P1

=

P2

T2

=

P2T1

T2

=

T1

T2 P1

( ( 205 + 14.7 )(144 )) ( 75 + 460) ( 38 + 14.7 )(144)

= 2230 R − 460 T2 = 1770°F T2


GEAS GEA

CHAPTER 4 -

Thermodynamics


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

3

Solution:

= PΔV 2 ⎛ lb ⎛ 12in ⎞ ⎞ ⎜ ⎟ ( 2.25 − 0.0256 ) ft3 W = 305 2 × ⎜ ⎟ ⎜ in ⎝ 1ft ⎠ ⎟⎠ ⎝ W = 97.7 × 103 ft-lbf W

13. Determine the compression ratio of an Otto cycle with an efficiency of 55% and r = 1.5. Solution:

Otto cycle: η

= 1−

0.55 = 1 −

1 r −1

⎛ V1 ⎞ ⎜ V ⎟ 2⎠ ⎝ 1

1.5 −1

⎛ V1 ⎞ ⎜ V ⎟ 2⎠ ⎝

⎛ V1 ⎞ = 5 ⇒ compression ratio ⎜ V ⎟ 2⎠ ⎝ 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 lowtemperature reservoir. What is the temperature of the latter reservoir? Solution:

Q1 Q2

=

T1 T2 Q2

T2

= T1

T2

⎛ 78 ⎞ = (150 + 273 ) ⎜ ⎟ = 300 K = 27°C ⎝ 110 ⎠

Q1


GEAS


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:

PA + F = mg + PatmA

(P − Patm ) A = mg − F (P − Patm ) = P = Patm +

mg − F

A mg − F A

⎛ 10kg × 9.8 m ⎞ − 100N ⎜ ⎟ s2 ⎠ P = 101× 103Pa + ⎝ 2⎞ ⎛ ⎜ 10 cm2 × ⎛⎜ 1m ⎞⎟ ⎟ ⎜ ⎝ 100cm ⎠ ⎟⎠ ⎝ P = 99 × 103Pa P = 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:

m=

PV RT

⎛ lb ⎛ 12in ⎞2 ⎞ ⎜ 20 ⎟ ( 30 × 20 × 15 ) ft3 ×⎜ ⎟ 2 ⎜ in ⎝ 1ft ⎠ ⎟ ⎝ ⎠ m= ft-lb ⎞ ⎛ ⎜ 53.3 lbm-R ⎟ ( 80 + 460 ) R ⎝ ⎠ m = 901 lbm


GEAS GEA

CHAPTER 4 -

Thermodynamics


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:

Pabs

= Patm + Pgage

Pabs

= 103 × 103Pa + 1× 106Pa = 1.103 MPa

Pabs

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 3 35°C, and the density of mercury is 13.6 g/cm . Solution:

( ρ Ga ) ( g ) (hGa ) = ( ρ Hg ) ( g )(hHg ) hGa

=

( ρ Hg )(hHg ) ρ Ga

1 atm pressure = hHg ρ Hg

hGa

= 13.6 g

= 760 mmHg = 76 cmHg

cm3

⎛ 13.6 g ⎞ 76 cmHg ) ⎜ ⎟( cm3 ⎠ ⎝ = = 169.7 cmGa = 1697 mmGa ⎛ 6.09 g ⎞ ⎜ ⎟ cm3 ⎠ ⎝

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:

P= P=

F A mg A

=

(5.2kg) (9.8 m s2 ) 2⎞ ⎛ ⎜ 400mm2 × ⎛⎜ 1m ⎞⎟ ⎟ ⎜ ⎝ 1000mm ⎠ ⎟⎠ ⎝

P = 127 kPa 187 Loading Next Page

GEAS


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:

m= R=

PV RT R Molar mass O2

=

8.314 J mol-K

⎛ 1kg ⎞ ⎜ 2 (16g) × 1000g ⎟ ⎝ ⎠ 101325

m=

N

m2 0.5m3 1bar

( 30 + 1.013 ) bar × 8.314 J mol-K

⎛ 1kg ⎞ ⎜ 2 (16g) × 1000g ⎟ ⎝ ⎠

(

)

= 8.8kg

( 70 + 273 ) K

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 ftlbf/lbm-R. Solution:

V

V

=

=

mRT P

⎛ ⎝

( 75lbm) ⎜ 35.13

ft-lb ⎞ ⎟ ( 240 + 460) R lbm-R ⎠

(14.7 + 25 ) V

⎛ 12in ⎞ × 2 ⎜ 1ft ⎟ in ⎝ ⎠ lb

2

= 322.6 ft 3


GEAS GEA

CHAPTER 4 -

Thermodynamics


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:

PV

= mRT R Molar mass

8.314 J

mol-K g 39.9 mol J J R(Argon) = 0.208 = 0.208 × 10−3 g-K kg-K R(Argon) =

Specific Volume

=

V m

=

=

RT P

⎛ J ⎞ 3 ⎜ 0.208 × 10 kg-K ⎟ ( 20 + 273) K ⎠ Specific Volume = ⎝ 3 150 × 10 Pa

(

Specific Volume = 0.407

)

m3 kg


GEAS 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:

Initial : P1 = 861.6kPa, V1 = 70.85L, T1 = 24 n1 =

P1V1 RT1

R = 8.314 n1 =

L-kPa

mol-K ( 861.6kPa )(70.85L )

L-kPa ⎞ ⎛ ⎜ 8.314 mol-K ⎟ ( 24 + 273 ) K ⎝ ⎠

n1 = 24.72 mols Final:P2

= 689.3kPa, V2 = 70.85L, T2 = 24

P2V2

n2

=

n2

=

n2

= 19.78 mols

RT2

( 689.3kPa )(70.85L ) L-kPa ⎞ ⎛ ⎜ 8.314 mol-K ⎟ ( 24 + 273 ) K ⎝ ⎠

Amount of oxygen leaked out: nleaked nleaked

= n1 − n2 = 24.72 mols − 19.78 mols = 4.94 mols

mleakedO2

= 4.94 mols ×

mleakedO2

= 158g O2

2 (16g) 1mol


Chap 4 Thermodynamics

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