engineering thermodynamics module-iii lecture-22 · the standard of comparison for refrigeration...

Prepared by Prof. (Dr.) Manmatha K. Roul ENGINEERING THERMODYNAMICS

MODULE-III LECTURE-22

Prepared

By Prof. (Dr.) Manmatha K. Roul

Professor and Principal

Gandhi Institute for Technological Advancement (GITA), Bhubaneswar – 752054

June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul Aircraft Gas Turbines or Jet-propulsion cycle:- Gas turbine engines are widely used to power aircraft because of their high power-to-weight ratio

Turbojet engines used on most large commercial and military aircraft Ideal air-standard jet propulsion cycle: Normally compression through the diffuser (a-1), and expansion through the nozzle (4-5) are taken as isentropic. In the ideal jet propulsion engine the gas is not expanded to ambient pressure Pa.

Nozzle Diffuser a 2 1 4 5 3

Prepared by Prof. (Dr.) Manmatha K. Roul

Instead the gas expands to an intermediate pressure P4 such that the power produced is just sufficient to drive the compressor, no net cycle power produced

( 0=cycleW& ), thus

( ) ( )4312 hhhh

m

W

m

W tc

−=−

=&

&

&

& After the turbine the gas expands to ambient pressure P5 which is the same as Pa. Apply the steady-state conservation of energy equation to the Diffuser and Nozzle

+−

++−=

220

22out

outin

inCVCV V

hV

hm

W

m

Q

&

&

&

&

Diffuser slows the flow to a zero velocity relative to the engine:

inQ&

outQ&

Prepared by Prof. (Dr.) Manmatha K. Roul Diffuser (a � 1)

kconstant for 2

2

22

2

1

2

1

221

1

P

aa

aa

aa

c

VTT

Vhh

Vh

Vh

+=

+=

+=+

Nozzle accelerates the gas leaving the turbine (turbine exit velocity negligible compared to nozzle exit velocity):

Nozzle (4 � 5) ( )

( ) kconstant for 2

222

545

545

25

5

24

4

TTcV

hhV

Vh

Vh

P −=

−=

+=+

The gas velocity leaving the nozzle is much higher than the velocity of the gas entering the diffuser, this change in momentum produces a propulsive force, or thrust Ft

( )at VVmF −= 5&

Where V is flow velocity relative to engine

For aircraft under cruise conditions the thrust just overcomes the drag force on the aircraft � fly at high altitude where the air is thinner and thus less drag

To accelerate the aircraft increase thrust by increasing V5

Prepared by Prof. (Dr.) Manmatha K. Roul In military aircraft afterburners are used to get very large thrust for short take-offs on aircraft carriers

Prepared by Prof. (Dr.) Manmatha K. Roul Page 1

ENGINEERING THERMODYNAMICS

MODULE-III

LECTURE-23

Prepared By

Prof. (Dr.) Manmatha K. Roul Professor and Principal


June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul Page 2 REFRIGERATION CYCLES:- A major application area of thermodynamics is refrigeration, which is the transfer of heat from a lower temperature region to a higher temperature one. Devices that produce refrigeration are called refrigerators, and the cycles on which they operate are called refrigeration cycles. The most frequently used refrigeration cycle is the vapor-compression refrigeration cycle in which the refrigerant is vaporized and condensed alternately and is compressed in the vapor phase. Another well-known refrigeration cycle is the gas refrigeration cycle in which the refrigerant remains in the gaseous phase throughout. The above figure shows the objectives of refrigerators and heat pumps. The purpose of a refrigerator is the removal of heat, called the cooling load, from a low temperature medium. The purpose of a heat pump is the transfer of heat to a high temperature medium, called the heating load. When we are interested in the heat energy removed from a low temperature space, the device is called a refrigerator. When we are interested in the heat energy supplied to the high temperature space, the device is called a heat pump. In general, the term “heat

Prepared by Prof. (Dr.) Manmatha K. Roul Page 3 pump” is used to describe the cycle as heat energy is removed from the low temperature space and rejected to the high temperature space. The performance of refrigerators and heat pumps is expressed in terms of coefficient of performance (COP), defined as

