Attempt the GATE XE (Engineering Sciences) 2018 previous year paper in real CBT exam mode or practice mode with the official answer key. Step-by-step explanations are coming soon.
All GATE XE (Engineering Sciences) papers
87 questions.
Marks: 1
“Going by the _________ that many hands make light work, the school _______ involved all the students in the task.” The words that best fill the blanks in the above sentence are
Answer: A. principle, principal
Marks: 1
“Her _______ should not be confused with miserliness; she is ever willing to assist those in need.” The word that best fills the blank in the above sentence is
Answer: C. frugality
Marks: 1
Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?
Answer: B. 7
Marks: 1
A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2 of area. What is the area of the original rectangle in square meters?
Answer: B. 2250
Marks: 1
A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?
Answer: B. 72
Marks: 2
For integers 𝑎, 𝑏 and 𝑐, what would be the minimum and maximum values respectively of 𝑎+ 𝑏+ 𝑐 if log |𝑎| + log |𝑏| + log |𝑐| = 0?
Answer: A. -3 and 3
Marks: 2
Given that 𝑎 and 𝑏 are integers and 𝑎+ 𝑎2 𝑏3 is odd, which one of the following statements is correct?
Answer: D. 𝑎 is odd and 𝑏 is even
Marks: 2
From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?
Answer: D. 175 and 200
Marks: 2
Which of the following functions describe the graph shown in the below figure?
Answer: B. 𝑦= ||𝑥| −1| −1
Marks: 2
Consider the following three statements: (i) Some roses are red. (ii) All red flowers fade quickly. (iii) Some roses fade quickly. Which of the following statements can be logically inferred from the above statements?
Answer: C. If (i) and (ii) are true, then (iii) is true.
Marks: 1
The largest interval in which the initial value problem ( ) ( ) () () 2 2 1 ln , (1) = 0 and 1 1, 5 x d y dy dy e x y x y dx x dx dx + + = = − has a unique solution is
Answer: D. (0, 5)
Marks: 1
The sum of the roots of the indicial equation at 0 x = of the differential equation ( ) 2 3 2 sin (tan ) 0, 0, d y dy x x x x y x dx dx + − = > is
Answer: A. 0
Type: NAT | Marks: 1
Let f be a three times continuously differentiable real valued function on (0, 5) such that its third derivative 1 ( ) 100 f x ′′′ = for all (0,5). x∈ If ( ) P x is a polynomial of degree 2 ≤ such that (1) (1), P f = (2) (2) P f = and (3) (3) P f = then | (4) (4) | f P − equals _______________
Answer: 0.01
Type: NAT | Marks: 1
For real numbers 1 α and 2, α if the formula () () 1 1 1 1 2 2 2 1 ( ) f x dx f f α α − − = + ∫ is exact for all polynomials of degree 1 ≤ then 1 2 2 3 α α + equals _______________
Answer: 5
Type: NAT | Marks: 1
Raju has four fair coins and one fair dice. At first Raju tosses a coin. If the coin shows head then he rolls the dice and the number that dice shows is taken as his score. If the coin shows tail then he tosses three more coins and the total number of tails shown (including the first one) is taken as his score. If Raju tells that his score is 2 then the probability that he rolled the dice is (up to two decimal places) _______________
Answer: 0.29 to 0.32
Type: NAT | Marks: 1
Let f be a continuously differentiable real valued function defined by 2 1, ( ) 5 1. bx a if x f x x if x + < = ≥ Then the value of 2 a b is _______________
Answer: 250
