thermo

1
Chapter 2 Energy Transfer by Works, Heat and
Mass

• 2.1 Definition of Heat Transfer
• 2.2 Energy Transfer by work
• 2.3 Mechanical Form of Work
• 2.4 Non-Mechanical Forms of work Heat
• 2.5 Conservation of Mass Principle
• 2.6 The Flow Work and Energy of a Flowing Fluid

2
2.1.1 Definition of Heat Transfer

• This chapter with a discussion of various forms
  of energy and energy transfer by heat. Then
  introduce various forms of work and discuss
  energy transfer by work. Discuss the four
  mechanisms of heat transfer such as conduction,
  convection, radiation and Advection
• What Is the Definition of Heat Transfer?
• Heat transfer is the transition of thermal
  energy or simply heat from a hotter object to a
  cooler object. This transition can be made by
  conduction, convection, radiation and Advection
• .
• Definition of Heat Transfer
• Heat transfer, also referred to simply as heat,
  is the movement of thermal energy from one thing
  to another thing of different temperature. These
  objects could be two solids, a solid and a liquid
  or gas, or even within a liquid or gas. There are
  three different ways the heat can transfer
  conduction (through direct contact), convection
  (through fluid movement), or radiation (through
  electromagnetic waves). Heat transfer occurs when
  the temperatures of objects are not equal to each
  other and refers to how this difference is
  changed to an equilibrium state. Thermodynamics
  then deals with things that are in the
  equilibrium state.

3
2.1.2 Introductions Modes of Heat Transfer

• Modes of Heat Transfer

Conduction or diffusion The transfer of energy
between objects that are in physical contact. Ex
Solid bar Convection The transfer of energy
between an object and its environment, due to
fluid motion. Natural Convection- the fluid
motion is caused by buoyancy forces which are
induced by density differences
due to the variation of temperature in the
fluid Force Convection- the fluid is forced to
flow in a tube or over a surface by external
means such as fan, pump, or the
wind Radiation The transfer of energy to or
from a body by means of the emission or
absorption of electromagnetic radiation.
electromagnetic waves (or photons) as a result
of the changes in the electronic configurations
of the atoms or molecules Advection The
transfer of energy from one location to another
as a side effect of physically moving an object
containing that energy.
Heat can be transferred in four ways conduction,
convection radiation and advection
4
2.1.2 Introductions Modes of Heat Transfer

Conduction is the most significant means of heat
transfer within a solid or between solid objects
in thermal contact. when adjacent atoms vibrate
against one another, or as electrons move from
one atom to another. Thermal contact conductance
is the study of heat conduction between solid
bodies in contact. Example Quenching
where is the heat flow, is the thermal
conductivity, is the cross sectional area and is
the temperature gradient in the direction of flow.
Fig.2.1 Heat flow between two solids in contact
and the temperature distribution.
5
2.1.2 Introductions Modes of Heat Transfer

Convective heat transfer or convection, is the
transfer of heat from one place to another by the
movement of fluids, a process that is essentially
the transfer of heat via mass transfer(evaporation
, adsorption and etc) . Bulk motion of fluid
enhances heat transfer in many physical
situations, such as (for example) between a solid
surface and the fluid.9 Convection is usually
the dominant form of heat transfer in liquids and
gases.
Fig. 2.2 Simulation of thermal convection. Red
hues designate hot areas, while regions with blue
hues are cold. A hot, less-dense lower boundary
layer sends plumes of hot material upwards, and
likewise, cold material from the top moves
downwards. This illustration is taken from a
model of convection in the Earth's mantle.
6
2.1.2 Introductions Modes of Heat Transfer

where is the thermal energy in joules is
the heat transfer coefficient (assumed
independent of T here) (W/m2 K) is the
surface area of the heat being transferred
(m2) is the temperature of the object's
surface and interior (since these are the same
in this approximation) is the temperature
of the environment i.e. the emperature
suitably far from the surface t is the
time-dependent thermal gradient between
environment and object
Fig 2.3 Papers lifted on rising convective air
current from warm radiator
7
2.1.2 Introductions Modes of Heat Transfer

