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# Multiple choice question for engineering

## Set 1

1. When the surface temperature variation inside a solid are periodic in nature, the profile of temperature variation with time may assume
a) Triangular
b) Linear
c) Parabolic
d) Hyperbolic

Answer: a [Reason:] Any type of waveform can be analyzed and resolved into an infinite number of sine and cosine waves.

2. The surface temperature oscillates about the mean temperature level in accordance with the relation
a) α S,T – α S,A = 2 sin (2 π n T)
b) α S,T – α S,A = 5 sin (2 π n T)
c) α S,T – α S,A = sin (2 π n T)
d) α S,T – α S,A = 3 sin (2 π n T)

Answer: c [Reason:] α S,T = t S,T – t M.

3. The temperature variation of a thick brick wall during periodic heating or cooling follows a sinusoidal waveform. During a period of 24 hours, the surface temperature ranges from 25 degree Celsius to 75 degree Celsius. Workout the time lag of the temperature wave corresponding to a point located at 25 cm from the wall surface. Thermo-physical properties of the wall material are; thermal conductivity = 0.62 W/m K; specific heat = 450 J/kg K and density = 1620 kg/m3
a) 3.980 hour
b) 6.245 hour
c) 2.648 hour
d) 3.850 hour

Answer: b [Reason:] d T = x/2 (1/α π n) ½ where x = 0.25 m and n = frequency.

4. A single cylinder 2-stroke engine operates at 1500 rpm. Calculate the depth where the temperature wave due to variation in cylinder is damped to 1% of its surface value. For the cylinder material, thermal diffusivity = 0.042 m2/hr
a) 0.1996 cm
b) 0.3887 cm
c) 0.2774 cm
d) 0.1775 cm

Answer: d [Reason:] α X,A = α S,A exponential [-x (π n/α) ½] where frequency = 1500 * 60.

5. The temperature distribution at a certain time instant through a 50 cm thick wall is prescribed by the relation
T = 300 – 500 x – 100 x2 + 140 x3
Where temperature t is in degree Celsius and the distance x in meters has been measured from the hot surface. If thermal conductivity of the wall material is 20 k J/m hr degree, calculate the heat energy stored per unit area of the wall
a) 4100 k J/hr
b) 4200 k J/hr
c) 4300 k J/hr
d) 4400 k J/hr

Answer: a [Reason:] d t/d x = -500 + 200 x + 420 x2. Now heat storage rate = Q IN – Q OUT = 10000 – 5900 = 4100 k J/hr.

6. A large plane wall, 40 cm thick and 8 m2 area, is heated from one side and temperature distribution at a certain time instant is approximately prescribed by the relation
T = 80 – 60 x +12 x2 + 25 x3 – 20 x4
Where temperature t is in degree Celsius and the distance x in meters. Make calculations for heat energy stored in the wall in unit time.
For wall material:
Thermal conductivity = 6 W/m K and thermal diffusivity = 0.02 m2/hr
a) 870.4 W
b) 345.6 W
c) 791.04 W
d) 238.5 W

Answer: c [Reason:] Q IN = – k A (d t/d x)X = 0 = 2880 W and Q OUT = – k A (d t/d x)X = 0.4 = 2088.96 W.

7. Consider the above problem, calculate rate of temperature change at 20 cm distance from the side being heated
a) 0.777 degree Celsius/hour
b) 0.888 degree Celsius/hour
c) 0.999 degree Celsius/hour
d) 0.666 degree Celsius/hour

Answer: b [Reason:] d t/d T = α d 2t/d x 2 = 0.888 degree Celsius/hour.

