SHEFFIELD HALLAM UNIVERSITY
SCHOOL OF ENVIRONMENT AND DEVELOPMENT
(+ ENGINEERING + SCIENCE)
Course : BSc ENVIRONMENTAL MANAGEMENT
Unit : SED1063 PHYSICAL SCIENCE
End-Test 2002 minus Radiation/Noise
INSTRUCTIONS
1. Attempt ALL questions in Section A.
2. Attempt ONE question from Section B.
A formula sheet is attached for your use.
SECTION A
Answer ALL the questions in Section A
A4
A voltage of 6 V is applied across a 2-ohm resistor. Calculate the current
flowing in the resistor and the power dissipated in it.
(5 marks)
(Ohm's Law i = 6/2 = 3A; Power = 3 x 6 = 18 W - same answer by i2R or v2/R))
A5.
Explain briefly the principles on which electric motors and generators
work.
(6 marks)
(Motors - if a magnetic field of flux density B and a wire of length l carrying a
current i are at right-angles to each other, the wire will experience a force
Bil. Generators - if a magnetic field of flux density B and a wire of length l
are at right-angles to each other, and the wire is moved at a speed u at
right-angles both to itself and to the magnetic field direction, a voltage Blu
will be produced between the ends of the wire).
A6.
A car engine produces an output power of 20 kW and uses 8 kg of fuel of
calorific value 40 000 kJ kg-1 during each hour of operation. What is the
efficiency of the engine ?
(6 marks)
(Energy out per hour = 20 x 60 x 60 = 72000 kJ, energy in per hour = 8 x 40000
= 320000 kJ. So efficiency = 72000/320000 = 0.225 = 22.5%)
A7.
A piece of metal of mass 2 kg is dropped to the ground from a height of
30 m. Its specific heat is 3.0 kJ kg-1 C-1 and the acceleration of gravity is
9.81 m s-2. Making reasonable assumptions, calculate:
i) the loss of potential energy as the metal fell,
ii) the speed it reached immediately before hitting the ground, and
iii) the amount by which its temperature rose on hitting the ground.
In what way (if any) would you expect the answers to be different in
practice ?
(8 marks)
(Loss of PE = mgh = 2 x 9.81 x 30 = 588.6 J.
Assuming no air resistance, KE gained = 0.5mv2 = PE lost = 588.6 J
So 2 x 0.5 x v2 = 588.6 and v = 24.26 m s-1.
Temperature rise T from DE = smT ... 0.5886 (NB kJ) = 3 x 2 x T, so
T = 0.5886/6 = 0.0981 C.
Possibly different in practice owing to air resistance (speed and temp. rise
lower).
Please note that Section B starts here
SECTION B
Answer ONE question in Section B
B3.
(a)
What magnetic flux density would you expect at typical human head
height beneath a power line 10 m above the ground carrying a current of
1000 A ? Sketch a diagram indicating the direction of the flux produced.
The value of the permeability of free space is 4 x 10-7 H m-1.
(5 marks)
-7
-5
(B=μI/(2r), so B = approx 4 x 10 x 1000/(8 x 2) = 2.5 x 10 T. The flux
encircles the wire clockwise as we look in the direction of the current)
(b)
A recent article stated that the internationally-recommended maximum
safe level of electromagnetic field exposure from a typical mobile phone
mast would only be reached at a distance of 3 m from the antenna.
Assuming the above statement to be true and the inverse-square law to
apply:
i) What fraction of the maximum safe field strength will be experienced by
someone 100 m from the mast ?
ii) If a typical mobile phone has a transmitter power of one-tenth of that
transmitted by the mast, will the field in the user's head (assumed to
be 0.1 m from the phone antenna) be at a safe level ?
iv) What else should we take into account in assessing the field strength
of such transmissions ?
(11 marks)
(If the mast produces a field of FRED/r2, and this is the safe level when r = 3 m,
the safe level must be 9 x FRED. The level 100m away will be FRED/100 2
= 10-4FRED, which is 0.0009 times the safe level (far below it !).
The phone will produce a field of 0.1 x FRED/r2, which will be 10 x FRED at a
distance of 0.1 m. This is slightly higher than the safe level.
The radiation is absorbed to a fair degree by stone, brick etc (and undoubtedly
the bone surrounding the user's brain !)