Type: NAT | Marks: 1
A rectangular box without top cover having a square base is to be made from a sheet of 108 square meters. Then the largest possible volume of the box in cubic meters is ______________
Answer: 108
Marks: 2
Let 5 3 . 6 4 A − = − Then the trace of 1000 A equals
Answer: B. 1000 2 1 +
Marks: 2
Let denote the set of complex numbers and 2 1. i =− Let γ be the simple positively oriented circle | | 1 z = and { } 0 | | 2 S z z = ∈ < < . If : f S → is analytic in S and is given by 2 0 1 7 ( ) , 8 2 n n n f z a z z S z z ∞ = = + + ∈ ∑ then the value of the contour integral 1 ( ) cos ze f z dz i z γ π + ∫ is
Answer: C. 7
Type: NAT | Marks: 2
Let 3 denote the three dimensional Euclidean space and ˆ ˆ ˆ ( , , ) x y z yi x j z k =− + + F for all 3 ( , , ) . x y z ∈ If C is the curve described by the parametric equation 2 ˆ ˆ ˆ ( ) cos sin 2 , 0 1, t t i t j t k t = + + ≤≤ r then the value of the line integral d C ⋅ ∫F r is_______________
Answer: 3
Type: NAT | Marks: 2
Let ( , ) u x t satisfy the initial and boundary value problem 2 2 2 , 0 , 0, u u x t t x π ∂ ∂ = < < > ∂ ∂ (0, ) 0 ( , ), 0, u t u t t π = = > ( ,0) sin 2sin 4 , 0 . u x x x x π = + < < Then the value of , ln(5) 2 u π is_______________
Answer: 0.04
Marks: 1
Rheological diagram of different types of fluids is shown in figure. Column I represents the nature of the fluid and column II represents the curve showing the variation of shear stress against shear strain rate. Column I (i) Newtonian (ii) Shear thinning (iii) Shear thickening (iv) Bingham plastic Column II M N O P The most appropriate match between columns I and II is,
Answer: B. (i) – O; (ii) – P ; (iii) – N; (iv) – M
Marks: 1
In a two-dimensional, incompressible and irrotational flow, stream function ( ( , ) x y ψ ψ = ) and velocity potential ( ( , ) x y φ φ = ) exist. The velocities in x and y directions are non-zero. The product of constant dy dx φ= and constant dy dx ψ= , is
Answer: A. −1
Marks: 1
The inviscid flow past a rotating circular cylinder can be generated by the superposition of
Answer: D. uniform flow, doublet and vortex
Marks: 1
The velocity field and the surface normal vector are given by, ˆ ˆ ˆ V ui v j wk = + + and 1 2 3 ˆ ˆ ˆ n n i n j n k = + + , respectively. If Euler equations are to be solved, the boundary condition that must be satisfied at the wall is,
Answer: A. 𝑉⃗ ∙𝑛⃗ = 0
Marks: 1
The influence of Froude number is most significant in
Answer: C. free surface flows
Marks: 1
If the stream function ( ( , ) x y ψ ) for a two-dimensional incompressible flow field is given as ( ) 2 2 2y x y − , the corresponding velocity field is
Answer: B. ( ) 2 2 ˆ ˆ 2 3 4 V x y i xy j = − −
Marks: 1
Water is flowing in two different tubes of diameters D and 2D, with the same velocity. The ratio of laminar friction factors for the larger diameter tube to the smaller diameter tube is
Answer: A. 0.5
Type: NAT | Marks: 1
If the velocity field is 2 ˆ ˆ 4 V xy i xy j = + m/s, vorticity of the fluid element in the field at (x=1, y=2) in s-1 is ____.
Answer: 4
Type: NAT | Marks: 1
A pitot-static tube is used to measure air velocity in a duct by neglecting losses. The density of air is 1.2 kg/m3. If the difference between the total and static pressures is 1 kPa, the velocity of air at the measuring location, in m/s, is _______.
