Thermodynamics - Lecture Notes [IIT KGP]

8/10/2019 Thermodynamics - Lecture Notes [IIT KGP]

1/208

Thermodynamics (ME22002) Spring 2006Indian Institute of Technology KharagpurDepartment of Mechanical Engineering

Course Outline

1. In troduct ion:Fundamental Concepts: definitions of system and surrounding, concept of control volume,thermodynamic state, concepts of simple compressible substances, pure substance and phase,thermodynamic processes and thermodynamic equilibrium; Temperature and Zeroth law; Thermodynamicproperties and use of tables of thermodynamic properties; Idea of a generalized chart and the law ofcorresponding states; Concept of ideal gases and their equations of state; Thermodynamic concept ofenergy; Modes of work and heat transfer.

2. First Law of T hermodynamics: The first law referred to cyclic and non-cyclic processes, concept ofinternal energy of a system, conservation of energy for simple compressible closed systems; Definitions ofenthalpy and specific heats; Conservation of energy for an open system or control volume, steady &transient processes.

3. Second Law of Therm odynamics: The directional constraints on natural processes; Formal statements;Concept of reversibility; Carnot principle; Absolute thermodynamic temperature scale; ClausiusInequality, entropy, change in entropy in various thermodynamic processes, Tds relations, entropybalance for closed and open systems, Principle of increase- in- Entropy, entropy generation.

4. Exergy:Concept of reversible work & irreversibility;Second law efficiency; Exergy change of a system:

closed & open systems, exergy transfer by heat, work and mass, exergy destruction, exergy balance inclosed & open systems.

5. Thermodynamic Propert y Relat i ons:Maxwell relations; Clausius-Clapeyron equation; Difference in heatcapacities; Ratio of heat capacities; Joule-Thompson coefficient; a revisit to property diagrams of simplecompressible substances.

6. Intr oducti on t o Proper t ies of Mix t ures and Phases:

Ideal gas mixtures: Amagat and Dalton model for mixture of ideal gases, Equation of state and properties

of ideal gas mixtures, Change in entropy on mixing. Non ideal mixtures: Partial molal properties, fugacity of a component in a mixture, changes in property on

mixing, free energy of mixing, concept of an ideal solution, conditions of phase equilibrium and chemicalequilibrium of multi-component systems, Gibbs phase rule.

7. Thermodynamics of Reacti ve Systems: First law analysis of reactive system; Internal energy andenthalpy of reaction; Enthalpy of formation; Second law applied to a reactive system.

8 Air St andar d Cycl es: Carnot Stirling Ericssion Otto Diesel and Dual cycles Brayton cycle:


2/208

Thermodynamics: ME22002Course Instructor: Suman Chakraborty

ASSIGNMENT PROBLEMS SET 1

Chapters 3-5 (Fundamentals of Thermodynamics, 6th

Ed., by Sonntag, Borgnakke and

Van Wylen)

Problem numbers

Chapter 3: 41, 44, 49, 57, 60, 65, 73, 78, 97, 99, 101, 103, 105, 107,109, 113

Chapter 4: 33, 41, 42, 53, 54, 61, 63, 64, 67, 73, 77, 110

Chapter 5: 35, 48, 50, 57, 58, 62, 70, 73, 95, 99, 101, 130, 132, 134


3/208

Thermodynamics: ME22002

Course Instructor: Suman Chakraborty

SOLUTIONS TO ASSIGNMENT PROBLEMS FROM Chapter 3 (Fundamentalsof Thermodynamics, 6

thEd., by Sonntag, Borgnakke and Van Wylen)


4/208


5/208


6/208


7/208


8/208


9/208


10/208


11/208


12/208


13/208



SOLUTIONS TO ASSIGNMENT PROBLEMS FROM Chapter 4 (Fundamentalsof Thermodynamics, 6

thEd., by Sonntag, Borgnakke and Van Wylen)


14/208


15/208


16/208


17/208


18/208


19/208


20/208


21/208


22/208



SOLUTIONS TO ASSIGNMENT PROBLEMS FROM Chapter 5 (Fundamentalsof Thermodynamics, 6th

Ed., by Sonntag, Borgnakke and Van Wylen)


23/208


24/208


25/208


26/208


27/208


28/208


29/208


30/208


31/208


32/208


33/208


34/208


35/208


36/208


ASSIGNMENT PROBLEMS SET 2

Chapters 6-9 (Fundamentals of Thermodynamics, 6th

Ed., by Sonntag, Borgnakke and

Van Wylen)