Thermal radiation is energy emitted by matter as
electromagnetic waves, due to the pool of thermal
energy in all matter with a temperature above
absolute zero. Thermal radiation propagates
without the presence of matter through the vacuum
of space.Thermal radiation is a direct result of
the random movements of atoms and molecules in
matter. Since these atoms and molecules are
composed of charged particles (protons and
electrons), their movement results in the
emission of electromagnetic radiation, which
carries energy away from the surface.is usually
the dominant form of heat transfer in liquids and
gases.ex Radiation from the sun, or solar
radiation, can be harvested for heat and power.
Fig. 2.4 Earth's longwave thermal radiation
intensity, from clouds, atmosphere and ground
8
2.1.2 Introductions Modes of Heat Transfer

The radiative heat transfer from one surface to
another is equal to the radiation entering the
first surface from the other, minus the radiation
leaving the first surface.
For a black body
where are the respective emissivities of each
surface. However, this value can easily change
for different circumstances and different
equations should be used on a case per case basis
and T is absolute temperature.
where is the StefanBoltzmann constant and is
the view factor from surface 1 to surface 2.
5.67 x 108 W/m2 K4
9
2.1.2 Introductions Modes of Heat Transfer

Advection By transferring matter,
energyincluding thermal energyis moved by the
physical transfer of a hot or cold object from
one place to another.15 This can be as simple
as placing hot water in a bottle and heating a
bed, or the movement of an iceberg in changing
ocean currents. A practical example is thermal
hydraulics.citation needed
This can be described by the formula where Q is
heat flux (W/m²), ? is density (kg/m³), cp is
heat capacity at constant pressure (J/(kgK)),
?T is the change in temperature (K), v is
velocity (m/s).
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2.2 Energy Transfer by work

• Heat-the form of energy that is transferred
  between two systems by virtue of a temperature
  difference.
• Heat has energy units kJ (or BTU).
• Rate of heat transfer is the amount of heat
  transferred per unit time.
• Heat is a directional (or vector) quantity
• has magnitude, direction, and point of action.
• Specific heat-the energy required raising the
  temperature of a unit mass of a substance by one
  degree.
• Specific heat
• constant pressure, Cp.
• Cp is the energy required to raise the
  temperature of the unit mass of a substance by
  one degree as the pressure is maintained
  constant.
• constant volume, Cv.
• Cv is the energy required to raise the
  temperature of the unit mass of a substance by
  one degree as the volume is maintained constant
• CpgtCv because at constant pressure

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2.2 Energy Transfer by work

Refer figure 2.5 . Heat Transfer to a system is
positive, and heat transfer from a system is
negative
Fig. 2.5 Sign convention positive if to the
system, negative if from the system.
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2.2 Energy Transfer by work

• Energy can be neither created nor destroyed it
  can only change forms
• - based on experimental observations
• - the first law of thermodynamics /
  conservation of energy principle
• - the first law of thermodynamics during an
  interaction between a system and its
  surroundings, the amount of energy gained by the
  system must be exactly equal to the amount
  of energy lost by the surroundings.
• Energy can cross the boundary of a closed
  system in two distinct forms heat and work  
• Definition the capacity of a physical system
  to do work the units of energy are joules or
  ergs
• E f T, p, V, t and etc
• In thermodynamics, generally combination of
  potential energy, kinetic energy and internal
  energy
• where PE potential energy
• KE kinetic energy
• U - internal energy

13
2.2 Energy Transfer by work

• Figure 2.6 shows the temperature difference is
  the driving force for heat transfer

2.6 Temperature difference is the driving force
for heat transfer.
14
2.2 Energy Transfer by work

• Work the energy transfer associated with a
  force acting through a distance
• - a form of energy
• - has unit such as kJ
• - the work done during a process between
  states 1 and 2 is denoted W12 or simply W
• The work done per unit mass of a system is
  denoted w and is defined as
• (kJ/kg)
• The work done per unit time of a system is called
  power and denoted as . The unit of power is
  kJ/s, or kW
• Production of work/ work done by a system -
  positive work/ sign
• Consumption of work/ work done on the system
  negative work / negative sign
• Example Work produced by car engines,
  hydraulic, steam, or gas turbines positive
• Work consumed by compressors, pumps,
  and mixers - negative

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2.2 Energy Transfer by work
Heat, Q