COP QW

COP QW

RL

net in

HPH

net in

= = =

= = =

Desired outputRequired input Cooling effectWork inputDesired outputRequired input Heating effectWork input ,, Both COPR and COPHP can be larger than 1. Under the same operating conditions, the COPs are related by COP COPHP R= + 1 Refrigerators, air conditioners, and heat pumps are rated with a SEER number or Seasonal Adjusted Energy Efficiency Ratio. The SEER is defined as the Btu/hr of heat transferred per Watt of work energy input. The Btu is the British Thermal Unit and is equivalent to 778 ft-lbf of work (1 W = 3.4122 Btu/hr). An EER of 9 yields a COP of 2.6. Refrigeration systems are also rated in terms of TONS of refrigeration. One ton of refrigeration is equivalent to 12,000 Btu/hr or 211 kJ/min. Reversed Carnot

Refrigerator and Heat Pump Shown below is the cyclic refrigeration device operating between two constant temperature reservoirs and the T-s diagram for the working fluid when the reversed Carnot cycle is used. Recall that in the Carnot cycle heat transfers take place at constant temperature. If our interest is the cooling load, the cycle is called the Carnot refrigerator. If our interest is the heat load, the cycle is called

Prepared by Prof. (Dr.) Manmatha K. Roul Page 4 the Carnot heat pump. The standard of comparison for refrigeration cycles is the reversed Carnot

cycle. A refrigerator or heat pump that operates on the reversed Carnot cycle is called a Carnot refrigerator or a Carnot heat pump, and their COPs are C O P

T TT

T T

C O PT T

TT T

R C arnotH L

L

H L

H P C arnotL H

H

H L

,, / /=−

=−

=−

=−

1 111 Notice that a turbine is used for the expansion process between the high and low temperatures. While the work interactions for the cycle are not indicated on the figure, the work produced by the turbine helps supply some of the work required by the compressor from external sources. Why not use the reversed Carnot refrigeration cycle? • Easier to compress vapor only and not liquid-vapor mixture Cheaper to have irreversible expansion through an expansion valve

Prepared by Prof. (Dr.) Manmatha K. Roul Page 1 ENGINEERING THERMODYNAMICS

MODULE-III

LECTURE-24

Prepared By



June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul Page 2 GAS REFRIGERATION CYCLE As explained earlier, the Carnot cycle (the standard of comparison for power

cycles) and the reversed Carnot cycles (the standard of comparison for

refrigeration cycles) are identical, except that the reversed Carnot cycle operates

in the reverse direction. This suggests that the power cycles discussed in earlier

chapters can be used as refrigeration cycles by simply reversing them. In fact,

the vapor-compression refrigeration cycle is essentially a modified Rankine

cycle operating in reverse. Another example is the reversed Stirling cycle,

which is the cycle on which Stirling refrigerators operate. In this section, we

discuss the reversed Brayton cycle, better known as the gas refrigeration

cycle.It is also known as Bell-Coleman Cycle.

Consider the gas refrigeration cycle shown in Fig. 11–16. The surroundings are

at T0, and the refrigerated space is to be maintained at TL. The gas is compressed

during process 1-2. The high-pressure, high-temperature gas at state 2 is then

cooled at constant pressure to T0 by rejecting heat to the surroundings. This is

followed by an expansion process in a turbine, during which the gas

temperature drops to T4. (Can we achieve the cooling effect by using a throttling

valve instead of a turbine?) Finally, the cool gas absorbs heat from the

refrigerated space until its temperature rises to T1.

All the processes described are internally reversible, and the cycle executed is

the ideal gas refrigeration cycle. In actual gas refrigeration cycles, the

compression and expansion processes deviate from the isentropic ones, and T3 is

higher than T0 unless the heat exchanger is infinitely large.

