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GATE 2020Mechanical Engineering
(Volume - I)
TOPIC WISE GATE SOLUTIONS
1987 - 2019
TM
GATE A PCADEMY UBLICATIONS®
S. No. Topics Page No.
1. Fluid Mechanics 1.1 - 1.000
1. Properties of Fluid 1.1 - 1.00
2. Pressure & Its Measurement 1.00 - 1.00
3. Hydrostatic Forces 1.00 - 1.00
4. Buoyancy & Floatation 1.00 - 1.00
5. Kinematics of Fluid 1.00 - 1.00
6. Dynamics of Fluid 1.00 - 1.00
7. Laminar & Turbulent Flow, Viscous Flow, Flow Through Pipes 1.00 - 1.00
8. Boundary Layer Theory 1.00 - 1.00
9. Hydraulic Machines 1.00 - 1.00
2. Thermodynamics 2.1 - 2.000
1. Thermodynamics System & Process 2.1 - 2.00
2. First Law of Thermodynamics 2.00 - 2.00
3. Second Law of Thermodynamics 2.00 - 2.00
4. Entropy 2.00 - 2.00
5. Availability & Irreversibility 2.00 - 2.00
6. Pure Substances 2.00 - 2.00
7. Steam Power Cycles 2.00 - 2.00
8. Gas Power Cycles 2.00 - 2.00
9. Internal Combustion Engine 2.00 - 2.00
3. Heat Transfer 3.1 - 3.000
1. Conduction 3.1 - 3.0
2. Fins & Unsteady Heat Transfer 3.0 - 3.00
3. Free & Forced Convection 3.00 - 3.00
4. Heat Exchanger 3.00 - 3.00
5. Radiation 3.00 - 3.00
CONTENTS
4. Refrigeration & Air-Conditioning 4.1 - 4.000
1. Vapour Refrigeration 4.1 - 4.0
2. Properties of Moist Air & Psychrometric Processes 4.0 - 4.00
3. Heat Pumps & Cycles 4.00- 4.00
5. Mechanics of Solids 5.1 - 5.000
1. Stress & Strain 5.1 - 5.0
2. Complex Stress 5.0 - 5.00
3. Elastic Constants & Theory of Failure 5.00 - 5.00
4. Thin Cylinder 5.00 - 5.00
5. Shear Force & Bending Moment Diagrams 5.00 - 5.00
6. Bending of Beam 5.00 - 5.00
7. Torsion of Shaft 5.00 - 5.00
8. Springs 5.00 - 5.00
9. Euler's Theory of Column 5.00 - 5.00
10. Strain Energy & Thermal Stresses 5.00 - 5.00
6. Machine Design 6.1 - 6.000
1. Design Against Static Load (Theory of Failure) 6.1 - 6.0
2. Design Against Dynamic Load (Fatigue Strength & SN Diagram) 6.0 - 6.00
3. Gears 6.00 - 6.00
4. Bearings, Shaft & Keys 6.00 - 6.00
5. Clutches, Ropes & Belts 6.00 - 6.00
6. Brakes 6.00 - 6.00
7. Joints (Bolted, Riveted & Welded) 6.00 - 6.00
8. Power Screws & Springs 6.00 - 6.00
7. General Aptitude 7.1 - 7.000
1. Numerical Ability 7.1 – 7.0
2. Logical Reasoning 7.0 - 7.00
3. Verbal Ability 7.00 - 7.00
© Copyrightwww.gateacademy.co.inH Oead ffice : A/114-115, Smriti Nagar, Bhilai (C.G.), Contact : 9713113156, 9589894176
B Oranch ffice : Raipur : 79743-90037, Bhopal : 83198-88401
1.1 An insulated rigid vessel contains a
mixture of fuel and air. The mixture is
ignited by a minute spark. The contents
of the vessel experience. [1 Mark]
(A) Increase in temperature, pressure
and energy
(B) Decrease in temperature, pressure
and energy
(C) Increase in temperature and pressure
but no change in energy
(D) Increase in temperature and pressure
but decreases in energy
1.2 A body or weight 100 N falls freely a