• Heat is defined as the form of energy that is
  transferred between two systems (or a system and
  its surroundings) by virtue of a temperature
  difference
• An energy interaction is heat only if it takes
  place because of temperature difference, and at
  same temperature- no heat transfer
• A mild steel rod is heated from room temperature
  to melting temperature, so, the heat in in
  addition to temperature rise is
• Heat Transfer, or
• where C Specific heat, kJ/kg.K
• Specific heat is defined as the energy required
  to raise the temperature of a unit mass of a
  substance by one degree
• specific heat at constant pressure, Cp
• Cp - The energy required to raise the
  temperature of the unit mass of a substance by
  one degree as the pressure is maintained
  constant
• specific heat at constant volume, Cv
• Cv The energy required to raise the
  temperature of the unit mass of a substance by
  one degree as the volume is maintained
  constant
• Cp is always greater than Cv because at constant
  pressure, the system is allowed to expand and the
  energy for this expansion work must also be
  supplied to the system

16
Energy Transfer by work

• Heat loss of 7 kJ can be expressed as either Q
  -7 kJ or Qout 7 kJ
• Work output of 7 kJ can be expressed as either W
  7 kJ or Wout 7 kJ

Fig. 2.7 Sign convection for heat and work
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2.2 Energy Transfer by work

• Work is the energy interaction between a system
  and its surroundings or commonly definition as
  force acting through a distance.
• Unit-kJ and the work done during a process
  between states 1 and 2 is denoted W12 or simply
  W.
• The work done per unit mass of a system is
  denoted w and is defined as,
• (kJ/kg)
•  
• The work done per unit time of a system is
  called power and denoted as .
• The unit of power is kJ/s, or kW.
•  

Fig. 2.8 Sign convention for heat and work.
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2.2 Energy Transfer by work

•  
• Example
• Work produced by car engines, hydraulic, steam,
  or gas turbines positive.
• Work consumed by compressors, pumps, and mixers
  negative.
• Energy of a system decreases as it does work
  and increases as work is done on the system.
  Identifiers in and out are direction of any heat
  or work interaction. Heat transfer to a system is
  denoted as Qin. Heat transfer from a system is
  denoted as Qout.
•  
•  Similarities between work and heat transfer
• Both are recognized at the boundaries of the
  system as they cross them (boundary phenomena).
• Both are related with a process, not a state.
  Heat or work has no meaning at a state.
• Both are path functions, their magnitudes depend
  on the path followed during a process as well as
  the end states.

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2.2 Energy Transfer by work
Example 2.1 The inner and outer surfaces of a
window glass are 10C and 3C respectively,
maintained at specified temperatures. The amount
of heat transfer through the glass in 5 h and
the glass sizes are 2m high x 2m length and 0.5
cm width. Determine. a. the rate of heat
transfer, b. the heat transfer through the glass
in 5 hour and c. the amount of heat transfer if
the thickness of the glas double to 1 cm.
 Assumptions 1.Steady operating conditions exist
since the surface temperatures of the glass
remain constant at the specified
values. 2.Thermal properties of the glass are
constant.  Properties The thermal conductivity
of the glass is given to be k0.78
W/mC. Analysis a. Under steady conditions, the
rate of heat transfer through the glass by
conduction is (0.78W/m/mC)(2x2m2)(10-3)C/
0.005m4.368kW b. Then the amount of heat
transfer over a period of 5 h becomes (4.368kJ
/s)(5x3600s)78,620kJ c. If the thickness of the
glass double to 1 cm, then the amount of heat
transfer will go down by half to 39,310kJ
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2.2 Energy Transfer by work

• Example 2.2
• A cylindrical resistor on a circuit board
  dissipates 0.8 W of power. The amount of heat
  dissipated in 24 h and the resistor sizes are 0.4
  cm diameter and 2cm length respectively.
  Determine
• The amount of heat resistor
• The heat flux on the surface
• The heat transfer coefficient

Assumptions Heat is transferred uniformly from
all surfaces.   Analysis a) The amount of heat
this resistor dissipates during a 24-hour period
is (0.8 W)(24 h)69.1 kJ(since 1 Wh
3600 Ws 3.6 kJ) b) The heat flux on the
surface of the resistor is q10.8/0.2513.18W/
cm2 q20.8/2.5130.32 W/cm2 c) Assuming the
heat transfer coefficient to be uniform, heat
transfer is proportional to the surface area.
Then the fraction of heat dissipated from the top
and bottom surfaces of the resistor
becomes    Discussion  Heat transfer from the
top and bottom surfaces is small relative to that
transferred from the sidesurface.
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2.2 Energy Transfer by work