Prepared by Prof. (Dr.) Manmatha K. Roul Page 3 On a T-s diagram, the area under process curve 4-1 represents the heat removed

from the refrigerated space, and the enclosed area 1-2-3-4-1 represents the net

work input. The ratio of these areas is the COP for the cycle, which may be

expressed as

Prepared by Prof. (Dr.) Manmatha K. Roul Page 4 Gas Refrigeration cycle with regenerator:-


MODULE-III

LECTURE-25

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June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul Page 2 The Vapor Compression Refrigeration Cycle:- The vapor compression refrigeration cycle has four components: evaporator,

compressor, condenser, and expansion (or throttle) valve. The most widely used

refrigeration cycle is the vapor-compression refrigeration cycle. In an ideal

vapor-compression refrigeration cycle, the refrigerant enters the compressor as a

saturated vapor and is cooled to the saturated liquid state in the condenser. It is

then throttled to the evaporator pressure and vaporizes as it absorbs heat from

the refrigerated space.

The ideal vapor compression cycle consists of four processes.

Process Description

1-2 isentropic compression

2-3 Constant pressure heat rejection in the condenser

3-4 Throttling in an expansion valve

4-1 Constant pressure heat addition in the evaporator

Prepared by Prof. (Dr.) Manmatha K. Roul Page 3 The P-h diagram is another convenient diagram often used to illustrate the refrigeration cycle.

The ordinary household refrigerator is a good example of the application of this cycle.

Results of First and Second Law Analysis for Steady-Flow Component Process First Law Result Compressor s = Const. & & ( )W m h hin = −2 1 Condenser P = Const. & & ( )Q m h hH = −2 3 Throttle Valve ∆s > 0 h h4 3=

&Wnet = 0 &Qnet = 0 Evaporator P = Const. & & ( )Q m h hL = −1 4

Prepared by Prof. (Dr.) Manmatha K. Roul Page 4 COP of vopuor compression refrigeration system: -

Actual Vapor-Compression Refrigeration Cycle:-


MODULE-III

LECTURE-26

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June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul Page 2 Vapour Absorption Refrigeration System:- Vapour Absorption Refrigeration Systems (VARS) belong to the class of vapour cycles similar to vapour compression refrigeration systems. However, unlike vapour compression refrigeration systems, the required input to absorption systems is in the form of heat. Hence these systems are also called as heat operated or thermal energy driven systems. Since conventional absorption systems use liquids for absorption of refrigerant, these are also sometimes called as wet absorption systems. Similar to vapour compression refrigeration systems, vapour absorption refrigeration systems have also been commercialized and are widely used in various refrigeration and air conditioning applications. Since these systems run on low-grade thermal energy, they are preferred when low-grade energy such as waste heat or solar energy is available. Since conventional absorption systems use natural refrigerants such as water or ammonia they are environment friendly. Basic principle:- In this lesson, the basic working principle of absorption systems, the maximum COP of ideal absorption refrigeration systems, basics of properties of mixtures and simple absorption refrigeration systems will be discussed. When a solute such as lithium bromide salt is dissolved in a solvent such as water, the boiling point of the solvent (water) is elevated. On the other hand, if the temperature of the solution (solvent + solute) is held constant, then the effect of dissolving the solute is to reduce the vapour pressure of the solvent below that of the saturation pressure of pure solvent at that temperature. If the solute itself has some vapour pressure (i.e., volatile solute) then the total pressure exerted over the solution is the sum total of the partial pressures of solute and solvent. If the solute is non-volatile (e.g. lithium bromide salt) or if the boiling point difference between the

Prepared by Prof. (Dr.) Manmatha K. Roul Page 3 solution and solvent is large (≥ 300oC), then the total pressure exerted over the solution will be almost equal to the vapour pressure of the solvent only. In the simplest absorption refrigeration system, refrigeration is obtained by connecting two vessels, with one vessel containing pure solvent and the other containing a solution. Since the pressure is almost equal in both the vessels at equilibrium, the temperature of the solution will be higher than that of the pure solvent. This means that if the solution is at ambient temperature, then the pure solvent will be at a temperature lower than the ambient. Hence refrigeration effect is produced at the vessel containing pure solvent due to this temperature difference. The solvent evaporates due to heat transfer from the surroundings flows to the vessel containing solution and is absorbed by the solution. This process is continued as long as the composition and temperature of the solution are maintained and liquid solvent is available in the container. The most widely used absorption refrigeration system is the ammonia-water system, where ammonia serves as the refrigerant and water as the transport medium. The work input to the pump is usually very small, and the COP of absorption refrigeration systems is defined as COP