Answer: 39 to 42
Marks: 2
A parallelepiped of (2 m × 2 m) square cross-section and 10 m in length, is partially floating in water upto a depth of 1.2 m, with its longest side being horizontal. The specific gravity of the block is
Answer: B. 0.6
Marks: 2
The velocity field in a two-dimensional, unsteady flow is given by 2 ˆ ˆ ( , , ) 2 3 V x y t xy i xyt j = + m/s. The magnitude of acceleration of a fluid particle located at x = 1 m, y = 1 m at the time t = 1 s, in m/s2, is
Answer: C. 24.1
Marks: 2
In a two-dimensional, incompressible and irrotational flow, fluid velocity (v) in the y- direction is given by 2 5 v x y = − . The velocity (u) in the x-direction is
Answer: C. 5 2 u x y = +
Marks: 2
A two-dimensional laminar viscous liquid film of constant thickness (h) steadily flows down an incline as shown in figure. Acceleration due to gravity is g. If the velocity profile in the liquid film is given as, (2 ); 0 u ky h y v = − = , the value of constant k is
Answer: A. sin 2 g ρ θ μ
Type: NAT | Marks: 2
A water jet of 100 mm diameter issuing out of a nozzle at a speed of 50 m/s strikes a vane and flows along it as shown in figure. The vane is attached to a cart which is moving at a constant speed of 20 m/s on a frictionless track. The jet is deflected at an angle of 30o. Take the density of water as 1000 kg/m3. Neglecting the friction between the vane and the fluid, the magnitude of the force exerted by water on the cart in the x-direction, in N, is ______.
Answer: 900 to 990
Type: NAT | Marks: 2
Capillary waves are generated in the sea. The speed of propagation (C) of these waves is known to be a function of density (ρ), wave length (λ), and surface tension (σ). Assume, ρ and λ to be constant. If the surface tension is doubled, in the functional form of the relevant non-dimensional group, the percentage increase in propagation speed (C) is _______ .
Answer: 40 to 42
Type: NAT | Marks: 2
Consider a fully developed, two-dimensional and steady flow of a viscous fluid between two fixed parallel plates separated by a distance of 30 mm. The dynamic viscosity of the fluid is 0.01 kg/m-s and the pressure drop per unit length is 300 Pa/m. The fluid velocity at a distance of 10 mm from the bottom plate, in m/s, is ________.
Answer: 2.9 to 3.1
Type: NAT | Marks: 2
A 2.6 gram smooth table-tennis (ping-pong) ball has a diameter of 38 mm. Density (ρ) of air is 1.2 kg/m3. Neglect the effect of gravity. Take coefficient of drag as 0.5. If the ball is struck with an initial velocity of 30 m/s, the initial deceleration, in m/s2, is _________.
Answer: 107 to 127
Type: NAT | Marks: 2
On a flat plate, transition from laminar to turbulent boundary layer occurred at a critical Reynolds number (Recr). The empirical relations for the laminar and turbulent boundary layer thickness are given by 0.5 m 5.48Re la x x δ − = and 0.2 0.37Re turb x x δ − = , respectively. The ratio of laminar to turbulent boundary layer thickness, at the location of transition, is 0.3. The value of Recr is _______.
Answer: 440000 to 442000
Type: NAT | Marks: 2
In a capillary tube of radius R = 0.25 mm, a fully developed laminar velocity profile is defined as, 2 2 2 1 4 R dp r u dx R μ = − − . In this expression, dp dx − =1 MPa/m, μ is the dynamic viscosity of the fluid, and r is the radial position from the centerline of the tube. If the flow rate through the tube is 1000 mm3/s, the viscosity of the fluid, in Pa-s, is ______________.
Answer: 0.001 to 0.002
Type: NAT | Marks: 2
The skin friction coefficient for a turbulent pipe flow is defined as, 2 1 2 w f C V τ ρ = , where w τ is the wall shear stress and V is the average flow velocity. The value of f C is empirically given by the relation: f C = ( ) 0.25 2 0.065 Re , where Re is the Reynolds number. If the average flow velocity is 10 m/s, diameter of the pipe is 250 mm, kinematic viscosity of the fluid is 0.25×10−6 m2/s, and density of the fluid is 700 kg/m3, the skin friction drag induced by the flow over 1 m length of the pipe, in N, is ___________.
Answer: 30 to 45
Type: NAT | Marks: 2
A (150 mm × 150 mm) square pillar is located in a river with water flowing at a velocity of 2 m/s, as shown in figure. The height of the pillar in water is 8 m. Take density of water as 1000 kg/m3 and kinematic viscosity as 1×10 −6 m/s2. The coefficient of drag of the pillar is 2.0. The drag force exerted by water on the pillar in N is _______.