Problem numbers

Chapter 6: 39, 57, 59, 75, 82, 88,105,107, 108,111, 115, 116, 117,

118,119, 120, 121, 122, 131,133, 134

Chapter 7: 38, 44, 48, 58, 62, 64, 65, 71, 76, 82, 84, 86, 88, 89, 90,91

Chapter 8: 14, 15, 16, 33, 45, 52, 54, 65, 70, 71, 76, 82, 85, 86, 90,98, 100, 101, 103, 109, 120, 126, 128, 129, 130, 131, 133, 134, 137

Chapter 9: 26, 28, 37, 38, 39, 41, 51, 68, 74, 77, 96, 101, 116, 119,126, 127, 130, 132


37/208



SOLUTIONS TO ASSIGNMENT PROBLEMS FROM Chapter 6 (Fundamentals

of Thermodynamics, 6thEd., by Sonntag, Borgnakke and Van Wylen)


38/208


39/208


40/208


41/208


42/208


43/208


44/208


45/208


46/208


47/208


48/208


49/208


50/208


51/208


52/208


53/208


54/208


55/208


56/208


57/208


58/208




of Thermodynamics, 6th



59/208


60/208


61/208


62/208


63/208


64/208


65/208


66/208


67/208


68/208


69/208


70/208


71/208


72/208




73/208


SOLUTIONS TO ASSIGNMENT PROBLEMS FROM Chapter 8(Fundamentals of

Thermodynamics, 6

th



74/208


75/208


76/208


77/208


78/208


79/208


80/208


81/208


82/208


83/208


84/208


85/208


86/208


87/208


88/208


89/208


90/208


91/208


92/208


93/208


94/208


95/208


96/208


97/208


98/208


99/208


100/208


101/208







102/208


103/208


104/208


105/208


106/208


107/208


108/208


109/208


110/208


111/208


112/208


113/208


114/208


115/208


116/208


117/208


118/208


119/208







120/208


121/208


122/208


123/208


124/208


125/208


126/208


127/208


128/208


129/208


130/208


131/208


132/208


133/208


134/208


135/208







136/208


137/208


138/208


139/208


140/208


141/208


142/208


143/208


144/208


145/208


146/208


147/208


148/208


149/208


150/208


151/208


152/208


153/208







154/208


155/208


156/208


157/208


158/208


159/208


160/208


161/208


162/208


163/208


ASSIGNMENT PROBLEMS CHAPTER 15

(Fundamentals of Thermodynamics, 6th


Problem numbers

32, 38, 49, 52, 54, 60, 62, 72, 80


164/208







165/208


166/208


167/208


168/208


169/208


170/208


171/208


172/208


173/208

Thermodynamics (ME22002), IIT Kharagpur, Spring 2006

Problem set onProperties of Mixtures and Phases

Q1. Equation of state of a non-ideal 2-component gas mixture is given as:2

1 11 1 2 12 2 222RT

v y B y y B yp

= + + + 2B , where yi is the mole fraction of the ith

component in

the mixture. For a binary mixture of 10 mole % chloroform (component 1) in acetone

(component 2) at 333K and 10 bar, the coefficients Bijare given as follows: B11= -910

cm3/mol B22= 1330 cm

3/mol and B12 = 2005 cm

3/mol Determine: (i) Molar specific


174/208

cm /mol, B22= -1330 cm /mol, and B12= -2005 cm /mol. Determine: (i) Molar specificvolume of pure chloroform (ii) Partial molal volume of chloroform in the mixture, and

(iii) Change in volume on mixing.

(Ans: (i) 1860 cm3/mol, (ii) 991 cm3/mol, (iii) -372 cm3/mol)

Q2. (a) For a binary system (constituents A + B) at constant temperature and pressure,the molar volume (cm

3/mol) is obtained in terms of the respective mole fractions as:

v = 100yA+ 80yB+2.5yAyB, where yA is the mole fraction of the A and yBis the mole

fraction of the B in the mixture.(i) What is the partial molal volume of the component A in the mixture, as the mole

fraction of A tends to zero, in a limiting sense?

(ii) Illustrate with a sketch, how would you obtain the above result from a graphical plot

of molar volume versus mole fraction of the component B? No explicit numericalcalculations are necessary.

(iii) Obtain an expression for change in volume due to mixing, as a function of mole

fraction of individual constituents. What is the mole fraction for which this change is amaximum? Does the volume increase or decrease, on account of mixing?