Q

Q W

Q

QR

L

gen pump in

L

gen

= = =+

≅Desired outputRequired input Cooling effectWork input ,

Prepared by Prof. (Dr.) Manmatha K. Roul Page 4 Schematic diagram:-

Prepared by Prof. (Dr.) Manmatha K. Roul Page 1


MODULE-III

LECTURE-27

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June 2016

Prepared by Prof. (Dr.) Manmatha K. Roul Thermodynamic relations:

Maxwell's relations are a set of equations in from the definitions of the for the nineteenth-century physicist The Maxwell relations are statements of equality among the second derivatives of the thermodynamic potentials. They follow directly from the fact thadifferentiation of an analytic functionthermodynamic potential and potential, then the Maxwell relation for that potential and those variables is:Maxwell relations(general) where the partial derivativesconstant. It is seen that for every thermodynamic potential there are possible Maxwell relations where potential The four most common Maxwell relations are the equalities of the second derivatives of each of the four thermodynamic potentials, with respect to their thermal natural variable (temperaturevariable (pressureP; or volume by Prof. (Dr.) Manmatha K. Roul :- are a set of equations in thermodynamics which are derivable from the definitions of the thermodynamic potentials. These relations are named century physicist James Clerk Maxwell. The Maxwell relations are statements of equality among the second derivatives of the thermodynamic potentials. They follow directly from the fact thaanalytic function of two variables is irrelevant. If Φ is a thermodynamic potential and xi and xj are two different natural variablespotential, then the Maxwell relation for that potential and those variables is:

(general) partial derivatives are taken with all other natural variables held constant. It is seen that for every thermodynamic potential there are tions where n is the number of natural variables for that The four most common Maxwell relations are the equalities of the second derivatives of each of the four thermodynamic potentials, with respect to their temperatureT; or entropyS) and their mechanicalvolumeV): Page 2 which are derivable . These relations are named The Maxwell relations are statements of equality among the second derivatives of the thermodynamic potentials. They follow directly from the fact that the order of of two variables is irrelevant. If Φ is a natural variables for that potential, then the Maxwell relation for that potential and those variables is: are taken with all other natural variables held constant. It is seen that for every thermodynamic potential there are n(n − 1)/2 is the number of natural variables for that The four most common Maxwell relations are the equalities of the second derivatives of each of the four thermodynamic potentials, with respect to their mechanical natural

Prepared by Prof. (Dr.) Manmatha K. Roul Maxwell's relations where the potentials as functions of their natural thermal and mechanical variables are the internal energyU(S, VGibbs free energyG(T, P). The to recall and derive these relationsDerivation of the Maxwell relation can be deduced from thedifferential forms of the The differential form of internal energy U This equation resemble It can be shown that for any equation of the formby Prof. (Dr.) Manmatha K. Roul Maxwell's relations(common) where the potentials as functions of their natural thermal and mechanical variables S, V), EnthalpyH(S, P), Helmholtz free energy. The thermodynamic square can be used as a to recall and derive these relations

Derivation Derivation of the Maxwell relation can be deduced from thedifferential forms of the thermodynamic potentials: The differential form of internal energy U is This equation resemble total differentials of the form It can be shown that for any equation of the form Page 3 where the potentials as functions of their natural thermal and mechanical variables Helmholtz free energyA(T, V) and can be used as a mnemonic Derivation of the Maxwell relation can be deduced from the