8. At a certain time instant, the temperature distribution in a long cylindrical fire tube can be represented approximately by the relation
T = 650 + 800 r – 4250 r2
Where temperature t is in degree Celsius and radius r is in meter. Find the rate of heat flow such that the tube measures: inside radius 25 cm, outside radius 40 cm and length 1.5 m.
For the tube material
K = 5.5 W/m K
α = 0.004 m2/hr
a) 3.672 * 10 8 W
b) 3.672 * 10 2 W
c) 3.672 * 10 5 W
d) – 3.672 * 10 5 W

Answer: d [Reason:] Q = – k A (d t/d r), Rate of heat storage = Q IN – Q OUT = – 3.672 * 10 5 W.

9. Consider he above problem, find the rate of change of temperature at the inside surface of the tube
a) – 35 degree Celsius/hour
b) – 45 degree Celsius/hour
c) – 55 degree Celsius/hour
d) – 65 degree Celsius/hour

Answer: c [Reason:] d t/d T = α [d 2t/d r2 + d t/r d r] = – 55 degree Celsius/hour.

10. Time lag is given by the formula
a) x/2 [1/ (α π n) ½].
b) x/3 [1/ (α π n) ½].
c) x/4 [1/ (α π n) ½].
d) x/5 [1/ (α π n) ½].

Answer: a [Reason:] The time interval between the two instants is called the time lag.

## Set 2

1. The energy emitted by a black surface should not vary in accordance with
a) Wavelength
b) Temperature
c) Surface characteristics
d) Time

Answer: d [Reason:] It is time independent. For a prescribed wavelength, the body radiates much more energy at elevated temperatures.

2. In the given diagram let r be the length of the line of propagation between the radiating and the incident surfaces. What is the value of solid angle W? a) A sin α
b) A cos α
c) 2A cos α
d) 2A cos α

Answer: b [Reason:] The solid angle is defined by a region by the rays of a sphere, and is measured as A n/r2.

3. Likewise the amount of emitted radiation is strongly influenced by the wavelength even if temperature of the body is
a) Constant
b) Increasing
c) Decreasing
d) It is not related with temperature

Answer: a [Reason:] Temperature must remain constant in order to emit radiation.

4. A small body has a total emissive power of 4.5 kW/m2. Determine the wavelength of emission maximum
a) 8.46 micron m
b) 7.46 micron m
c) 6.46 micron m
d) 5.46 micron m

Answer: d [Reason:] (Wavelength) max t = 2.8908 * 10 -3.

5. The sun emits maximum radiation of 0.52 micron meter. Assuming the sun to be a black body, Calculate the emissive ability of the sun’s surface at that temperature
a) 3.47 * 10 7 W/m2
b) 4.47 * 10 7 W/m2
c) 5.47 * 10 7 W/m2
d) 6.47 * 10 7 W/m2

Answer: c [Reason:] E = σ b t 4 = 5.47 * 10 7 W/m2.

6. The law governing the distribution of radiant energy over wavelength for a black body at fixed temperature is referred to as
a) Kirchhoff’s law
b) Planck’s law
c) Wein’s formula
d) Lambert’s law

Answer: b [Reason:] This law gives a relation between energy over wavelength.

7. The Planck’s constant h has the dimensions equal to
a) M L 2 T -1
b) M L T -1
c) M L T -2
d) M L T

Answer: a [Reason:] It has unit equal to J s and its value is 6.626 * 10 -34.

8. Planck’s law is given by
a) (E) b = 2 π c 2 h (Wavelength) -5/[c h/k (Wavelength) T] – 2
b) (E) b = π c 2 h [exponential [c h/k (Wavelength) T] – 3].
c) (E) b = 2 π c 2 h (Wavelength) -5/exponential [c h/k (Wavelength) T] – 1
d) (E) b = 2 c 2 h (Wavelength) -5/exponential [c h/k (Wavelength) T] – 6

Answer: c [Reason:] Planck suggested the following law for the spectral distribution of emissive power.