(c)
Explain briefly:
i) The principle of operation of a transformer.
ii) Why transformers do not work with direct currents and voltages.
(9 marks)
[TOTAL 25 MARKS]
(See Notes)
B4.
(a)
A particular gas turbine burns fuel of calorific value 38 000 kJ/kg at a rate
of 80 kg per minute. Its turbine produces 45 MW of which the compressor
uses 34 MW. Determine:
(i)
The heat energy supplied by the fuel each second.
(ii)
The output power.
(iii)
The efficiency.
(iv)
The heat energy per second that it was unable to utilise.
(11 marks)
-1
( i) Heat energy per second = 80/60 x 38000 = 50 667 kJ s .
ii) Output power = 45 -34 = 11 MW.
iii) Efficiency = 11/50.667 (50667 kJ s-1 = 50.667 MW !) = 21.7%.
iv) 50.667 - 11 = 39.667 MJ s-1.)
(b)
Explain, with the aid of a block diagram, how a combined-cycle
arrangement using a boiler and steam-turbine can add considerably to the
efficiency of a gas-turbine as a power generator. What alternative
methods of using the waste heat might be available ?
(8 marks)
(See Notes for the combined-cycle system. We could use the waste heat for
district or industrial heating)
(c)
Power stations using steam turbines usually use a condenser to convert
the exhaust steam back to water. Explain why it is advantageous to do so.
What constraint on the siting of such power stations is imposed by the
condenser ?
(6 marks)
[TOTAL 25 MARKS]
(See Notes for the full story but the reason is that the condenser means the
steam can expand to a pressure below atmospheric, so we extract more work
from the same steam. We need to put the power station near a source of large
quantities of water, for example a large river, to supply the condenser cooling).
B5.
Explain the following points in as much detail as you are able in the
time allowed.
a)
The operation of a refrigerator (or air conditioner) and why such a
device is likely to have an apparent "efficiency" greater than 100 %.
(see Notes)
(12 marks)
b)
Why it is usual to generate electrical power at typically 11 kV,
transmit it through the National Grid at up to 400 kV and more
locally at 11 kV, but utilise it at 240-415 V.
(7 marks)
(See Notes, but it is to do with the balance between minimising the current (by
using high voltages) to avoid I2R losses in the wires, and limitations of
technology, economics and safety which restrict the voltages we can use in the
power station generators and towards the user end).
c)
The operation of a dehumidifier.
(6 marks)
[TOTAL 25 MARKS]
(See notes)
FORMULAE
You will be provided with this formula sheet.
Mechanics
Potential Energy
=
mgh
Kinetic energy
=
1 2
mv
2
Work
=
Force x distance moved
=
Pressure x volume change)
(Or
Power = Force x Speed
Thermodynamics
First Law
Specific Heat
Q
=
W + E
E = smT
General Gas Equation
PV = mRT
Electrical
Ohm’s Law:
E = IR
(R = 287 J kg-1 K-1)
Kirchhoff’s Current Law: At any junction in a circuit, the total current flowing in
must equal the total current flowing out.
Electrical power = V x I ( = V2/R or I2R in resistances)
Inverse Square Law:
Field strength at a distance d from the source =
K
d2
where K is a constant proportional to the total power emitted by the source.
Magnetic flux density at a distance r from a wire carrying a current i =
0ri
2r
Where The "Goalposts" are
I recommend knowing/being able to do calculations on (as appropriate):
Electrical
Circuits, Ohm's Law, Kirchhoff's Current Law. Electromagnetism and transformer
and motor principles. Power systems and a.c.
Thermal/Mechanical
Work, energy and power
Conservation of energy - potential, kinetic, thermal (icluding internal energy)
First Law Q = W + ΔE (and ΔE = smT)
General Gas Equation, Boyle's Law, Charles's Law
Efficiency, energy in engines etc.
Fridge/aircon - principles, COP calculation, dehumidifier
Some more examples
A4
A current of 0.5 A passes through a 5-ohm resistor. Calculate the voltage
produced across the resistor and the power dissipated in it.
(5 marks)
(Voltage = 0.5 x 5 = 2.5 V. Power = 2.5 x 0.5 = 1.25 W)
A6.
