GATE XE (Engineering Sciences) 2013 Question Paper & Solutions

Question 1

Marks: 1

If 3 ≤ ≤5 and 8 ≤ ≤11 then which of the following options is TRUE?

• A. ଷ ହ≤ ௑ ௒≤଼ହ
• B. ଷ ଵଵ≤ ௑ ௒≤ ହ଼
• C. ଷ ଵଵ≤ ௑ ௒≤଼ହ
• D. ଷ ହ≤ ௑ ௒≤଼ଵଵ

Question 2

Marks: 1

The Headmaster ___________ to speak to you. Which of the following options is incorrect to complete the above sentence?

• A. is wanting
• B. wants
• C. want
• D. was wanting

Question 3

Marks: 1

Mahatama Gandhi was known for his humility as

• A. he played an important role in humiliating exit of British from India.
• B. he worked for humanitarian causes.
• C. he displayed modesty in his interactions.
• D. he was a fine human being.

Question 4

Marks: 1

All engineering students should learn mechanics, mathematics and how to do computation. I II III IV Which of the above underlined parts of the sentence is not appropriate?

• A. I
• B. II
• C. III
• D. IV

Question 5

Marks: 1

Select the pair that best expresses a relationship similar to that expressed in the pair: water: pipe::

• A. cart: road
• B. electricity: wire
• C. sea: beach
• D. music: instrument

Question 6

Marks: 2

to Q. 10 carry two marks each. Q.6 Velocity of an object fired directly in upward direction is given by = 80 −32 ݐ, where ݐ (time) is in seconds. When will the velocity be between 32 m/sec and 64 m/sec?

• A. (1, 3/2)
• B. (1/2, 1)
• C. (1/2, 3/2)
• D. (1, 3)

Question 7

Marks: 2

In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2?

• A. 0.35
• B. 0.45
• C. 0.5
• D. 0.4

Question 8

Marks: 2

Following table gives data on tourists from different countries visiting India in the year 2011. Country Number of Tourists USA England 3500 Germany 1200 Italy 1100 Japan 2400 Australia 2300 France 1000 Which two countries contributed to the one third of the total number of tourists who visited India in 2011?

• A. USA and Japan
• B. USA and Australia
• C. England and France
• D. Japan and Australia

Question 9

Marks: 2

If |−2 + 9| = 3 then the possible value of |−ܺ| − ଶ would be:

• A. 30
• B. -30
• C. -42
• D. 42

Question 10

Marks: 2

All professors are researchers Some scientists are professors Which of the given conclusions is logically valid and is inferred from the above arguments:

• A. All scientists are researchers
• B. All professors are scientists
• C. Some researchers are scientists
• D. No conclusion follows

Question 1

Marks: 1

The value of the integral ∫ ௗ௧ ඥ(ି௟௢௚೐௧) ଵ ଴ is

• A. √గ ଶ
• B. √ߨ
• C. −√ߨ
• D. −√గ ଶ

Question 2

Marks: 1

Which one of the following partial differential equations CAN NOT be reduced to two ordinary differential equations by the method of separation of variables?

• A. డ௨ డ௧− డమ௨ డ௫మ = 0
• B. డమ௨ డ௧మ− డమ௨ డ௫మ= 0
• C. డమ௨ డ௧మ+ డమ௨ డ௧డ௫+ డ௨ డ௫= 0
• D. డమ௨ డ௧మ+ డమ௨ డ௧డ௫+ డమ௨ డ௫మ= 0

Question 3

Marks: 1

The Fourier series of the periodic function ݂(ݔ) = |ݔ|, −1 < ݔ< 1, ݂(ݔ+ 2) = ݂(ݔ), ݔ Є ℝ is given by 1 2 − ∑ 4 cos(2݊−1)ߨݔ (2݊−1)2 ߨ2 ∞ =1 . Using the above, the sum of the infinite series 1 + ଵ ଷమ+ ଵ ହమ+ . . . is