Answer: 4800
Type: NAT | Marks: 2
An orifice plate is used to measure flow rate of air (density = 1.23 kg/m3) in a duct of 250 mm diameter as shown in figure. The volume flow rate is 1 m3/s. Flow at sections 1 and 3 is uniform and section 2 is located at vena contracta. The diameter ratio, Dt/D1, is 0.66. The flow area at vena contracta, A2 = 0.65At, where At is area of the orifice. The pressure difference between locations 2 and 3 in N/m2 is ____________.
Answer: 1200 to 1350
Marks: 1
A thin cylinder (thickness, ݐ and diameter, ) with closed ends is subjected to an internal pressure, . The ratio of hoop stress to longitudinal stress developed in the wall of the cylinder is
Answer: D. 2:1
Marks: 1
A steel rod is fixed at one end and free at the other end. The coefficient of thermal expansion of the steel is α, and modulus of elasticity is E. If the temperature of the rod is increased by ∆ܶ then the stress and strain developed in the rod are respectively
Answer: A. zero, α∆ܶ
Marks: 1
The effective lengths of the columns with ideal boundary conditions shown in Case-I, Case-II, and Case-III are respectively
Answer: D. ܮ, 2ܮ, ܮ/2
Marks: 1
At a point in a stressed body, sum of the normal stresses acting on perpendicular faces of an arbitrarily oriented plane stress element is always
Answer: B. constant and independent of angle of orientation of the element
Marks: 1
The principal stresses on a plane stress element are shown in the figure. The maximum shear stress (in MPa) is
Answer: B. 100
Type: NAT | Marks: 1
A rigid and thin L-shaped bracket is fixed to the wall at point B, and a force F is applied at point A as shown. For a given force F, the point B experiences the maximum clockwise moment when the inclination θ (in degrees) with the x-axis is……….[up to two decimal places].
Answer: 52.50 to 53.50
Type: NAT | Marks: 1
A cantilever beam with length, L = 1 m, modulus of elasticity, E = 210 GPa, and area moment of inertia, I = 1.2 ൈ10ିm4 carries a concentrated mass m = 100 kg at its free- end. By idealizing it as a single degree-of-freedom system and neglecting the mass of the cantilever beam, the natural frequency (in rad/s) of small transverse oscillations of the mass m is …….. [up to two decimal places]
Answer: 27.00 to 28.00
Type: NAT | Marks: 1
For a typical grade of steel, the value of modulus of elasticity (E) and Poisson’s ratio (ν) are 208 GPa and 0.3 respectively. The value of shear modulus (G) of the steel (in GPa) is …….. 8 mm P = 20 kN P = 20 kN 50 mm
Answer: 80
Type: NAT | Marks: 1
A tensile test is performed on a metallic specimen of diameter 8 mm and gauge length 50 mm. When the tensile load P reaches a value of 20 kN, the distance between the gauge marks increases by 0.09 mm. If the sample remains within the elastic limit, the modulus of elasticity (in GPa) of the test metal is………..[up to two decimal places]
Answer: 220.00 to 222.00
Marks: 2
A beam ABC is subjected to load P at its free end C as shown in the figure. The flexural rigidity of the beam is ܧܫ. The vertical support reaction at point B is
Answer: B. ହ ଶ
Marks: 2
A horizontal effort P is applied to raise a block of weight W on a rough surface inclined at an angle θ with the horizontal. If ߤ௦ is the coefficient of static friction between the block and the surface, the minimum effort P required to impend the upward motion of the block along the surface is
Answer: B. ቀ ఓೞା௧ఏ ଵିఓೞ௧ఏቁ
Marks: 2
Three round bars of same material, equal lengths, and different cross-sectional dimensions are shown in the figures as Case-I, Case-II and Case-III. All the bars are clamped at the upper end, and a concentrated load P is applied at the lower end of each bar. If the elastic strain energy stored in the bar shown in Case-I is ଵ then the elastic strain energy stored in Case-II and Case-III respectively is