Prepared by Prof. (Dr.) Manmatha K. Roul that Consider, the equation immediately see that Since we also know that for functions with continuous second derivatives, the mixed partial derivatives are identical (of second derivatives), that is, thatwe therefore can see thatand therefore that Derivation of Maxwell Relation from Helmholtz Free energyThe differential form of Helmholtz free energy is by Prof. (Dr.) Manmatha K. Roul Consider, the equation . We can now Since we also know that for functions with continuous second derivatives, the mixed partial derivatives are identical (Symmetry ), that is, that we therefore can see that Derivation of Maxwell Relation from Helmholtz Free energy The differential form of Helmholtz free energy is Page 4 Since we also know that for functions with continuous second Symmetry

Prepared by Prof. (Dr.) Manmatha K. Roul From symmetry of second derivativesand therefore that The other two Maxwell relation can be derived from differential form of enthalpy of Gibbs free energy all Maxwell Relationship above follows from one of the equations. Combined form first and second law of thermodynamics, U, S, and V are state functions. Let, by Prof. (Dr.) Manmatha K. Roul From symmetry of second derivatives The other two Maxwell relation can be derived from differential and the differential from of Gibbs free energy in a similar way. So all Maxwell Relationship above follows from one of the Gibbs Extended derivation Combined form first and second law of thermodynamics, (Eq.1) U, S, and V are state functions. Let, Page 5 The other two Maxwell relation can be derived from differential and the differential from in a similar way. So Gibbs

Prepared by Prof. (Dr.) Manmatha K. Roul Substitute them in Eq.1 and one gets,And also written as, comparing the coefficient of dx and dy, one getsDifferentiating above equations by y, x respectively(Eq.2) and (Eq.3) U, S, and V are exact differentials, therefore,by Prof. (Dr.) Manmatha K. Roul in Eq.1 and one gets, comparing the coefficient of dx and dy, one gets Differentiating above equations by y, x respectively U, S, and V are exact differentials, therefore, Page 6

Prepared by Prof. (Dr.) Manmatha K. Roul Subtract eqn(2) and (3) andNote: The above is called the general expression for Maxwell's thermo dynamicalMaxwell's first relation Allow x = S and y = V and one gets Maxwell's second relation Allow x = T and y = V and one gets Maxwell's third relation Allow x = S and y = P and one gets Maxwell's fourth relation Allow x = T and y = P and one gets by Prof. (Dr.) Manmatha K. Roul Subtract eqn(2) and (3) and one gets Note: The above is called the general expression for Maxwell's thermo dynamical relation. Maxwell's first relation Allow x = S and y = V and one gets Maxwell's second relation Allow x = T and y = V and one gets Maxwell's third relation Allow x = S and y = P and one gets Maxwell's fourth relation Allow x = T and y = P and one gets Page 7 Note: The above is called the general expression for Maxwell's

Prepared by Prof. (Dr.) Manmatha K. Roul Maxwell's fifth relation Allow x = P and y = V Maxwell's sixth relation Allow x = T and y = S and one gets by Prof. (Dr.) Manmatha K. Roul Maxwell's fifth relation Allow x = P and y = V = 1 Maxwell's sixth relation Allow x = T and y = S and one gets = 1 Page 8