vertical distance of 50 m. The
atmospheric drag force is 0.5 N. For the
body, the work interaction is [1 Mark]
(A) 5000 J (B) – 5000 J
(C) – 25 J (D) 25 J
1.3 The definition of 1K as per the
internationally accepted temperature
scale is [1 Mark]
(A) th(1/100) , the difference between
normal boiling point and normal
freezing point of water
(B) th(1/ 273.15) , the normal freezing
point of water
(C) 100 times the difference between the
triple point of water and normal
freezing point of water
(D) th(1/ 273.16) the triple point of water
1.4 The specific heats of an ideal gas depend
on its [1 Mark]
(A) temperature
(B) pressure
(C) volume
(D) molecular weight and structure
1.5 Match List-I with List-II [2 Marks]
List-I List-II
A. Cetane
number
1. Ideal gas
B. Approach
and range
2. Vander
Waals gas
C. 0
T
P
3. S.I. engine
D. ,Pdh c dT
even when
pressure
varies
4. C.I. engine
5. Cooling
towers
6. Heat
exchangers
1Thermodynamics
System & Process
1993 IIT Bombay
1994 IIT Kharagpur
1996 IISc Bangalore
2.2 Topic Wise GATE Solutions [ME] GATE ACADEMY®
© Copyrightwww.gateacademy.co.inH Oead ffice : A/114-115, Smriti Nagar, Bhilai (C.G.), Contact : 9713113156, 9589894176
B Oranch ffice : Raipur : 79743-90037, Bhopal : 83198-88401
1.6 An isolated thermodynamic system
executes a process. Choose the correct statements from the following :
[2 Marks] (A) No heat is transferred. (B) No work is done. (C) No mass flows across the boundary
of the system. (D) No chemical reaction takes place
within the system.
1.7 What is the speed of sound in Neon gas
at a temperature of 500 K (Gas constant of Neon is 0.4210 kJ/kg.K)? [2 Marks]
(A) 492 m/s (B) 460 m/s (C) 592 m/s (D) 543 m/s
1.8 The following four figures have been
drawn to represent a fictitious thermos-dynamic cycle, on the -p V and -T S
planes.
According to the first law of thermos-
dynamics, equal areas are enclosed by [1 Mark]
(A) Figure 1 and 2 (B) Figure 1 and 3 (C) Figure 1 and 4 (D) Figure 2 and 3
1.9 A reversible thermodynamic cycle containing only three processes and producing work is to be constructed. The constrains are : [2 Marks]
1. There must be one isothermal process.
2. There must be one isentropic process.
3. The maximum and minimum cycle pressures and the clearance volume are fixed.
4. Polytropic processes are not allowed.
Then the number of possible cycles are
(A) 1 (B) 2
(C) 3 (D) 4
1.10 Match items from groups I, II, III, IV
and V. [2 Marks]
Group I
Group II Group III Group IV Group V
When added to the system is
Differential Function Phenomenon
E Heat G Positive I Exact K Path M Transient
F Work H Negative J Inexact L Point N Boundary
(A) F-G-J-K-M, E-G-I-K-N
(B) E-G-I-K-M, F-H-I-K-N
(C) F-H-J-L-N, E-H-I-L-M
(D) E-G-J-K-N, F-H-J-K-M
A thermodynamic cycle with an ideal gas as working fluid is shown below.