Answer: D. ቀ5 8 ൗቁܷ ଵ, ቀ5 8 ൗቁܷ ଵ Case-I Case-II Case-III 2d L d P 2d d L/4 L/2 L/4 d 2d d P P L/4 L/2 L/4
Marks: 2
A rigid uniform rod with mass m, length L and center of gravity G is freely suspended from a hinge as shown in the figure. The rod is given a small angular displacement θ in the counter-clockwise direction from the position in which it hangs vertically (θ = 0). If ݃ is the acceleration due to gravity, the natural frequency of oscillations (in rad/s) is
Answer: C. ට ଷ ଶ
Marks: 2
A cylindrical member, made up of ductile material, is subjected to pure torsion as shown in the figure. The failure plane (from Option-I to Option-IV) for ductile material as per maximum shear stress theory is represented by
Answer: C. Option III
Marks: 2
A simply supported beam of span L is subjected to a couple Mo at a distance a from support A. Among the four options (Option-I to Option-IV) shown, the correct shear force diagram of the beam is
Answer: A. Option-I
Marks: 2
A circular shaft ABC of diameter, ݀ and length, ܮ is fixed at end A. It is subjected to the torsional moments at point B and point C as shown in the figure. The ratio of angle of twists at point B to point C is
Answer: D. 1 : 1.5 Mo/L Option-IV Mo/L Mo/L Mo a /L Mo (a/L-1) Option-I Option-II Mo L a A B Mo/L Option-III ܮ ܮ/2 ܣ ܤ ܥ + Sign convention of shear force for all options (+) (+) (-) (+) (-) (+)
Type: NAT | Marks: 2
A circular steel bar of diameter 10 mm is bent into the shape as shown in figure, and lies in x-z plane. A horizontal force P is applied along the positive z-direction as shown. The yield strength of the steel is 200 MPa. Neglecting the effect of transverse shear, the load P (in Newton) required to initiate yielding as per maximum shear stress theory of failure is…………[up to two decimal places]
Answer: 195.00 to 197.00
Type: NAT | Marks: 2
Two sliders A and B, connected by a rigid link of length L, slide in two mutually perpendicular and frictionless guide-ways. At a particular instance, the slider A is moving in the downward direction with a speed of 0.05 m/s. At this instance, the magnitude of the velocity of slider B (in m/s) is ……[up to two decimal places]
Answer: 0.01 to 0.02
Type: NAT | Marks: 2
A simply supported beam ABC is subjected to load as shown in the figure. The 20 kN load is applied at point B with the help of a welded bracket as shown. The beam has a rectangular cross-section of 15 mm width and 100 mm depth as shown. The maximum transverse shear stress developed in the beam (in MPa) is ……..[up to one decimal place] ݖ ݕ 100 50 ݔ Enlarged view of the cross-section 1 m 20݇N ܣ ܤ ܥ 1 m 0.25 m 5݇N/m 0.5 m 0.5 m 100 mm 15 mm
Answer: 14.5 to 15.5
Type: NAT | Marks: 2
A rigid rod ABC, in the form of a quarter-circular arc of radius R, is hinged at C and supported by a roller at B. A vertical force P is applied at the end A of the bar. For the reactions at B and C to be equal in magnitude, the value of the angle θ (in degrees) is ………. [up to two decimal places].
Answer: 26.00 to 27.00
Type: NAT | Marks: 2
A marble of mass m slides along a frictionless linear slide AB kept in a vertical plane. The marble is released from point A with zero initial velocity, and it reaches point B under the action of gravity. Assuming the acceleration due to gravity to be 9.81 m/s2, the speed (in m/s) of the marble when it just reaches point B is………[up to two decimal places].
Answer: 3.10 to 3.20
Type: NAT | Marks: 2
A horizontal force 10 N is applied at support B on the frame as shown in figure. Considering only bending deformation, the vertical reaction (in N) at support B is ………. [up to one decimal place] ܴ ܣ ܤ 10 N
Answer: 13.5 to 14.5
Marks: 1
When a fixed mass of air-water vapour mixture is heated at constant pressure,
Answer: B. relative humidity decreases, but specific humidity remains unchanged.