• A. ߨ2 4
• B. ଷగమ
• C. గమ
• D. గమ ଶ

Question 4

Marks: 1

Consider the function ݂(ݖ) = ݖଶݖ, ݖЄ ℂ. At ݖ= 0, the function ݂

• A. does not satisfy the Cauchy-Riemann equations
• B. satisfies the Cauchy-Riemann equations but is not differentiable
• C. is differentiable but not analytic
• D. is analytic

Question 5

Marks: 1

The integral ∮ (௭ାସ) (௭ାଵ)(௭ିଶ)య ஼ ݀ݖalong the contour ܥ: |ݖ−(1 +݅)| = 2, oriented anti- clockwise, is equal to

• A. 0
• B. ଶగ௜ ଽ
• C. − ଶగ௜ ଽ
• D. ସగ௜ ଽ

Question 6

Marks: 1

The integral ∫ ∫ ቀ ௫ ௬ቁ ௫ ௫మ ଵ ଴݁ ௫మ/௬ ݀ݕ݀ ݔ equals

• A. ௘ିଶ ௘
• B. ௘ିଵ ଶ௘
• C. ௘ିଵ ଶ
• D. ௘ିଶ ଶ௘

Question 7

Marks: 1

If the mean and variance of a binomial distribution are 6 and 2 respectively, then the probability of two failures is

• A. 4 ቀ2 3 ቁ 7
• B. 4 ቀ ଶమ ଷళቁ
• C. 17 ቀ ଶ ଷቁ ଻
• D. 17 ቀ ଶమ ଷళቁ

Question 8

Marks: 2

For the matrix ܯ= ൭ 1 0 −1 0 1 −1 1 1 −2 ൱, consider the following statements: (P) The characteristic equation of ܯ is ߣଷ−ߣ = 0. (Q) ܯିଵ does not exist. (R) The matrix ܯ is diagonalizable. Which of the above statements are true?

• A. P, Q and R
• B. P and R but not Q
• C. P and Q but not R
• D. Q and R but not P

Question 9

Marks: 2

The work done by the force ܨ⃗= (ݔ+ ݔଶ) ଓ̂ + (ݔଶ+ ݕଷ) ଔ̂ in moving a particle once along the triangle with vertices (0,0),(1,0) and (0,1) in the anti-clockwise direction is

• A. 0
• B. 1/6
• C. 1/3
• D. 5/3

Question 10

Marks: 2

The general solution of the differential equation ݔଷௗయ௬ ௗ௫య+ ݔଶௗమ௬ ௗ௫మ+ ݔ ௗ௬ ௗ௫−ݕ= 0, ݔ> 0 is

• A. ܥଵ ௫+ ௫/ଶቄܥଶcosቀ√ଷ ଶݔቁ+ ܥଷsin ቀ√ଷ ଶݔቁቅ
• B. ܥଵݔ+ ݔ ଵ/ଶቄܥଶcosቀ√ଷ ଶ݈݋݃ ௘ݔቁ+ ܥଷsin ቀ√ଷ ଶ݈݋݃ ௘ݔቁቅ
• C. ܥଵ ௫+݁ ௫/ଶቄܥଶcosቀ√ଷ ଶݔቁ+ ܥଷsin ቀ√ଷ ଶݔቁቅ
• D. ܥଵݔ+ ݔଵ/ଶቄܥଶcosቀ√ଷ ଶ݈݋݃ ௘ݔቁ+ ܥଷsin ቀ√ଷ ଶ݈݋݃ ௘ݔቁቅ

Question 11

Marks: 2

Using Euler’s method to solve the differential equation ௗ௬ ௗ௫ = 2 cos ቀ ସగ௫ ଷቁ− ݕ, ݕ(0) = 1 with step-size ℎ= 0.25, the value of ݕ(0.5) is

• A. 1.3125
• B. 1.1875
• C. 1.125
• D. 1.0625

Question 1

Marks: 1

The gauge pressure inside a soap bubble of radius ܴ, with ߪ denoting the surface tension between the soap solution and air, is.