V
Fig. 1
S
Fig. 2
Tp
V S
Tp
Fig. 3 Fig. 4
V
12
3
1V31m
100 kPa
400 kPa
pV�
=C
p
1999 IIT Bombay
2002 IISc Bangalore
2005 IIT Bombay
2006 IIT Kharagpur
2007 IIT Kanpur
Common Data for Questions 1.11 & 1.12
2.3GATE ACADEMY® Thermodynamics : Thermodynamic System & Process
© Copyrightwww.gateacademy.co.inH Oead ffice : A/114-115, Smriti Nagar, Bhilai (C.G.), Contact : 9713113156, 9589894176
B Oranch ffice : Raipur : 79743-90037, Bhopal : 83198-88401
1.11 The above cycle is represented on -T S
plane by, [2 Marks]
(A)
(B)
(C)
(D)
1.12 If the specific heats of the working fluid
are constant and the value of specific
heat ratio is 1.4, the thermal efficiency
(%) of the cycle is [2 Marks]
(A) 21 (B) 40.9
(C) 42.6 (D) 59.7
1.13 If a closed system is undergoing an
irreversible process the entropy of the system [1 Mark]
(A) Must increase (B) Always remains constant (C) Must decrease (D) Can increase, decrease or remain
constant
1.14 Heat and work are [1 Mark] (A) Intensive properties (B) Extensive properties (C) Point function (D) Path functions
1.15 A certain amount of an ideal gas is
initially at a pressure 1p and temperature
1.T First, it undergoes a constant
pressure process 1-2 such that 12
3.
4
TT
Then, it undergoes a constant volume
process 2-3 such that 13 .
2
TT The ratio
of the final volume to the initial volume of the ideal gas is [2 Marks]
(A) 0.25 (B) 0.75 (C) 1.0 (D) 1.5
1.16 Which of the following statements are
TRUE with respect to heat and work? [1 Mark]
(i) They are boundary phenomena (ii) They are exact differentials (iii)They are path functions (A) Both (i) and (ii) (B) Both (i) and (iii) (C) Both (ii) and (iii) (D) Only (iii)
S
1
3
T
2
S
13
T
2
S
1
3
T
2
S
13
T
2
2009 IIT Roorkee
2011 IIT Madras
2014 IIT Kharagpur
2016 IISc Bangalore
2.4 Topic Wise GATE Solutions [ME] GATE ACADEMY®
© Copyrightwww.gateacademy.co.inH Oead ffice : A/114-115, Smriti Nagar, Bhilai (C.G.), Contact : 9713113156, 9589894176
B Oranch ffice : Raipur : 79743-90037, Bhopal : 83198-88401
1.17 The volume and temperature of air
(assumed to be an ideal gas) in a closed
vessel is 2.87 3m and 300 K, respectively. The gauge pressure indicated by a manometer fitted to the wall of the vessel is 0.5 bar. If the gas constant of air is 287 J/kg KR and the atmospheric
pressure is 1 bar, the mass of air (in kg) in the vessel is [2 Marks]
(A) 1.67 (B) 3.33
(C) 5.00 (D) 6.66
1.18 If one mole of 2H gas is occupies a rigid
container with a capacity of 1000 litres
and the temperature is raised from 027 C
to 037 C , the change in pressure of the contained gas (round off to two decimal places), assuming ideal gas behaviour is ______ Pa. [2 Marks]
2017 IIT Roorkee
2019 IIT Madras
2.5GATE ACADEMY® Thermodynamics : Thermodynamic System & Process
© Copyrightwww.gateacademy.co.inH Oead ffice : A/114-115, Smriti Nagar, Bhilai (C.G.), Contact : 9713113156, 9589894176
B Oranch ffice : Raipur : 79743-90037, Bhopal : 83198-88401
1.1 C 1.2 D 1.3 D 1.4 D 1.5 A-4, B-5, C-2, D-1
1.6 A, B & C 1.7 C 1.8 A 1.9 D 1.10 D
1.11 C 1.12 A 1.13 D 1.14 D 1.15 B
1.16 B 1.17 C 1.18 83.14
Spark will result in combustion of fuel which
results in :
(i) Increase in temperature
(ii) As the vessel is rigid, volume will
remain constant and thus pressure will
increase.
(iii) As the vessel is insulated, 0Q
So the energy liberated due to combustion will
be stored as internal energy of combustion
products. Hence no change in energy.