Marks: 1
For a reversible isothermal expansion of one mole of an ideal gas from state 1 to state 2, the magnitude of work done is
Answer: A. 1 2 ln P RT P
Marks: 1
The statement which is NOT a consequence of the first law of thermodynamics is
Answer: C. Energy of an isolated system is not conserved
Marks: 1
For a refrigerator absorbing heat QL from a cold region and rejecting heat QH to a hot region, the coefficient of performance is written as
Answer: A. L H L Q Q Q −
Marks: 1
The value of the compressibility factor at the critical point evaluated using the van der Waals equation of state is
Answer: C. 3 8
Marks: 1
The vapour pressure of a liquid at 8 °C is 2.7 kPa. Its enthalpy of vaporization is constant and equal to 42700 kJ/kmol. Take R = 8.314 kJ/kmol.K. The temperature (in °C) at a vapour pressure of 13.5 kPa is
Answer: D. 35.2
Type: NAT | Marks: 1
One kmol of an ideal gas (Cp = 21 kJ/kmol.K) undergoes a constant pressure process from 300 K to 500 K. The molar entropy of the gas at 300 K is 150 kJ/kmol.K. The molar entropy (in kJ/kmol.K) at 500 K (up to 1 decimal place) is ________.
Answer: 160.0 to 161.0
Type: NAT | Marks: 1
A spring, having a spring constant of 350 kN/m, is initially compressed by 0.4 cm. The work required (in J) to compress it by another 0.6 cm (up to 1 decimal place) is ________.
Answer: 14.5 to 15.0
Type: NAT | Marks: 1
An ideal gas has a molar mass of 40 kg/kmol. Take R = 8.314 kJ/kmol.K. At a pressure of 2 bar and a temperature of 300 K, the volume (in m3) of 1 kg of this gas (up to 2 decimal places) is ________.
Answer: 0.30 to 0.32
Marks: 2
Consider the following statements for an ideal gas undergoing a reversible non-flow process: P. If the process is adiabatic, the change in enthalpy of the gas is necessarily zero. Q. If the process is adiabatic, the change in entropy of the gas is necessarily zero. R. If the process is isothermal, the change in enthalpy of the gas is necessarily zero. S. If the process is isothermal, the change in entropy of the gas is necessarily zero. Which one of the following options is valid?
Answer: C. Only Q and R are correct
Marks: 2
An ideal Otto cycle (O) and an ideal diesel cycle (D) have the same maximum temperature and reject equal amount of heat. Also, the working fluid enters at the same state before compression. One of the following statements always true about their efficiencies (𝜂) is
Answer: C. 𝜂O < 𝜂D
Marks: 2
A reversible engine receives 75 kJ/s of energy from a reservoir at 750 K and does 12 kJ/s of work. The heat is rejected to two reservoirs at 650 K and 550 K. The rate of heat rejection (in kJ/s) to the reservoir at 650 K is
Answer: D. 52
Marks: 2
A gas obeys the following equation of state: 2 ( ) , aP P v b RT T − = + where v is molar volume, and a, b are constants with values 5 10 a − = J.K/Pa2.kmol and 2 8 10 b − =× m3/kmol. Take Cp = 30 kJ/kmol.K. At 10 bar and 500 K, the value of the Joule-Thomson coefficient (in K/Pa) is
Answer: B. 6 4 10− −×
Marks: 2
In an ideal Rankine cycle, steam enters the turbine at 10 MPa and 500 °C (ℎ = 3375.1 kJ/kg, 𝑠 = 6.5995 kJ/kg.K). It is cooled in the condenser at a pressure of 10 kPa. At 10 kPa, ℎ𝑓 = 191.81 kJ/kg, 𝑠𝑓 = 0.6492 kJ/kg.K, ℎ𝑔 = 2583.9 kJ/kg and 𝑠𝑔 = 8.1488 kJ/kg.K. The heat rejected in the condenser (in kJ/kg) is
Answer: A. 1898
Marks: 2
Methane has compressibility factor value of 0.9 at reduced pressure of 1.0 and reduced temperature of 1.5. For propane, the critical temperature and pressure are 369.8 K and 42.48 bar, respectively. Take R = 8.314 kJ/kmol.K. Applying the principle of corresponding states, the molar volume of propane (in m3/kmol) at the same reduced pressure and temperature is
Answer: D. 0.977
Type: NAT | Marks: 2
A rigid insulated vessel is divided into two compartments by a partition. One compartment contains 12 kg of oxygen at 200 kPa and 280 K. The other compartment contains 26 kg of carbon dioxide at 400 kPa and 360 K. The specific heats at constant volume in kJ/kg.K for oxygen and carbon dioxide are 0.662 and 0.653, respectively. The partition is removed and the gases are allowed to mix. Considering both gases are ideal, the final temperature (in K) of the mixture (up to 1 decimal place) is ________.