• Example 2.3
• The filament of a 150 W incandescent lamp is 5 cm
  long and has a diameter of 0.5 mm. If the
  diameter of glass bulb is 8 cm and the TNB Rate
  is 0.08/kWh . Determine a). The heat flux on
  the surface of the filament, b). the heat flux on
  the surface of the glass bulb, and c) the annual
  electricity cost of the bulb are to be
  determined.
•  
•  Assumptions
• Heat transfer from the surface of the filament
  and the bulb of the lamp is uniform.
•   Analysis
•  
• The heat transfer surface area and the heat flux
  on the surface of the filament are
• The heat flux on the surface of glass bulb is

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2.3 Mechanical Forms of Work

• There are several ways of doing work, each in
  some way related to a force acting through a
  distance.
• W F.s (kJ)
• If the force is not constant, we need to
  integrate
• (kJ)
•    
•  
• There are two requirements for a work
  interaction between a system and its surroundings
  to exist
• There must be a force acting on the boundary and
• The boundary must move
•  
• In many thermodynamic problems, mechanical work
  is the only form of work involved. It is
  associated with the movement of the boundary of a
  system or with the movement of the entire system
  as a whole .Some common forms of mechanical work
  are

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2.3 Mechanical Forms of Work-Shaft Work

• A force F acting through a moment arm r
  generates a torque
• This force acts through a distance s,
• Shaft Works work,
•  
• The power transmitted through the shaft is the
  shaft work done per unit time
•  
•  
•  
•  
•  

Fig 2.10 Shaft work is proportional to the
torque applied and the number of revolutions of
the shaft.
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2.3 Mechanical Forms of Work-Spring Work

• When the length of the spring changes by
• a differential amount dx under the influence of
  a force F, the work done is
• Substituting and integrating yield
• x1 and x2 the initial and the final
  displacements
• For linear elastic springs, the displacement x
  is proportional to the force applied
• k spring constant (kN/m)

Fig 2.11 The displacement of a linear spring
doubles when the force is doubled.
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2.3 Mechanical Forms of Work- Work Done on
Elastic Solid Bars

• Work Associated with the Stretching of a Liquid
  Film

Fig. 2.12 Solid bars behave as springs under the
influence of a force.
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2.3 Mechanical Forms of Work- Work Done to Raise
or to Accelerate a Body-Potential Energy

• Potential energy PE the energy that a system
  possesses as result of its elevation in a
  gravitational field
• PE is expressed as
• PE mgz (kJ)
• or on a unit mass basis
• pe gz (kJ/kg)
• where g gravitational acceleration
• z elevation of the centre of a gravity of a
  system relative to some arbitrarily
  selected reference plane

i. The work transfer needed to raise a body is
equal to the change in the potential energy
of the body. Ii. The work transfer needed to
accelerate a body is equal to the change in
the kinetic energy of the body.
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2.3 Mechanical Forms of Work- Work Done to Raise
or to Accelerate a Body-Potential Energy
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2.3 Mechanical Forms of Work- Work Done to Raise
or to Accelerate a- Kinetic Energy

• Energy that a system possesses as a result of
  its motion relative to some reference frame
• When all parts of a system move with the same
  velocity, the kinetic energy is expressed as
• (kJ)
• or, on a unit mass basis,
• (kJ/kg)
• where V - velocity of a the system relative
  to some fixed reference frame
• m - mass of the system

29
2.3 Mechanical Forms of Work- Work Done to Raise
or to Accelerate a-Relation between potential
energy and kinetic Energy

• From the Third Newtons Law, F mg (1)
• PE mgz (2)
• F ma mdv/dt (3)
• 
  where v velocity
• t time
• If,
• where f force
• x distance
• Then, (4)
• Substitute Eq. (3) into Eq. (4)
• (5)
• ,so

and
or
30
2.3 Mechanical Forms of Work- Work Done to Raise
or to Accelerate

• Example 2.4
• A water jet that leaves a nozzle at 60 m/s at a
  flow rate of 120 kg/s is to be used to generate
  power by striking the buckets located on the
  perimeter of a wheel. Determine
• the power generation potential of this water
  jet.
• Solution
• Assumption Water jet flows steadily at the
  specified speed and flow rate.
• Analysis Kinetic energy is the only form of
  harvestable mechanical energy the water jet
  possesses, and it can be converted to work
  entirely. Therefore, the power potential
• of the water jet is its kinetic energy, which is
  V2/2 per unit mass, and m V2/2 for a given
  mass flow rate