• A. ఙ ଶగோ
• B. ସఙ ோ
• C. ଶఙ ோ
• D. ఙ ସగோ

Question 2

Marks: 1

Let ܯ, ܤ and ܩ represent respectively the metacentre, centre of buoyancy and the centre of mass of a floating buoy. Which of the following statements is correct?

• A. ܯ is above ܩ; Buoy unstable
• B. ܤ is above ܩ; Buoy stable
• C. ܯ is above ܩ; Buoy stable
• D. ܤ is above ܩ; Buoy unstable

Question 3

Type: NAT | Marks: 1

A reservoir connected to a pipe line is being filled with water, as shown in the Figure. At any time t, the free surface level in the reservoir is h. Find the time in seconds for the reservoir to get filled up to a height of 1 m, if the initial level is 0.2 m. _________

Question 4

Marks: 1

Bernoulli’s equation is valid for the following type of flow:

• A. Compressible, steady, inviscid
• B. Incompressible, steady, viscous
• C. Compressible, unsteady, viscous
• D. Incompressible, steady, inviscid

Question 5

Marks: 1

If ܣ is the area of a circle of radius ݎ enclosing a plane forced vortex flow, with origin at the centre of the vortex and if ω is the angular velocity, ζ is the vorticity, ܸሬ⃗ is the velocity vector, then the circulation around the contour of the circle is given by

• A. 2߱ܣ
• B. 2ζܣ
• C. 2ܸሬ⃗ܣ
• D. 0

Question 6

Marks: 1

Flow past a circular cylinder can be produced by superposition of the following elementary potential flows:

• A. Uniform flow, doublet
• B. Uniform flow, vortex
• C. Source, vortex
• D. Sink, vortex

Question 7

Marks: 1

Let δ, δ1 and δ2 denote respectively the boundary-layer thickness, displacement thickness and the momentum thickness for laminar boundary layer flow of an incompressible fluid over a flat plate. The correct relation among these quantities is

• A. δ < δ1< δ2
• B. δ > δ1> δ2
• C. δ > δ1< δ2
• D. δ < δ1> δ2

Question 8

Marks: 1

In the hydrodynamic entry region of a circular duct, the pressure forces balance the sum of

• A. viscous and buoyancy forces
• B. inertia and buoyancy forces
• C. inertia and surface tension forces
• D. inertia and viscous forces

Question 9

Marks: 1

Bodies with various cross-sectional shapes subjected to cross-flow of air are shown in the following figures. The characteristic dimension of all the shapes is the same. The cross- sectional shape with the largest coefficient of drag (i.e. sum of the pressure and skin- friction drags), at any moderately large Reynolds number, is

• A.
• B.
• C.
• D.

Question 10

Marks: 2

A U-tube of a very small bore, with its limbs in a vertical plane and filled with a liquid of density ρ, up to a height of h, is rotated about a vertical axis, with an angular velocity of ω, as shown in the Figure. The radius of each limb from the axis of rotation is R. Let pa be the atmospheric pressure and g, the gravitational acceleration. The angular velocity at which the pressure at the point O becomes half of the atmospheric pressure is given by

• A. ට ௣ೌାଶఘ௚௛ ఘோమ
• B. ට ଶ(௣ೌାఘ௚௛) ఘோమ
• C. ට ௣ೌାଶఘ௚௛ ଶఘோమ
• D. ට ௣ೌାఘ௚௛ ଶఘோమ

Question 11

Marks: 2

An incompressible fluid at a pressure of 150 kPa (absolute) flows steadily through a two- dimensional channel with a velocity of 5 m/s as shown in the Figure. The channel has a 90o bend. The fluid leaves the channel with a pressure of 100 kPa (absolute) and linearly- varying velocity profile. vmax is four times vmin. The density of the fluid is 914.3 kg/m3. The velocity vmin, in m/s, is