Answer: 332.5 to 336.5
Type: NAT | Marks: 2
Moist air having 60% relative humidity, enters a steady-flow air-conditioning unit at 102 kPa and 30 °C. The volume flow rate of the moist air entering the unit is 0.1 m3/s. The moist air leaves the unit at 95 kPa and 15 °C with a relative humidity of 100%. Liquid condensate leaves the unit at 15 °C. For water: at 15 °C, ℎ𝑓 = 62.982 kJ/kg, ℎ𝑔 = 2528.3 kJ/kg, 𝑃𝑠𝑎𝑡 = 1.7057 kPa. at 30 °C, ℎ𝑓 = 125.74 kJ/kg, ℎ𝑔 = 2555.6 kJ/kg, 𝑃𝑠𝑎𝑡 = 4.2469 kPa. For air, specific heat at constant pressure is 1.004 kJ/kg.K and the specific gas constant is 0.287 kJ/kg.K. Neglecting heat leakage to the surrounding, the magnitude of heat extracted (in kW) from the air stream (up to 2 decimal places) is __________.
Answer: 3.01 to 3.07
Type: NAT | Marks: 2
Air at 150 kPa and 323 K is filled in a rigid vessel of 0.05 m3 capacity. For air, assumed as an ideal gas, specific heat at constant volume is 0.7163 kJ/kg.K and the specific gas constant is 0.287 kJ/kg.K. Neglect kinetic and potential energy changes. If 30 kJ of heat is added, the final temperature (in K) of air (up to 1 decimal place) is __________.
Answer: 838.0 to 844.0
Type: NAT | Marks: 2
Superheated steam at 2 bar and 300 °C, with an enthalpy of 3072.1 kJ/kg, enters a horizontal adiabatic nozzle with negligible velocity and leaves at 0.2 bar as saturated vapour with an enthalpy of 2609.9 kJ/kg. Assuming steady flow and neglecting the potential energy changes, the exit velocity (in m/s) of the steam (up to 1 decimal place) is __________.
Answer: 961.0 to 962.0
Type: NAT | Marks: 2
A given mass of a simple compressible substance undergoes a reversible cycle, as shown in the P-V diagram. The magnitude of the net work done during the cycle is 3 kJ. The pressure (in bar) at point C (up to 1 decimal place) is ________.
Answer: 5.7 to 6.1
Type: NAT | Marks: 2
One kmol of an ideal gas at 300 K and 10 bar is reversibly heated in a constant volume process to 500 K. It is then reversibly and isothermally expanded to 2 bar. Take Cv = 20.8 kJ/kmol.K and R = 8.314 kJ/kmol.K. The total heat supplied (in kJ) to the gas (up to 1 decimal place) is ________.
Answer: 12950.0 to 13000.0
Type: NAT | Marks: 2
A rigid container is completely filled with a liquid having a constant isothermal compressibility of 4 1 1.09 10 bar − − × and a constant coefficient of volume expansion of 3 1 1.12 10 K − − × . The liquid is initially at 300 K and 1 bar. Heat is supplied to the liquid to raise its temperature to 350 K. Assuming that no phase change occurs, the final pressure (in bar) of the liquid (up to 1 decimal place) is ________.
Answer: 513.0 to 517.0