31
2.4 Nonmechanical Forms of Work

• Electrical work
•   The generalized force is the voltage (the
  electrical potential) and the generalized
  displacement is the electrical charge.
•  
•   Magnetic work
• The generalized force is the magnetic field
  strength and the
• generalized displacement is the total magnetic
  dipole moment.
•  
• Electrical polarization work The generalized
  force is the electric field
• strength and the generalized displacement is
  the polarization of the
• medium.

Fig. 2.14 The energy transferred to a body while
being raised is equal to the change in its
potential energy.
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2.5 Conservation of Mass Principle

•   A large number of engineering problems involve
  mass flow in and out of a system as control
  volumes (e.g water heater, radiator, turbine,
  compressor, etc...). In general, any arbitrary
  region may be selected as a control volume, but
  making a proper choice simplifies the solution
  process. The boundaries of a control volume are
  called the control surface, and they can be real
  or imaginary (e.g. see figure 2.15).

Fig. 2.15 A control volume can be fixed in size
and shape or possess moving boundaries (e.g.
shock absorber)
33
Conservation of Mass Principle

• The conservation of mass is one of the
  fundamental principles in nature. Simply stated,
  it asserts that mass is a conserved property. It
  cant be created or destroyed. The conservation
  of mass principle for a control volume (CV)
  undergoing a process can be expressed as

34
2.6Flow Work and the Energy of a Flowing
Fluid-Internal energy
Internal energy, U

• The energy that contains in the molecular
  structure of a system and the degree of the
• molecular activity
• Internal energy can be increase by work in or
  heat in that make an increase of temperature
• In thermodynamics, the internal energy is always
  cause by temperature change
• Internal energy is increase with increase in
  temperature
• If no temperature rise, no change in potential
  energy 0
• Internal energy, U (kJ)
• Specific internal energy, u (kJ/kg) where u U/m
  (kJ/kg)

35
2.6Flow Work and the Energy of a Flowing Fluid-
Ideal-gas Equation of State
Equation state

• Any equation that relates the pressure,
  temperature and specific volume of a substance
• Properties which involve the properties of a
  substance at equilibrium states
• The best known equation of state for substances
  in the gas phase is called the ideal-gas equation
  of state
• - predict the P-v-T behavior of a gas quite
  accurately within some properly selected region
• Gas and vapor are often used as synonymous words
• - vapor phase of a substance is called gas
  when it is above the critical temperature
• - vapor usually a gas which is not far from a
  state of condensation
• At low pressure, the volume of a gas is
  proportional to its temperature
• or where the constant R is the gas
  constant
• Equation is ideal-gas equation of state, or
  simply the ideal-gas relation a gas which obeys
  this relation is called an ideal gas
• The gas constant R is different for each gas and
  it is determined from

36
2.6 Flow Work and the Energy of a Flowing Fluid-
Internal Energy, Enthalpy and Specific Heats of
Ideal Gases

• For a pure substance, specific heat can be
  determined where U, h f T
• If the process is at a constant pressure and
  volume, so Cp and Cv will be
• Cp dh/dT --- (1)
• Cv dv/dT --- (2)
• From (1) and (2), the change of internal energy
  and enthalpy
• dU Cv dT and dh Cp dT --- (3)
• Integrating (3)
• U2-U1 Cv (T2-T1) and h2 h1 Cp
  (T2-T1) --- (4)
• The difference in specific heat of ideal gas can
  be expressed from enthalpy definition, h
• h u Pv W ? Pv, Pv mRT
• u RT --- (5)

37
2.6Flow Work and the Energy of a Flowing Fluid-
Internal Energy, Enthalpy and Specific Heats of
Ideal Gases

• Differentiate
• dh du RdT or dh/dT du/dT R
  --- (6)
• Substitute (2) into (6),
• So, Cp Cv R or Cp - Cv R --- (7)
• So, the ratio of specific heat can be expressed
  as
• ? Cp / Cv --- (8)
• Substitute (7) and (8) in Cv and Cp expression
• Cv R/ ? -1 and Cp ?R/ ?-1

