January 2020

Question 1

Define an Independent Variable

Answer 1

The variable that is controlled or whose values are selected in an experiment

Question 2

Define a Dependant Variable

Answer 2

The variable that is measured to correspond with each independent variable

Question 3

Express –12 °C in the thermodynamic scale.

Answer 3

–12 + 273 = 261 K

Question 4

Express 304 K in the Celsius
scale.

Answer 4

304 – 273 = 31 °C

Question 5

The temperature of a beaker of water is to be measured using a
resistance temperature detector (RTD). The resistance of the RTD in
ice at 0 °C is 8 Ω while the resistance of the RTD in steam at 100 °C is
84 Ω. When the RTD is placed into the beaker of water, the resistance
is found to be 34 Ω. Determine the temperature of the water, assuming
a linear relationship between temperature and resistance.

Answer 5

T − 0 / 100 − 0

34 − 8 / 84 − 8

⇒ T = 34.2 °C

Question 6

A flat plate solar collector is placed on the roof of a house. The collector is
1.2 m wide and 3.5 m long and the emissivity of the surface of the collector is 0.85. The average temperature of the exposed surface of the collector is
36 °C while the temperature of the surrounding air is 18 °C.

Determine the total rate of heat loss from the collector by convection and radiation when the convection heat transfer coefficient on the exposed surface is 14 W/m2 K.

Answer 6

Q̇ convection = h A ΔT = 14 (1.2)(3.5)(36 − 18) = 1058.4 W

Q̇radiation = ε σ A (Tbody 4 − Tsurr 4)

Tbody = 36 °C = 309 K

Tsurr = 18 °C = 291 K

Q̇ radiation = 0.85 (5.67 × 10−8) (1.2) (3.5) (3094 − 2914) = 393.9 W

Q̇total = 1058.4 + 393.9 = 1452.3 W

Question 7

A kettle contains 1.4 kg of water. During a three minute period, the temperature of the water rises from 16 °C to 95 °C. Assuming all of the electrical energy is used to heat the water, calculate:

(i) The energy gained by the water.

(ii) The power rating of the kettle

Answer 7

Q = m c ∆T = 1.4 (4200)(95 − 16) = 464520 J

Power =Energy/Time
= 464520 / 3 (60)
= 2580.7 W

Question 8

Define specific heat capacity.

Answer 8

The quantity of heat required ro raise the temperature of 1 kg of a substance by 1 K.

Question 9

Define specific
latent heat.

Answer 9

The amount of energy needed to change the state of 1 kg of a substance.

Question 10

Define U-Value

Answer 10

a measure of the rate at which energy is conducted through a structure, for a given temperature difference between the two sides of it. E.g. a
good insulating structure has a low U-value.

Question 11

A cavity wall has a 120 mm outer brickwork layer, a 35 mm air gap, a 40 mm insulating layer and a 95 mm inner concrete layer. Calculate the U-value of
this wall, given the following values:

Thermal conductivity (W/m K)

1. Brick - 0.8
2. Insulation - 0.05
3. Concrete - 0.5

Thermal resistance (m2 K/W)

1. Exterior Surface - 0.04
2. Air Cavity - 0.16
3. Interior Surface - 0.1

Answer 11

Rtotal = 0.04 + 0.12/0.8 + 0.16 + 0.04/0.05 + 0.095/0.5 + 0.1
= 1.44 m2 K/W

Uvalue = 1/Rtotal = 1/1.44 = 0.69 W/m2 K

Question 12

35 g of ice at 0 °C are added to a glass containing 100 g of warm water. All of the ice melts and the final temperature of the water is 8 °C. Assuming no
heat transfer to the surroundings or to the glass, determine:

(i) The total energy needed to convert the ice into water at 8 °C.

(ii) The starting temperature of the water.

Answer 12

i) Change of state
Q = m l f
= 0.035 (334000)
= 11690 J

Heating water from 0 °C to 8 °C
Q = m c ΔT
= 0.035 (4200)(8)
= 1176 J

Total energy = 11690 + 1176 = 12866 J

ii) Heat lost by hot water = Heat gained by ice

m c ∆T

0.1 (4200)(T − 8) = 12866

Solve for T = 38.6 °C

Question 13

Explain the difference between transverse and longitudinal waves, giving an example of each.

Answer 13

Longitudinal wave – the wave front travels in a direction that is the same as the direction of the vibration of the wave. Answer to include example.

Transverse wave – the wave front travels in a direction that is perpendicular to the direction of the vibration of the wave. Answer to include example.

Question 14

Explain why sound travels faster in solids than in air

Answer 14

Sound travels faster in solids because the particles that make up solids are closer than air particles, so vibrations transmit across them more quickly.

Question 15

Calculate the density of zinc given that the speed of sound in zinc is 3890 m/s and its Young’s modulus is 108 GPa.