• A. 25
• B. 2.5
• C. 2.0
• D. 0.2

Question 12

Marks: 2

The velocity vector corresponding to a flow field is given, with usual notation, by ܸሬ⃗= 3ݔଓ̂ + 4ݔݕଔ̂. The magnitude of rotation at the point (2,2) in rad/s is

• A. 0.75
• B. 1.33
• C. 2
• D. 4

Question 13

Marks: 2

The stream function for a potential flow field is given by ψ = ݔଶ−ݕଶ. The corresponding potential function, assuming zero potential at the origin, is

• A. ݔଶ+ ݕଶ
• B. 2ݔݕ
• C. ݔଶ−ݕଶ
• D. ݔ−ݕ

Question 14

Type: NAT | Marks: 2

Fully developed flow of an oil takes place in a pipe of inner diameter 50 mm. The pressure drop per metre length of the pipe is 2 kPa. Determine the shear stress, in Pa, at the pipe wall. __________

Question 15

Type: NAT | Marks: 2

The Darcy friction factor ݂ for a smooth pipe is given by = 64/Re for laminar flow and by = 0.3/Re଴.ଶହfor turbulent flow, where Re is the Reynolds number based on the diameter. For fully developed flow of a fluid of density 1000 kg/m3 and dynamic viscosity 0.001 Pa.s through a smooth pipe of diameter 10 mm with a velocity of 1 m/s, determine the Darcy friction factor. _________

Question 16

Type: NAT | Marks: 2

Air flows steadily through a channel. The stagnation and static pressures at a point in the flow are measured by a Pitot tube and a wall pressure tap, respectively. The pressure difference is found to be 20 mm Hg. The densities of air, water and mercury, in kg/m3, are 1.18, 1000 and 13600, respectively. The gravitational acceleration is 9.81 m/s2. Determine the air speed in m/s. _____________

Question 17

Type: NAT | Marks: 2

Calculate the x-direction component of the acceleration in m/s2 at the point ݔ= 0.5 m and ݕ= 50 mm. _________

Question 18

Type: NAT | Marks: 2

Find the slope of the streamline passing through the point ݔ= 0.5 m and ݕ= 50mm. ____

Question 19

Marks: 2

The velocity in m/s, at which the model is towed, is

• A. 0.75
• B. 1.33
• C. 3
• D. 192

Question 20

Marks: 2

The resistance of the prototype, in kN, is

• A. 6
• B. 25
• C. 26.9
• D. 100.1

Question 21

Marks: 2

The gauge pressure at section-1, in kPa, is

• A. 0.6
• B. 13.5
• C. 135
• D. 600

Question 22

Marks: 2

The magnitude of the force, in kN, required to hold the pipe in place, is

• A. 2.7
• B. 5.4
• C. 19
• D. 27

Question 1

Type: NAT | Marks: 1

At a point in a body subjected to plane stress, the state of stress is as shown in the Figure. One of the principal stresses is 180 MPa. Find the unknown shear stress τ (in MPa). __________

Question 2

Type: NAT | Marks: 1

A point in a body is subjected to a hydrostatic pressure of 100 MPa. Find the maximum shear stress at this point in MPa. ___________

Question 3

Type: NAT | Marks: 1

A circular shaft of diameter 10 mm and length 3m is subjected to a torque of T = π N-m at a location 2m away from the fixed end as shown in the Figure. Find out the angle of twist (in radians) at the free end. Shear modulus of the material of the shaft is 10 GPa. ___________

Question 4

Marks: 1

A rigid massless rod ABC is hinged at A and carries a point mass M (in kg) at C. Point B is connected to a linear spring with spring constant k (in N/m) as shown in the figure. The length AB and AC area and L, respectively. Neglecting the effect of gravity, the natural frequency of this spring-mass system in rad/s is

• A. ට௞௅మ ெ௔మ
• B. ට௞௔మ ெ௅మ
• C. ට ௞௅ ெ௔
• D. ට௞௔ ெ௅ 160 MPa τ τ 160 MPa F 0 30 60 0 1 2 0 60 F M