9. A furnace emits radiation at 2000 K. Treating it as a black body radiation, calculate the monochromatic radiant flux density at 1 micron m wavelength
a) 5.81 * 10 7 W/m2
b) 4.81 * 10 7 W/m2
c) 3.81 * 10 7 W/m2
d) 2.81 * 10 7 W/m2

Answer: d [Reason:] (E) b = C 1 (Wavelength) -5/exponential [C 2/ (Wavelength) T] – 1.

10. A metal sphere of surface area 0.0225 m2 is in an evacuated enclosure whose walls are held at a very low temperature. Electric current is passed through resistors imbedded in the sphere causing electrical energy to be dissipated at the rate of 75 W. If the sphere surfaces temperature is measured to be 560 K, while in steady state, calculate emissivity of the sphere surface
a) 0.498
b) 0.598
c) 0.698
d) 0.798

Answer: b [Reason:] E = e A σ b T.

## Set 3

1. A small thermo-couple is positioned in a thermal boundary layer near a flat plate past which water flows at 30 degree Celsius and 0.15 m/s. The plate is heated to a surface temperature of 50 degree Celsius and at the location of the probe, the thickness is 15 mm. The probe is well-represented by
t – t S/t INFINITY – t S = 1.5 (y/δ) – 0.5 (y/δ) 3
Determine the heat transfer coefficient
a) 33.3 W/m2 K
b) 43.3 W/m2 K
c) 53.3 W/m2 K
d) 63.3 W/m2 K

Answer: d [Reason:] h = Q/A (t INFINITY – t S) = 63.3 W/m2 K.

2. Air at 25 degree Celsius approaches a 0.9 m long and 0.6 m wide flat plate with a velocity 4.5 m/s. Let the plate is heated to a surface temperature of 135 degree Celsius. Find local heat transfer coefficient from the leading edge at a distance of 0.5 m
a) 5.83 W/m2 K
b) 6. 83 W/m2 K
c) 7. 83 W/m2 K
d) 8. 83 W/m2 K

Answer: a [Reason:] h = Nu k/x = 5. 83 W/m2 K.

3. Consider the above problem, find the total rate of heat transfer from the plate to the air
a) 316.78 W
b) 416.78 W
c) 516.78 W
d) 616.78 W

Answer: c [Reason:] Q = h A d t = 516.78 W.

4. A small thermo-couple is positioned in a thermal boundary layer near a flat plate past which water flows at 30 degree Celsius and 0.15 m/s. The plate is heated to a surface temperature of 50 degree Celsius and at the location of the probe, the thickness of thermal boundary layer is 15 mm. If the temperature profile as measured by the probe is well-represented by
t – t S/t INFINITY – t S = 1.5 (y/δ t) – 0.5 (y/δ t) 3
Determine the heat flux from plate to water
a) 266 W/m2
b) 1266 W/m2
c) 2266 W/m2
d) 3266 W/m2

Answer: b [Reason:] Q/A = – k (t INFINITY – t S) d/d y [t – t S/t INFINITY – t S] Y = 0. So, heat flux = 1266 W/m2.

5. Atmospheric air at 30 degree Celsius temperature and free stream velocity of 2.5 m/s flows along the length of a flat plate maintained at a uniform surface temperature of 90 degree Celsius. Let length = 100 cm, width = 50 cm and thickness = 2.5 cm. Thermal conductivity of the plate material is 25 W/m K, find heat lost by the plate
a) 155.88 W
b) 165.88 W
c) 175.88 W
d) 185.88 W

Answer: d [Reason:] Q = h A d t where, Nu = h l/k. So, Q = 185.88 W.

6. Consider the above problem, find the temperature of bottom surface of the plate for steady state condition
a) 90.372 degree Celsius
b) 80.372 degree Celsius
c) 70.372 degree Celsius
d) 60.372 degree Celsius

Answer: a [Reason:] Q = – k A (t S – t B)/δ.