(Ans: (i) 102.5 cm3/mol, (iii) )2.5 0mix A BV y y = >

Q3. At 21C, the enthalpy of mixing of sulphuric acid and water can be fit to thefollowing equation: kJ/mol. Molar enthalpies of

2 4 2 2 474.4 (1 0.561 )mix H SO H O H SOH y y y =

( ) ( )2ln ln

a a b a bmixa a

a mix

y n y a av b pf b

y p RT v b RTv

+ = +

, where v is the mixture

specific volume and .mix a a b bb y b y= + b

Q6.Derive the Clapeyron equation from the considerations of equilibrium of a two-phasesingle component system.

Q7. What pressure is required to make diamond from graphite at 25C? For yourcalculations, following data are given for a temperature of 25C and pressure of 0.1 MPa:

Graphite Diamond


175/208

Graphite Diamondg 0 2867.8 kJ/kmol

v 0.000284 m3/kg 0.000284 m

3/kg

T 0.30410-6

1/MPa 0.01610-61/MPa

(Ans: 1493 MPa)

Q8. Air (~21% O2, 79% N2) is cooled to 80 K, 0.1 MPa. Calculate the composition ofliquid and vapour phases in this condition. Given: saturation pressure of O2= 0.137 MPa

and saturation pressure of N2= 0.03006 MPa.

(Ans: mole fraction of O2in liquid phase =0.654 and in vapour phase = 0.896)

Q9. Determine the mole fraction of air at the surface of a lake whose temperature is

17C. Take the atmospheric pressure at the lake level to be 92 kPa. Given, Henrysconstant for air dissolved in water at 290 K= 62000 bar.

(Ans: 1.4510-5)

Q10. Fresh water is to be obtained from sea water at 15C, with a salinity of 3.48% onmass basis. Determine the minimum work input required to separate 1 kg of sea water

completely into pure water and pure salt. State any assumptions you make. Given:

molecular weight of water= 18, molecular weight of salt= 58.44.(Ans: 7 87 kJ/kg of seawater assumption: the mixture behaves as an ideal solution)


176/208


177/208


178/208


179/208


180/208


181/208


182/208


183/208


184/208


Problem Set on Air Standard Cycles

1. A stoichiometric mixture of gasoline and air has an energy release upon

combustion of approximately 2800 kJ/kg of the mixture. To approximate anactual spark- ignition engine using such a mixture, consider an air-standard Otto

cycle that has a heat addition of 2800 kJ/kg of air, a compression ratio of 7, and a

pressure and temperature at the beginning of the compression process of 90 kPa,10C. Assuming constant specific heat, with the value from Table A.l0, determine

a) The maximum pressure and temperature of the cycle.

b) The thermal efficiency of the cycle.

c) The mean effective pressure.


185/208

) p

2.

In the air-standard Otto cycle, all the heat transfer qh occurs at constant volume. Itwould be more realistic to assume that part of qh occurs after the piston has startedits downward motion in the expansion stroke. Therefore, consider a cycle

identical to the Otto cycle, except that the first two-thirds of the total qh occurs at

constant volume and the last one-third occurs at constant pressure. Assume thatthe total qhis 2400 kJ/kg, that the pressure and temperature at the beginning of the

compression process are 90 kPa, 20C, and that the comparison ratio is 7

Calculate the maximum pressure and temperature and the thermal efficiency of

this cycle. Compare the results with those of a conventional Otto cycle having thesame given variables.

3. Consider an ideal air-standard diesel cycle in which the state before the

compression process is 95 kPa, 290 K, and the compression ratio is 20. Whatmaximum temperature must the cycle have to have a thermal efficiency of 60%?

4.

An air-standard Ericsson cycle has an ideal regenerator. Heat is supplied at

1000C and heat is rejected at 20C. Pressure at the beginning of the isothermalcompression process is 70 kPa The heat added is 600 kJ/kg Find the compressor

1600 K. The minimum pressure in the cycle is 100 kPa, and the compressor

pressure ratio is 14 to 1.a) Calculate the power output of the turbine. What fraction of the turbine

output is required to drive the compressor?

b) What is the thermal efficiency of the cycle?

7.

Repeat Problem 6, but assuming that the compressor has an isentropic efficiency

of 85% and the turbine an isentropic efficiency of 88%.