Hence, the correct option is (C).
Given : Weight ( ) 100 NW
Atmospheric dray force ( ) 0.5 NF
Vertical distance ( ) 50 ms
Work done for body
Atmospheric drag force (F)
Displacement (S)
0.5 50 25.0J
Hence, the correct option is (D).
The kelvin is defined as the fraction th(1/ 273.16) of the thermodynamic temperature
of the triple point of water (exactly 00.01 C or 032.018 F) .
Hence, the correct option is (D).
kJ/kg K1
vR
c
and kJ/kg K1
pR
c
The value of thus depends only one molecular
structure of the gas i.e., whether the gas is
monatomic, diatomic or polyatomic having one,
two or more atoms in a molecule. Again pc and
vc of on ideal gas depend only on and R i.e.,
the number of atoms in a molecule and the
molecular weight of the gas. They are
independent of temperature or pressure of the
gas.
Hence, the correct option is (D).
0u �
Body
Body
50 ms �
100 NW �
0.5 NF �
100 NW �
(Initial position)
(Final position)
0.5 NF �
Answers Thermodynamic System & Process
Explanations Thermodynamic System & Process
1.1 (C)
1.2 (D)
1.3 (D)
1.4 (D)
2.6 Topic Wise GATE Solutions [ME] GATE ACADEMY®
© Copyrightwww.gateacademy.co.inH Oead ffice : A/114-115, Smriti Nagar, Bhilai (C.G.), Contact : 9713113156, 9589894176
B Oranch ffice : Raipur : 79743-90037, Bhopal : 83198-88401
List-I List-II
A. Cetane Number C.I. engine
B. Approach and Range
Cooling towers
C. 0
h
T
P
Vander waals gas
D. ,Pdh c dT even
when pressure varies
Ideal gas
Isolate system does not interact with surroundings,
Hence, no heat is transferred, no work is done and no mass flows across boundary, note that chemical reaction can take place.
Hence, the correct option is (A), (B) & (C).
Given : Temperature of Neon gas (T) = 500 K
Gas constant (R) = 0.4210 kJ/kg K = 421 J/kg K
For monoatomic gas,
Specific heat ratio ( ) = 1.67
The speed of sound,
C = 1.67 421 500RT
592.90C m/s
Hence, the correct option is (C).
Firstly :
For closed cycle change in internal energy is 0. First law of thermodynamics for closed system.
cycle cycle( ) ( )Q W
Secondly :
Figure 1 and 2 both are power cycle, but figure 3 and 4 are not power cycle.
If you see p-V diagram in application of 1st law of thermodynamics, the rotation is always clockwise. For example,
Hence, the correct option is (A).
Total four cycles are possible under the given constraints. Two at constant volume and two at constant pressure as shown in figure.
Hence, the correct option is (D).
Heat (E) :
1. It is positive when added to the system.
2. It is inexact differential.
3. It is a path function.
4. It is a boundary phenomenon.
Work (F) :
1. It is negative when added to the system.
2. It is inexact differential.
3. It is a path function.
Hence, the correct option is (D).
V
p
1
4
2
3
D B
A
C
V
13
2
T c�
p c�
cV
maxp
minp
p
pV
c�
=
V
1
3
p
2
cV
maxp
minp
T c�
pV
c
�
=
V
1
32
T c�
p c�
cV
maxp
minp
1
3
2
V c�
T c�
p
pV
c�
=
pV
c�
=
Vc
V
maxp
minp
p
pV
c�
=
pV
c�
=
1.5 A-4, B-5, C-2, D-1
1.6 (A), (B) & (C)
1.7 (C)
1.8 (A)
1.9 (D)
1.10 (D)
2.7GATE ACADEMY® Thermodynamics : Thermodynamic System & Process
© Copyrightwww.gateacademy.co.inH Oead ffice : A/114-115, Smriti Nagar, Bhilai (C.G.), Contact : 9713113156, 9589894176
B Oranch ffice : Raipur : 79743-90037, Bhopal : 83198-88401
Explanation (I) : Since, 3-1 is adiabatic process, it will be represented by a straight line on -T S plane. 1-2 is isobaric process, so with decrease of volume, temperature will also decrease. Also for process 1-2, constant pressure lines in
-T S diagram starts from origin side and diverge in forward direction. Hence, the correct option is (C).