Answer 15

c = √E/ρ
3890 = √108 × 10^9/ρ
Solve for ρ = 7137 kg/m3

Question 16

Air in a pipe of length 375 mm, open at both ends, vibrates in its third harmonic. Assuming that the speed of sound in air is 330 m/s and neglecting
the end correction factor, determine the frequency of the sound emitted.

Answer 16

3rd harmonic, ⇒ 0.375 m = 1.5 λ
λ = 0.25 m
f =V/λ
f =330/0.25
f = 1320 Hz

Question 17

A ship detects the seabed by reflecting a pulse of high frequency sound from the seabed. The sound pulse is detected 0.4 seconds after it is sent out and the speed of sound in water is 1500 m/s.

(i) Determine the depth of the water under the ship.

(ii) Determine the wavelength of the sound pulse, if its frequency is 40 kHz.

Answer 17

i)Time to reach seabed = 0.4/2 = 0.2 seconds

Distance = Speed × Time
D = 1500 (0.2)
D = 300 m

ii)λ = v/f
λ =1500/40000
λ = 0.0375 m

Question 18

Define luminous intensity and give its unit.

Answer 18

Luminous intensity is the power of a light source to emit light in a particular direction.

Candella cd

Question 19

Define luminous flux
and give its unit.

Answer 19

Luminous flux is the rate of flow of light energy.

lumens (lm)

Question 20

Define illuminance and give its unit.

Answer 20

Illuminance is luminous flux per unit area.

Lux lx

Question 21

A remote control for a television transmits infrared radiation of frequency 1.65 x1012 Hz. Determine the wavelength of the infrared radiation, given that the speed of light in air is 3.0 x 108 m/s.

Answer 21

λ = v/f
λ = 3.0 × 10^8 /1.65 × 10^12
λ = 1.8 × 10^−4 m

Question 22

A light has an intensity of 300 cd. 20% of the resulting flux falls on to a rectangular surface measuring 1.2 m by 1.5 m. Determine the distance from the light source to the surface.

Answer 22

F = I (4 π)
F = 300 (4 π)
F = 3769.9 lm

E = F/A
E = 0.2 × 3769.9/1.2 × 1.5
E = 418.88 lx

E = I/d^2

d = √I/E
d = √300/418.88
d = 0.85 m

Question 23

A diffraction pattern is formed on a screen when green light from a laser passes through a diffraction grating. The grating has 100 lines per mm and the distance from the grating to the screen is 600 mm. The distance between
the zero order and the second order image is 65 mm.

(i) Determine the wavelength of the light.

(ii) If the theoretical value for the wavelength of the green laser light is 532 nm, determine the experimental percentage error.

Answer 23

i) H = √65^2 + 600^2
H = 603.5 mm

n λ = d Sin θ
2 λ = 1/100 (65/603.5)

λ = 5.385 x 10−4 mm
λ ≈ 538.5 nm

ii) Error = (538.5 − 532)/532
Error = 539 × 100
Error = 1.2%

Question 24

State Boyle’s law and give an equation to describe Boyle’s law.

Answer 24

For a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume.

P V = constant

Question 25

Name the three particles that make up an atom.

Answer 25

Protons
Neutrons
Electrons

Question 26

Explain what is meant by a mole of a substance.

What is the mass of a mole.

Answer 26

One mole of a substance is the amount that contains Avogadro’s number of particles.

16 × 10^−3 kg

Question 27

The molar mass of methane (CH4) is 16 x 10-3 kg. Determine:

(i) The number of moles in 3 kg of the gas.

(ii) The number of molecules in 3 kg of the gas.

Answer 27

i) Number of moles in 3 kg =

3 / 16 × 10^−3 = 187.5 moles

ii) Number of molecules = 187.5 (6.02 × 10^23)
=1.13 × 10^26

Question 28

The volume of air in a Boyle’s law apparatus was found to be 18.4 cm3 on a day when the atmospheric pressure was 1.02 x 105 N/m2. A few days later the volume was found to be 18.8 cm3. Determine the value of atmospheric
pressure on the second day.

Answer 28

P1 V1 = P2 V2

1.02 x 10^5 (18.4) = P2 (18.8)

P2 = 99829.8 N/m2

Question 29

An aircraft is surrounded by air at a pressure of 12 kN/m2 and a temperature of –48 °C. Air is drawn into the engine cylinder where it is compressed to a volume of 1600 cm3, a pressure of 125 kN/m2 and a temperature of 90 °C.

Determine the volume of the air drawn in at the surrounding conditions.

Answer 29

–48 °C = 225 K
1600 cm3 = 1.6 x 10^-3 m3
90 °C = 363 K

P1 V1 / T1 = P2 V2 / T2

12000 (V1) / 225 = 125000 (1.6 x 10^−3) / 363

V1 = 10.3 x 10^-3 m3