7. Ambient air at 20 degree Celsius flows past a flat plate with a sharp leading edge at 3 m/s. The plate is heated uniformly throughout its entire length and is maintained at a surface temperature of 40 degree Celsius. Calculate the distance from the leading edge at which the flow in the boundary layer changes from laminar to turbulent conditions. Assume that transition occurs at a critical Reynolds number of 500000
a) 4.67 m
b) 3.67 m
c) 2.67 m
d) 1.67 m

Answer: c [Reason:] Re = x U INFINITY/v.

8. Ambient air at 20 degree Celsius flows past a flat plate with a sharp leading edge at 3 m/s. The plate is heated uniformly throughout its entire length and is maintained at a surface temperature of 40 degree Celsius. Calculate the thickness of the hydrodynamic boundary layer. Assume that transition occurs at a critical Reynolds number of 500000
a) 16.5 mm
b) 17.5 mm
c) 18.5 mm
d) 19.5 mm

Answer: b [Reason:] Thickness = 4.64/ (Re) ½.

9. Ambient air at 20 degree Celsius flows past a flat plate with a sharp leading edge at 3 m/s. The plate is heated uniformly throughout its entire length and is maintained at a surface temperature of 40 degree Celsius. Calculate the thickness of the thermal boundary layer. Assume that transition occurs at a critical Reynolds number of 500000
a) 19.23 mm
b) 18.23 mm
c) 17.23 mm
d) 16.23 mm

Answer: a [Reason:] Thickness = 0.976 (Thickness of hydrodynamic boundary layer)/ (Pr) 1/3.

10. Ambient air at 20 degree Celsius flows past a flat plate with a sharp leading edge at 3 m/s. The plate is heated uniformly throughout its entire length and is maintained at a surface temperature of 40 degree Celsius. Calculate the local convective heat transfer coefficient. Assume that transition occurs at a critical Reynolds number of 500000
a) 4.519 k J/m2 hr degree
b) 5.519 k J/m2 hr degree
c) 6.519 k J/m2 hr degree
d) 7.519 k J/m2 hr degree

Answer: d [Reason:] h = Nu k/x.

## Set 4

1. A radiation shield should
a) Have high transmissivity
b) Absorb all the radiations
c) Have high reflexive power
d) Partly absorb and partly transmit the incident radiation

Answer: c [Reason:] Reflexive power is much high for radiation shield.

2. Radiation shield are used between the emitting surfaces such that
a) To reduce overall heat transfer
b) To increase overall heat transfer
c) To increase density
d) To reduce density

Answer: a [Reason:] Many situations are encountered where it is desired to reduce the overall heat transfer between two radiating surfaces.

3. Which of the following can be used as a radiating shield?
a) Carbon
b) Thin sheets of aluminum
c) Iron
d) Gold

Answer: b [Reason:] The shields are thin opaque partitions arranged in the direction perpendicular to the propagation of radiant heat.

4. Two large parallel planes with emissivity 0.4 are maintained at different temperatures and exchange heat only by radiation. What percentage change in net radiative heat transfer would occur if two equally large radiation shields with surface emissivity 0.04 are introduced in parallel to the plates? a) 65.1%
b) 75.1%
c) 85.1%
d) 95.1%

Answer: d [Reason:] When shields are not used, Q 12 = (F g) 12 A 1 σ b (T 14 – T 24) = 0.2 A 1 σ b (T 14 – T 24) and when shields are used Q 12 = 0.0098 A 1 σ b (T 14 – T 24).

5. Determine the net radiant heat exchange per m 2 area for two infinite parallel plates held at temperature of 800 K and 500 K. Take emissivity as 0.6 for the hot plate and 0.4 for the cold plate
a) 6200 W/m2
b) 7200 W/m2
c) 8200 W/m2
d) 9200 W/m2

Answer: a [Reason:] Q 12 = (F g) 12 A 1 σ b (T 14 – T 24) and (F g) 12 = 0.135. Therefore, Q 12 = 6200 W/m2.