Explanation (II) :
In the given ( - )p V diagram process :
(1 2) Isobaric compression
(2 3) Isochoric heat addition
(3 1) Isentropic expansion
Cycle on ( - )T S diagram
Explanation (III) : We can observe in the p-V diagram that temperature is not constant during any stage hence option (B) and (D) are rejected as temperature is constant during the stage 3-1 in both the option which is not possible option (A) is rejected because clockwise process in p-V diagram cannot have anticlockwise -T S diagram.
Hence the correct option (C).
Given : Specific heat ratio ( ) 1.4
This cycles shows the Lenoir cycle. For Lenoir cycle efficiency is given by,
1/
L
11
1p
p
r
r
where, 2
1
4004
100p
pr
p and 1.4p
v
c
c
1
1.4
L4 1
1 1.4 0.2104 1
So efficiency, L 21 %
Hence, the correct option is (A).
0, 0 or 0dS dS dS
The entropy may increase, decrease or remains constant depending upon heat involved and internal irreversibility. Hence, the correct option is (D).
Heat and work are path functions. Similarities between heat and work : 1. Both are recognised at the boundary of
the system, as they cross the boundary. Hence both are boundary phenomena.
2. System possesses energy, but neither heat nor work.
3. Both are associated with process, not state. Heat and work have NO meaning at a state.
4. Both are path functions. Path function : Magnitude depends on the path followed during the process, as well as the end states. Point function : Magnitude depends on state only, and not on how the system approaches that state. Hence, the correct option is (D).
For process 1 2 , we have
S
1
3
T
2
sQ
RQp = c
V=
c
V
p
V C=
p p2 1=
V V3 2=
12
3
1.11 (C)
1.12 (A)
1.13 (D)
1.14 (D)
1.15 (B)
2.8 Topic Wise GATE Solutions [ME] GATE ACADEMY®
© Copyrightwww.gateacademy.co.inH Oead ffice : A/114-115, Smriti Nagar, Bhilai (C.G.), Contact : 9713113156, 9589894176
B Oranch ffice : Raipur : 79743-90037, Bhopal : 83198-88401
2 13
4T T
2
1
3
4
T
T
At constant pressure, we have
2 2
1 1
3
4
T V
T V
For process 2 3 , we have
23
2
TT
Since, 3 2V V (Constant volume process)
Ratio of final to initial volume is given by,
3 2
1 1
V V
V V
30.75
4
Hence, the correct option is (B).
Heat and work are :
(i) They are boundary phenomena
(ii) They are inexact differential
(iii) They are path functions
(iv) They are not property of system
Hence, the correct option is (B).
Given : Volume of air 3
1( ) 2.87 mV
Temperature of air 1( ) 300KT
Gas constant of air,
287 J / kg KR 0.287 kJ/kg K
1.5abs atm gaugep p p bar
1.5 100 150absp kPa
Using ideal gas equation, we have
pV mRT
150 2.87 0.287 300m
5.0m kg
Hence, the correct option is (C).
Given : Volume of rigid container
3( ) 1000 litre 1 mV
Initial temperature of the gas 01( ) 27 CT
Final temperature of the gas 02( ) 37 CT
Number of mole of hydrogen ( ) 1n
1 1PV nRT
2 2PV nRT
2 1 2 1( ) ( )P P V nR T T
1 1 8.314 (37 27)P
83.14 PaP
Hence, the change in pressure of the contained gas, assuming ideal gas behaviour is 83.14 Pa.
1.16 (B)
1.17 (C)
1.18 83.14