Explain with the aid of a suitable diagram how an air-conditioner works.
Why can the Coefficient of Performance of such a device be greater than
1 without infringing the First Law of Thermodynamics ?
(8 marks)
(See Notes for operation. It doesn't contravene the First Law because the heat is
being moved from one place to another, not created out oof nothing !)
A7.
A piece of metal is dropped to the ground from a height of 20 m. Its
specific heat is 3.5 kJ kg-1 C-1 and the acceleration of gravity is 9.81 m s2. Making reasonable assumptions, calculate the speed it will have
reached immediately before hitting the ground and the amount by which
its temperature will rise on hitting the ground. How would the answers be
likely to be slightly different in practice ?
(7 marks)
(Another of these ! PE lost = m x 9,.81 x 20 = 196.2m joule. This equals the KE
gained ignoring air resistance which is 0.5 mv2, so v2 = 196.2m/(0.5m) = 392.4
and v = 19.8 m s-1. Temp. rise from 0.1962m = smT = 3.5m x T, so T =
0.1962/3.5 = 0.056 C).
B3.
(a)
By reference to the First Law of Thermodynamics, explain why air
pumped into a bicycle tyre becomes hot as it is pumped.
(5 marks)
(See Notes - no heat added and work is done ON the system so W is negative.
This means ΔE must be positive, so the air heats up).
(b)
(i)
At a pressure of 1 bar and a temperature of 16 C, a
particular mass of gas occupies a volume of 8 litre. If it is compressed to a
pressure of 2 bar at the same temperature, what volume will it occupy?
(ii)
If it were then heated to 50 C at the same pressure of 2
bar, what would its final volume be ?
(9 marks)
( i) Boyle's Law PV = constant, so 8 x 1 = new volume x 2, so new volume = 4
litre
ii) Now constant pressure, so it is Send For Mr. Charles - and remember he
works in absolute temperature = C + 273.
So volume = 4 x 323/289 = 4.4706 litre.)
(c)
During one cycle of operation of a particular Diesel engine, the
combustion of the fuel produces 25 kJ of energy. The power stroke
delivers 31 kJ and the work done in compression is 26 kJ.
(i)
Calculate the efficiency of the engine and the heat rejected during
the cycle.
(ii)
It is frequently argued that Diesel engines are more polluting than
petrol engines. Present one argument that they are more polluting and
one argument that they are less so.
(11 marks)
[TOTAL 25 MARKS]
( i) Mech. out = power - compression = 31 - 26 = 5 kJ.
Heat in from fuel = 25 kJ, so efficiency = 5/25 = 0.2 = 20%.
Heat rejected = heat in - mech. out = 20 kJ.
ii) Their heavier fuel produces fine carbon particles when it burns which are
injurious to health - petrol engines do not produce these to anything like the
same extent. But the diesel uses less fuel overall in producing the same power,
so less total pollution esp. CO2.)
B4.
(a)
Sketch a block diagram of a boiler-steam turbine-alternator plant
for electrical power generation. Indicate the main energy flows, including
heat losses. Why is it beneficial to allow the steam to expand to a
pressure lower than atmospheric and how is such an expansion achieved
in practice ?
(9 marks)
(See Notes)
(b)
Explain, with the aid of a block diagram, how a combined-cycle
arrangement using a boiler and steam-turbine can add considerably to the
efficiency of the system of Part (a) as a power generator.
(See Notes)
(8 marks)
(c)
Explain the operation of a dehumidifier for reducing dampness in
building interiors. (Again .. see Notes)
(8 marks)
[TOTAL 25 MARKS]
B5.
Explain the following points in as much detail as you are able in the
time allowed.
a)
Why alternating current, rather than direct current, is almost
universally used for electrical power supplies.
(7 marks)
(Transformers .. and easier to generate .. see Notes)
b)
Why it is usual to generate electrical power at typically 11 kV,
transmit it through the National Grid at up to 400 kV and more
locally at 11 kV, but utilise it at 240-415 V.
(9 marks)
(See Notes - and the earlier similar question)
c)
How Kirchhoff's Current Law could be verified in the laboratory.