8. The gas turbine cycle shown in the figure below is to be used as an automotive

engine. In the first turbine, the gas expands to a pressure P5, just low enough for

this turbine to drive the compressor. The gas is then expanded through the second


186/208

turbine connected to the drive wheels. The data for this engine are shown in the

figure. Consider the working fluid to be air throughout the entire cycle, andassume that all processes are ideal. Determine.

a) The intermediate pressure P5.b) The net specific work output of the engine, and the mass flow rate

through the engine.

c) The air temperature entering the burner T3, and the thermal efficiency ofthe engine.

=150 kW

7


187/208


188/208


189/208


190/208


191/208


192/208


193/208


194/208


195/208


196/208


Problem Set on Vapour Cycles

1. A steam power plant has a boiler exit at 4MPa, 5000C and a condenser exit

temperature of 450C. Assume all components are ideal and find the cycle

efficiency and the specific work and heat transfer in the components.

2. Consider a simple ideal Rankine cycle that uses steam as the working fluid. The

highpressure side of the cycle is at a supercritical pressure. Such a cycle has apotential advantage of minimizing local temperature differences between the

fluids in the steam generator, such as the instance in which the hightemperatureenergy source is the hot exhaust gas from a gasturbine engine. Calculate the

thermal efficiency of the cycle if the state entering the turbine is 25 MPa, 5000C,


197/208

t e a e c e cy o t e cyc e t e state e te g t e tu b e s 5 a, 500 C,

and the condenser pressure is 5 kPa. What is the steam quality at the turbine exit?

3. Consider an ideal steam regenerative cycle in which steam enters the turbine at

3.5 MPa, 400C, and exhausts to the condenser at 10 kPa. Steam is extracted from

the turbine at 0.8 MPa and also at 0.2 MPa for heating the boiler feed water in twoopen feed water heaters. The feed water leaves each heater at the temperature of

the condensing steam. The appropriate pumps are used for the water leaving the

condenser and the two feed water heaters. Calculate the thermal efficiency of the

cycle and the net work per kilogram of steam.

4. Consider an ideal steam combined reheat and regenerative cycle in which steamenters the high-pressure turbine at 3.5 MPa, 400C, and is extracted for feed water

heating at 0.8 MPa. The remainder of the steam is reheated to 400C at this

pressure, 0.8 MPa, and is fed to the low-pressure turbine. Steam is extracted fromthe low-pressure turbine at 0.2 MPa for feed water heating. The condenser

pressure is 10 kPa. Both feed water heaters are open heaters. Calculate the

thermal efficiency of the cycle and the net work per kilogram of steam.

5. An ideal steam power plant is designed to operate on the combined reheat and re-

6. Steam leaves a power plant steam generator at 3.5 MPa, 400C, and enters the

turbine at 3.4 MPa, 375C. The isentropic turbine efficiency is 88%, and theturbine exhaust pressure is 10 kPa. Condensate leaves the condenser and enters

the pump at 35C, 10 kPa. The isentropic pump efficiency is 80%, and the

discharge pressure is 3.7 MPa. The feed water enters the steam generator at 3.6

MPa, 30C. Calculate the following.

a. The thermal efficiency of the cycle.

b. The irreversibility of the process in the line between the steam generator exitand the turbine inlet, assuming an ambient temperature of 25C.

7. For the steam power plant described in Problem 1, assume the isentropicefficiencies of the turbine and pump are 85% and 80%, respectively. Find the

t ifi k d h t t f d th l ffi i


198/208

component specific work and heat transfers and the cycle efficiency.

8. Find the availability .of the water at all the states in the steam power plant de-

scribed in the previous problem. Assume. The heat source in the boiler is at600"C and the low-temperature reservoir is at 25C. Give the second law

efficiency of all the components.

9. In a particular reheat-cycle power plant, steam enters the high-pressure turbine at5 MPa, 450C and expands to 0.5 MPa, after which it is reheated to 450C. The

steam is then expanded through the low-pressure turbine to 7.5 kPa. Liquid waterleaves the condenser at 30C, is pumped to 5 MPa, and then returned to the steamgenerator. Each turbine is adiabatic with an isentropic efficiency of 87% and the

pump efficiency is 82%. If the total power output of the turbines is 10 MW, deter-

mine

a. The mass flow rate of steam

b. The pump power input

c. The thermal efficiency of the power plant


199/208


200/208


201/208


202/208


203/208


204/208


205/208


206/208


207/208


208/208

Thermodynamics - Lecture Notes [IIT KGP]

Documents

Transcript of Thermodynamics - Lecture Notes [IIT KGP]