6. Consider the above problem, what should be the emissivity of a polished aluminum shield placed between them if heat flow is to be reduced to 40 percent of its original value?
a) 0.337
b) 0.347
c) 0.357
d) 0.367

Answer: b [Reason:] (F g) 12 = 1/E 1 +1/E 2 +2/E 3 – 2 = 7.936.

7. Consider radiative heat transfer between two large parallel planes of surface emissivities 0.8. How many thin radiation shields of emissivity 0.05 be placed between the surfaces is to reduce the radiation heat transfer by a factor of 75?
a) 1
b) 2
c) 3
d) 4

Answer: c [Reason:] (Q 12) ONE SHIELD = A σ b (T 14 – T 24)/ 1/E 1 +1/E 2 +2/E 3 – 2 and 75 = (Q 12) NO SHIELD / (Q 12) N SHIELD.

8. Two parallel square plates, each 4 m2 area, are large compared to a gap of 5 mm separating them. One plate has a temperature of 800 K and surface emissivity of 0.6, while the other has a temperature of 300 K and surface emissivity of 0.9. Find the net energy exchange by radiations between the plates
a) 61.176 k W
b) 51.176 k W
c) 41.176 k W
d) 31.176 k W

Answer: b [Reason:] Q 12 = (F g) 12 A 1 σ b (T 14 – T 24).

9. The furnace of a boiler is laid from fire clay brick with outside lagging from the plate steel, the distance between the two is quite small compared with the size of the furnace. The brick setting is at an average temperature of 365 K whilst the steel lagging is at 290 K. Calculate the radiant heat flux. Assume the following emissivity values
For brick = 0.85
For steel = 0.65
a) 352.9 W/m2
b) 452.9 W/m2
c) 552.9 W/m2
d) 652.9 W/m2

Answer: a [Reason:] Q 12 = (F g) 12 A 1 σ b (T 14 – T 24).

10. Consider the above problem, find the reduction in heat loss if a steel screen having an emissivity value of 0.6 on both sides is placed between the brick and steel setting
a) 5.56
b) 4.46
c) 3.36
d) 2.36

Answer: d [Reason:] (F g) 12 = 0.247 and Q = 149.51 W/m2.

## Set 5

1. What is the dimension of coefficient of volumetric expansion?
a) α
b) α 1
c) α -2
d) α -1

Answer: d [Reason:] Its unit is per degree. Coefficient of volumetric expansion is defined as the percentage increase in volume.

2. What is the dimension of convective film coefficient?
a) M T -3 α -1
b) M T -3 α -2
c) M T -2 α -1
d) M T -1 α -1

Answer: a [Reason:] Its unit is k cal/m2 hr degree. It is used in thermodynamics to calculate the heat and it is denoted by h.

3. What is the dimension of velocity?
a) L T -2
b) L T 1
c) L T -1
d) L T

Answer: c [Reason:] Its unit is m/s. Velocity is defined as a speed in a particular direction.

4. What is the dimension of area?
a) M L 2
b) L 2
c) L 1
d) L 3

Answer: b [Reason:] Its unit is m2. It is defined as a range of activity or an interest.

5. What is the dimension of volume?
a) L 2
b) M L 3
c) L
d) L 3

Answer: d [Reason:] Its unit is m3. It is defined as a region or part of a town, a country or the world.

6. What is the dimension of work?
a) M L 2 T -2
b) M L 2 T -1
c) M L 2 T
d) M L 1 T -2

Answer: a [Reason:] Its unit is m N. Work can be defined as transfer of energy.

7. What is the dimension of temperature?
a) α -2
b) α 2
c) α
d) M α

Answer: c [Reason:] Its unit is Kelvin. It refers to how cold or hot something is.

8. What is the dimension of mass?
a) M
b) M L
c) L
d) M L T

Answer: a [Reason:] Its unit is kg. It is the property of a physical body which determines the strength of its mutual gravitational attraction to the earth.

9. What is the dimension of length?
a) T
b) M
c) L
d) M L