Question 5

Type: NAT | Marks: 1

A two bar truss is shown in the Figure. The cross-sectional area and Young’s modulus of bar 1 are 0.02 m2 and 200GPa, respectively. The cross-sectional area and Young’s modulus of bar 2 are 0.01 m2and 80GPa, respectively. The force F applied on the truss is 2 N. Find out the stress developed in bar 2 in Pa. ___________

Question 6

Type: NAT | Marks: 1

A spring balance reads 10 kg in a lift when the lift is stationary. When the lift starts moving with a constant acceleration, the new reading is 12.3 kg. If the upward acceleration is considered positive, what is the acceleration of the lift? Acceleration due to gravity may be taken as 10 m/s2downwards.______________

Question 7

Type: NAT | Marks: 1

A force F = 2 N is applied on a block of mass M = 0.5 kg as shown in the figure. The block is constrained to move along the horizontal direction in a guideway. Find out the distance (in meters) travelled by the block in 2 s starting from rest. Neglect any friction between the block and the guideway. ____________ P B A L k t Ice surface Wooden board V x y

Question 8

Type: NAT | Marks: 1

A man of mass 50 kg is walking on a long wooden board of mass 200 kg (as shown in the Figure). The wooden board is initially at rest on a frictionless ice surface. If the man walks with a velocityof V =1 m/s in the positive x direction relative to the wooden board, find the velocity of the board in m/s. Velocity is positive in the positive x direction. _____________

Question 9

Marks: 1

A rigid bar AB is hinged at B through a torsional spring with spring constant kt.. For small rotations of the bar AB about B, the critical load Pcr is given by

• A. ௞೟ ଶ௅
• B. ௞೟ ௅
• C. ଶ௞೟ ௅
• D. ସ௞೟ ௅ A B C 4m 3m M K

Question 10

Type: NAT | Marks: 2

A disk of mass M= 14kg and radius 1 m is attached to a spring which has a stiffness k = 75 N/m and an unstretched length of 1m. If the disk is released from rest in the position shown in the Figure and the disk rolls without slipping, find its angular velocity (in rad/s) at the instant the center of mass is displaced by 3 m. ______________

Question 11

Type: NAT | Marks: 2

A strain gauge is mounted on the outer surface of a thin cylindrical pressure vessel in the circumferential direction. The mean diameter and thickness of the cylinder are 4.0 m and 20 mm, respectively. Young’s modulus and Poisson’s ratio of the material of the cylinder are 200 GPa and 0.25, respectively. Find the pressure in MPa inside the cylindrical vessel when the strain gauge indicates a strain of 7.0x 10-4. ____________

Question 12

Type: NAT | Marks: 2

A solid shaft of diameter 100 mm is rotating at a constant angular speed of (10/ π) rad/s. The shaft carries three rigid pulleys A, B and C as shown in the Figure. Pulley B is connected to a motor supplying 10kW power. Pulley B and C are connected to two pumps consuming 5kW each. Find the maximum shear stress (in MPa) in the shaft due to torsion alone. __________ EI L k P 40 kN 20 kN A B C D 2.5 m 2 m 3 m

Question 13

Marks: 2

A beam is fixed at the left end and supported by a spring at the other end. The length of the beam is L and its flexural rigidity is EI. The spring constant of the spring is = ଷாூ ௅య. A vertical downward load P is applied at the right end. The deflection of the point under the load P is

• A. ௉௅య ଽாூ
• B. ௉௅య ଺ாூ
• C. ଶ௉௅య ଽாூ
• D. ହ௉௅య ଽாூ

Question 14

Type: NAT | Marks: 2

Find the maximum bending moment (magnitude wise) in kN-m for the beam shown in the Figure. ______ H 45 o S v r x Y q Arc of a circle P