(9 marks)
[TOTAL 25 MARKS]
(Arrange for three .. or more .. voltage sources, resistances and ammeters to
supply current to a common return wire also containing an ammeter. The total
current supplied by the sources should equal the total return current if Kirchhoff
was right. To be sure, try several combinations of source currents)
SECTION A
Answer ALL the questions in Section A
A4
A voltage of 5 V is applied across a 5-ohm resistor. Calculate the current
flowing in the resistor and the power dissipated in it.
(5 marks)
(Current = 5/5 = 1 A; power = 5 x 1 = 5 W)
A5.
I
I
1
3 ohm
1 ohm
+
4V
2
+
2 ohm
2V
--
-I
3
For the circuit above, use Kirchhoff’s laws to write down three equations from
which the currents I1, I2 and I3 could be determined. It is NOT necessary to solve
the equations.
(7 marks)
(Not set for this year, but for completeness ..
I1 + I2 = I3 (Current Law)
4 = 3I1 + 2(I2 + I3) .. Voltage Law round LH loop
2 = I2 + 2(I2 + I3) .. Voltage Law round RH loop.)
A6.
Explain the principle of operation of a transformer. Why is the transformer
one of the main reasons for the almost invariable use of alternating
current rather than direct current in electrical power systems ?
(6 marks)
(See Notes for operation - it doesn't work with d.c.)
A7 is the same as an earlier example.
SECTION B
B3.
(a)
By reference to the First Law of Thermodynamics, explain why air
pumped into a bicycle tyre becomes hot as it is pumped.
(5 marks)
(See Notes and the similar earlier question)
(b)
(i)
At a pressure of 1 bar and a temperature of 27 C, a particular mass
of gas occupies a volume of 8 litre. If it is compressed to a pressure of 3
bar at the same temperature, what volume will it occupy? (2.667 litre)
(ii)
If it were compressed from 1 bar to 3 bar adiabatically, would its
volume be greater or less than that calculated in (i) above ? Explain your
answer.
(Greater .. the gas will have heated up because of the work
done in compressing it)
(9 marks)
(c)
During one cycle of operation of a particular petrol engine, the combustion
of the fuel produces 30 kJ of energy. The power stroke delivers 31 kJ and
the work done in compression is 25 kJ.
(i)
Calculate the efficiency of the engine and the heat rejected during
the cycle.
(20%, 24 kJ)
(ii)
It is now probable that such an engine will be fitted with a catalytic
convertor to reduce harmful emissions from the engine. What pollutants
does the convertor remove or reduce ? (Carbon monoxide (the major
one), nitrogen oxides, oxides of sulphur)
(11 marks)
[TOTAL 25 MARKS]
B4.
(a)
A particular gas turbine burns fuel of calorific value 39 000 kJ/kg at
a rate of 92 kg per minute. Its turbine produces 52 Mw of which the
compressor uses 39 Mw. Determine:
(i)
The heat energy supplied by the fuel each second.
(ii)
The output power.
(iii)
The efficiency.
(iv)
The heat energy per second that it was unable to utilise.
(9 marks)
(Heat in/second = 39000 x 92/60 = 59800 kJ s-1 = 59.8 MJ s-1.
Output power = turbine - compressor = 52 - 39 = 13 MW.
Efficiency = 13/59.8 = 0.2174 = 21.74%.
Heat energy not utilised = 59.8 - 13 = 46.8 MJ s-1.)
(b)
Explain, with the aid of a block diagram, how a combined-cycle
arrangement using a boiler and steam-turbine can add considerably to the
efficiency of a gas-turbine as a power generator. What alternative
methods of using the waste heat might be available ?
(8 marks)
(c)
Explain the operation of a dehumidifier for reducing dampness in
building interiors.
(8 marks)
[TOTAL 25 MARKS]
(See Notes for b) and c) )
B5.
Explain the following points in as much detail as you are able in the
time allowed.
a)
The operation of a refrigerator (or air conditioner) and why such a
device is likely to have an apparent "efficiency" greater than 100 %.
(9 marks)
b)
Why it is usual to generate electrical power at typically 11 kV,
transmit it through the National Grid at up to 400 kV and more
locally at 11 kV, but utilise it at 240-415 V.
(8 marks)
c)
How Kirchhoff's Current Law could be verified in the laboratory.
(8 marks)
[TOTAL 25 MARKS]
(All of these are dealt with earlier !)