38
2.6 Flow Work and the Energy of a Flowing Fluid-
Work and pressure volume diagram

• A close system (cylinder and piston reversible)
  where a working fluid had expanded and compressed
  as Fig. 2.16
• If dl is a distance of piston after moved, so the
  work done is
• dW -(PA) dl
• For 1 unit mass of working fluid, so
• dW -mPdv
• W -m?Pdv
• area plotted in graph
• work done on the working fluid
• - ve work work consumed ( compression
  process)
• - ve work work produced

39
2.6 Flow Work and the Energy of a Flowing Fluid-
Work and pressure volume diagram
Fig. 2.16 Cylinder and piston system
40
2.2 Energy Transfer by work

• Example 2.5
• A house is heated from 10C to 22C by an
  electric heater, and some air escapes through the
  cracks as the heated air in the house expands at
  constant pressure. Calculate the amount of heat
  transfer to the air and its cost if the Room size
  are 4m x 5m x 3m
•   Assumptions
• 1.Air as an ideal gas with a constant specific
  heats at room temperature.(P101.3kPa,R0.287kPa
  m3/kgK)
• 2.The volume occupied by the furniture and other
  belongings is negligible.
• 3.The pressure in the house remains constant at
  all times.
• 4.Heat loss from the house to the outdoors is
  negligible during heating.
• 5.The air leaks out at 22C.
•  Properties
• The specific heat of air at room temperature is
  cp 1.007 kJ/kgC.
•  Analysis
•  The volume and mass of the air in the house are
• V(floor space )(height)(20m2)(3m)60m3
• a. Amount of heat transfer
• Noting that the pressure in the house remains
  constant during heating, the amount of heat that
  must be transferred to the air in the house as it
  is heated from 10C to 22ºC determined to be
  Qmcp(T2-T1)(747.9kg)(1.007kJ/kg.C)(22-10)9038k
  J

41
2.6 Flow Work and the Energy of a Flowing Fluid-
Work and pressure volume diagram
Example 2.6 A resistance heater is to raise the
air temperature in the room from 7C to 25C
within 15 min and size of the room are 4m x 5m x
6m . Determine the required power rating of the
resistance heater .   Assumptions  1.The kinetic
and potential energy changes are
negligible,?ke??pe?0. 2.Constant specific heats
at room temperature can be used for air. This
assumption results in negligible error in heating
and air-conditioning applications. 3.Heat losses
from the room are negligible.  PropertiesStandar
d ideal airThe gas constant of air is R 0.287
kPam3/kgK (Table A-1). Also,cp1.007kJ/kgK for
air at room temperature (Table A-15) and room
pressure is 1.013 bar.Answ 3.01 kW  Analysis We
observe that the pressure in the room remains
constant during this process. Therefore, some air
will leak out as the air expands. However, we can
take the air to be a closed system by considering
theair in the room to have undergone a constant
pressure expansion process. The energy balance
for this steady-flow system can be expressed as
42
2.6 Flow Work and the Energy of a Flowing Fluid-
Work and pressure volume diagram
Solution
43
2.6 Flow Work and the Energy of a Flowing Fluid-
Work and pressure volume diagram
Example 2.7 A room is heated by an electrical
resistance heater placed in a short duct in the
room in 18 min while the room is losing heat to
the outside is 200 kJ/min, and a 300-W fan
circulates the air steadily through the heater
duct. The outer and inner temperature are 25C
and 15C respectively. Room size5mx6mx8 m and
room pressure is 98kJ/kgK. Determine The power
rating of the electric heater and the temperature
rise of air in the duct Ans4.93 kW
6.2C  Assumptions  1.The kinetic and potential
energy changes are negligible,?ke??pe?0.
2.Constant specific heats at room temperature can
be used for air. This assumption results in
negligible error in heating and air-conditioning
applications. 3.Heat loss from the duct is
negligible. 4.The house is air-tight and thus no
air is leaking in or out of the
room.  Properties The gas constant of air is R
0.287 kPa.m3/kg.K (Table A-1). Also,cp1.007
kJ/kgK for air at room temperature (Table A-15),
cvcpR0.720 kJ/kgK  Analysis a)The Power
rating b)The temperature rise
44
2.6 Flow Work and the Energy of a Flowing Fluid-
Work and pressure volume diagram
Solution