Question 15

Type: NAT | Marks: 2

A projectile is fired with a velocity V= 3√2 m/s from a point at height H = 0.8 m at an angle of 450 with respect to the horizontal direction as shown in the Figure. Find the horizontal distance S in meters travelled by the projectile when it hits the ground. Take acceleration due to gravity as10 m/ s2. __________

Question 16

Type: NAT | Marks: 2

A particle P is moving on a circular path of radius r = 1m. The angular location θof the particle is measured as shown in the Figure. The motion of the particle is described by ߠ= 2 sin(ݐ). Find the magnitude of the total acceleration (in m/s2) of the particle at time t = π/3 seconds. _________ A B C P 900 100 MPa 40 MPa 100 MPa 40 MPa 40 MPa 40 MPa 45 o A B

Question 17

Marks: 2

Neglecting the axial compression of member AB, the deflection of point C in the direction of the load is

• A. ଶ௉௅య ா௔ర
• B. ସ௉௅య ா௔ర
• C. ௉௅య ா௔ర
• D. ଵ଺௉௅య ா௔ర

Question 18

Marks: 2

The maximum bending stress in the frame is

• A. ଷ௉௅ ௔య
• B. ଺௉௅ ௔య
• C. ଽ௉௅ ௔య
• D. ଵଶ௉௅ ௔య

Question 19

Marks: 2

One of the principal stresses(in MPa) is

• A. 40
• B. 80
• C. 120
• D. 140

Question 20

Marks: 2

The normal stress on the plane AB (in MPa) is

• A. 30
• B. 70
• C. 100
• D. 110 2 m 1 m 1 2

Question 21

Marks: 2

The stress in rod 1 (in MPa) is

• A. -4.0
• B. -3.0
• C. -2.5
• D. -1.0

Question 22

Marks: 2

Considering the displacement to the right as positive, the displacement (in mm) of the interface between the two rods is

• A. -0.2
• B. -0.1
• C. 0.1
• D. 0.2

Question 1

Marks: 1

The measured temperature of a system is 30oC.Its exact absolute temperature in K is

• A. 303.00
• B. 303.10
• C. 303.15
• D. 303.16

Question 2

Marks: 1

The fuel air mixture in a pertrol engine is ignited with a spark plug at the end of compression stroke. This process

• A. increases the entropy of the fuel air mixture but decreases the entropy of the spark plug
• B. decreases the entropy of the fuel air mixture but increases the entropy of the spark plug
• C. decreases the entropy of the fuel air mixture and of the spark plug
• D. increases the entropy of the fuel air mixture and of the spark plug

Question 3

Marks: 1

In the van der Waals equation of state given below: (݌+ܽݒଶ)(ݒ−ܾ) = The constant a represents the effect of

• A. attractive forces between molecules
• B. repulsive forces between molecules
• C. deviation from molecules being spherical
• D. finite size of the molecule

Question 4

Marks: 1

For a reversible isothermal expansion of an ideal gas from a state 1 to a state 2,

• A. s1=s2
• B. s1>s2
• C. s1<s2
• D. h1>h2

Question 5

Marks: 1

For a pure substance the critical isotherm on the p-v plane exhibits

• A. a maximum
• B. a minimum
• C. a point of inflection
• D. a discontinuity

Question 6

Marks: 1

For an ideal gas as a working fluid for a given heat input Q, the process that gives the maximum work among the following four processes is

• A. isothermal
• B. constant volume
• C. constant pressure
• D. isentropic

Question 7

Marks: 1

An air standard Otto cycle has the following shape on a thermodynamic property plane. The x and y coordinates, respectively, are

• A. v and p
• B. s and v
• C. v and T
• D. s and p

Question 8

Type: NAT | Marks: 1

The specific volume of steam after expansion in a turbine is 12 m3/kg. At this pressure the saturated liquid and saturated vapour specific volumes are 0.001 and 15.25 m3/kg respectively. What is the dryness fraction to second decimal place accuracy? _________

Question 9

Marks: 1

Which of the following processes, shown in the figure below, represents the throttling of an ideal gas?

