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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

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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®



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



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




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




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) .


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.


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)




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


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.


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.


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)




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 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


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

gate 2020 · boranch ffice : raipur : 79743-90037, bhopal : 83198-88401 1.6 an isolated...

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