Prepared Prof. (Dr.) Manmatha K. Roul Page 1


MODULE-III

LECTURE-28

Prepared By



June 2016

Prepared Prof. (Dr.) Manmatha K. Roul Isothermal compressibility and volumetric expansivity:In a single phase region, where pressure and temperature are independent, we can think of the volume as being a function of pressure and temperature. or, Applying the chain rule of the calculus The derivative represents the slope of a line of constant pressure on V plane. A similar interpretation can be given for the second derivative. These derivatives are themselves intensive thermodynamic properties, since they have definite values at any fixed thermodsensitivity of the specific volume changes in temperature at constant pressure, and the second is a measure of the change in specific volume associated with a change in pressure at constant temperature. Isothermal comcompressibility and volume expansivity are defined as Isothermal compressibility: Volume expansivity: The compressibility factors are frequently tabulated functions of state. The “coefficient of linear expansion” used in elem3β Young's modulus of elasticity is proportional to k(1.148) can be written as Manmatha K. Roul Isothermal compressibility and volumetric expansivity:- In a single phase region, where pressure and temperature are independent, we can think of the volume as being a function of pressure and temperature. V = V (T, p) v = v(T, p) Applying the chain rule of the calculus represents the slope of a line of constant pressure on V plane. A similar interpretation can be given for the second derivative. These derivatives are themselves intensive thermodynamic properties, since they have definite values at any fixed thermodynamic state. The first represents the sensitivity of the specific volume changes in temperature at constant pressure, and the second is a measure of the change in specific volume associated with a change in pressure at constant temperature. Isothermal compressibility, isentropic compressibility and volume expansivity are defined as Isothermal compressibility: The compressibility factors are frequently tabulated functions of state. The “coefficient of linear expansion” used in elementary strength of materials texts is 3β Young's modulus of elasticity is proportional to kT in terms of β and kdv = β vdT - kTvdp Page 2 In a single phase region, where pressure and temperature are independent, we can think of the volume as being a function of pressure and temperature. represents the slope of a line of constant pressure on V - T a plane. A similar interpretation can be given for the second derivative. These derivatives are themselves intensive thermodynamic properties, since they have ynamic state. The first represents the sensitivity of the specific volume changes in temperature at constant pressure, and the second is a measure of the change in specific volume associated with a change pressibility, isentropic The compressibility factors are frequently tabulated functions of state. The “co-entary strength of materials texts is in terms of β and kT, Eq.

Prepared Prof. (Dr.) Manmatha K. Roul Usefulness of Eq. 1.149 arises from the fact that β and kvarying functions of T and P. Another term in use is the isothermal compressibility defined as Based on the definitions of isothermal compressibility and volume expansivity, the specific heat differences can be written as Ratio of heat capacities At constant entropy S , the two Dividing Eq. (1.152) by Eq. (1.153) and using Theorem 3Energy Equation For a system undergoing an infinitesimalequilibrium states, the change in internal energy isSubstituting the first T - dS relation, Manmatha K. Roul Usefulness of Eq. 1.149 arises from the fact that β and kT are sometimes slowly functions of T and P. Another term in use is the isothermal compressibility

Based on the definitions of isothermal compressibility and volume expansivity, the specific heat differences can be written as , the two T - dS relations become

Dividing Eq. (1.152) by Eq. (1.153) and using Theorem 3 For a system undergoing an infinitesimal reversible process between two equilibrium states, the change in internal energy is dU = Tds - pdV dS relation, Page 3 are sometimes slowly functions of T and P. Another term in use is the isothermal compressibility Based on the definitions of isothermal compressibility and volume expansivity, the reversible process between two

Prepared Prof. (Dr.) Manmatha K. Roul If U = U(T, V), then Comparing Eq. (1.157) with Eq. (1.158),Eq. (1.159) is known as the energy equation. Application of energy equation to an For an ideal gas in a closed system, equation of state is U does not change with Further, applying Theorem 2,

Hence, Manmatha K. Roul Comparing Eq. (1.157) with Eq. (1.158), Eq. (1.159) is known as the energy equation.

Application of energy equation to an ideal gas For an ideal gas in a closed system, equation of state is

does not change with V at constant temperature.

Page 4

at constant temperature.


Since,

From Eqs.(1.162) and Eq. (1.165) it is clear that U is neither a function of V nor a function of P at constant temperature. Only possibility is that internal energy is a function of temperature only.

For an open system

dH = Tds + Vdp

From second T - dS relation,

Now,

Let, H = H(T, p)

Hence,

Comparing Eq. (1.167) and Eq. (1.168),

Now,


For an ideal gas

Hence,

∴ H does not change with p while temperature remaining unchanged.

From, we can infer that

∴ H does not change with V while temperature remaining unchanged.

elations - II QUESTIONS: 1. Write down the first and second T-dS relations. 2. Under what condition(s) specific heat at constant pressure and constant volume become same. 3. Why Cp>Cv ? 4. Express Cp - Cv in terms of volume expansivity and isothermal compressibility. 5. State the applications of energy equation.

engineering thermodynamics module-iii lecture-22 · the standard of comparison for refrigeration...

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