• A. 1to2
• B. 1to 3
• C. 1to 4
• D. 1to 5

Question 10

Marks: 2

On a ln pvsh coordinate system, where ln p is the y-coordinate and h is the x coordinate, the slope of a constant entropy line is

• A. 1/v
• B. v
• C. p/v
• D. 1/(pv)

Question 11

Marks: 2

Starting from the definition of Gibbs free energy function g=h-Ts, the Maxwell relation that can be derived is

• A. డ௣ డ்ቚ ௦= ௩ ௦
• B. డ௣ డ்ቚ ௦= ݒ
• C. డ௩ డ௦ቚ = − డ௣ డ்ቚ ௦
• D. డ௩ డ்ቚ ௣= − డ௦ డ௣ቚ் y x T S 1 2 3 4 5

Question 12

Type: NAT | Marks: 2

A thermodynamic cycle operates between one source at a temperature of 600 K, another source at a temperature of 300 K and a sink at a temperature T as shown in the figure below If the First and Second laws of thermodynamics are not violated, what should be the value of T in K? _____________

Question 13

Marks: 2

A closed system containing an ideal gas undergoes a cycle as shown in the figure shown below. For the process1-2, which one of the following statements is true?

• A. Heat added = ଷ ସ݌ݒ
• B. Heat rejected = ଷ ସ݌ݒ
• C. Heat added = ଵ ଶ݌ݒ
• D. Heat rejected = ଵ ସ݌ݒ 600 K 300 K T 1 kJ 1 kJ p v v/2 2p 2 1 3

Question 14

Type: NAT | Marks: 2

A well-insulated rigid hot water tank receives steady flow of water from two sources as shown in the figure below There is no accumulation of water in the tank. A back-up heater is provided to ensure a constant outflow temperature of water at 60 oC from the tank under steady state. What is the required capacity of the back-up heater to the nearest kW? __________

Question 15

Type: NAT | Marks: 2

1 kg of air in an insulated rigid tank of volume 1 m3is churned with a friction-less fan (see figure below) of 600 W capacity for 10 minutes. The fan efficiency is 100 %. Treating air as an ideal gas and neglecting kinetic and potential energy changes, what is the increase of pressure, to the nearest kPa? _________

Question 16

Type: NAT | Marks: 2

The isothermal compressibility of a liquid is 5 × 10-6 /kPa. If it is compressed at constant temperature from 5000 to 10000kPa, what is the ratio of final volume to initial volume, to second decimal place accuracy? ____________

Question 17

Type: NAT | Marks: 2

What is the partial pressure of water vapour in kPa to the first decimal place accuracy before the high pressure front moves in? ____________

Question 18

Type: NAT | Marks: 2

What is the relative humidity of air under the influence of high pressure front to integer precision in %? _____ 1 kg/ s at 80 oC 5 kg/ s at 50 oC at 60 oC Back-up heater 600 W

Question 19

Type: NAT | Marks: 2

What is the ratio of the volumes of chambers A and B, i.e. VA/VB, to first decimal place accuracy? ________

Question 20

Type: NAT | Marks: 2

If the barrier is removed and the gases are allowed to mix and reach thermodynamic equilibrium, what is the final temperature of the mixture, to the nearest K? ________

Question 21

Type: NAT | Marks: 2

What is the mass flow rate of the working fluid through the turbine, in kg/s, to first decimal place accuracy? __________

Question 22

Type: NAT | Marks: 2

What is the power required to drive the compressor, to the nearest kW? ________ ln h (kJ/kg) 538. 518. 417.2 404. 241.7 1 2 4 3 5 6 A (0.5 kg N2+0.5 kg He) 300 K p B (1 kg pure N2) 400 K 2p Rigid insulating barrier Specific Heat Data: For He cp= 5181 J/kg.K cv= 3102 J/kg.K For N2 cp= 1039 J/kg.K cv= 742 J/kg.K