1.
The table shows the specific heat capacities c of alcohol and water.
c / J kg–1 K–1
(i)
alcohol
2460
water
4180
An alcohol thermometer is placed in 80 g of water at 20 °C. The mass of alcohol
in the thermometer is 0.050 g. The water is then heated from 20 °C to 60 °C.
Calculate the ratio
energy required to warm the water from 20 C to 60C
energy required to warm the alcohol from 20 C to 60 C
ratio = ........................................................
[2]
(ii)
State and explain a situation in which the very high value of specific heat capacity
for water is useful.
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[2]
[Total 4 marks]
Ambrose College
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2.
The ideal gas equation may be written as
pV = nRT.
State the meaning of the terms n and T.
n ...........................................................................................................................
T ...........................................................................................................................
[Total 2 marks]
3.
Fig. 1 shows a cylinder that contains a fixed amount of an ideal gas. The cylinder is
fitted with a piston that moves freely. The gas is at a temperature of 20 °C and the
initial volume is 1.2 × 10–4 m3. Fig. 2 shows the cylinder after the gas has been heated
to a temperature of 90 °C under constant pressure.
volume = 1.2 × 10–4 m 3
90ºC
20ºC
Fig. 1
Ambrose College
Fig. 2
2
(i)
Explain in terms of the motion of the molecules of the gas why the volume of the
gas must increase if the pressure is to remain constant as the gas is heated.
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[4]
(ii)
Calculate the volume of the gas at 90 °C.
volume = ................................................... m3
[2]
[Total 6 marks]
Ambrose College
3
4.
(i)
Explain the term internal energy.
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[2]
(ii)
Define specific heat capacity of a substance.
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[1]
[Total 3 marks]
5.
Most cars are now fitted with safety airbags. During a sudden impact, a triggering
mechanism fires an ammunition cartridge that rapidly releases nitrogen gas into the
airbag.
In a particular simulated accident, a car of mass 800 kg is travelling towards a wall.
Just before impact, the speed of the car is 32 m s–1. It rebounds at two-thirds of its
initial speed.
The car takes 0.50 s for the car to come to rest. During the crash, the car’s airbag fills
up to a maximum volume of 3.4 × 10–2 m3 at a pressure of 1.0 × 105 Pa. The
temperature inside the airbag is 20 °C. Calculate:
(i)
the change in the momentum of the car
momentum change = ............................................................
[2]
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(ii)
the magnitude and direction of the average force acting on the car during impact.
force = .........................................................N
[2]
direction:...........................................................................................................
[1]
(iii)
the mass of nitrogen inside the cartridge.
Molar mass of nitrogen = 0.014 kg mol–1
mass = .....................................................kg
[3]
[Total 8 marks]
6.
Although the idea for the airbag was first suggested more than fifty years ago, it has
only been a compulsory safety feature in the modern motor car since 1998. When a car
experiences a serious head-on collision, the seat belt is designed to restrain the
driver’s body. However, without the cushioning effect of an airbag, the inertia in the
driver’s head will cause it to carry on moving at the speed of the car until it is stopped
by the steering wheel or the windscreen. When activated, the airbag must be fully
inflated before the driver’s head reaches it so that the head hits a soft target.
One early system stored the gas for the airbag in a cylinder under the driver’s seat.
When the deceleration of the car was sufficiently large, a sensor caused an electrical
circuit to operate and open a valve so that the compressed gas could rush into the
airbag on the steering wheel.
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The sensor used a steel ball and spring in a cylinder as shown below.
spring
direction of movement
of car
to electrical circuit
3.6 cm
steel ball
electrical contacts
When the car was being driven normally, the spring kept the steel ball apart from the
two electrical contacts inside the cylinder. But if the deceleration became large enough,
the inertia of the free ball compressed the spring and the ball touched the two contacts,
thus activating the electrical circuit.
The method of storing compressed gas in a cylinder was not very reliable because
some cylinders slowly leaked gas and so all had to be checked regularly.
The modern method of inflating an airbag is to generate the gas chemically by
activating an electrical heater or detonator in an explosive chemical mixture. The
heating starts a very rapid chemical reaction which produces nitrogen for the airbag.
This means that the folded airbag along with chemicals and heater can all be located
together in a compact container and positioned anywhere inside the car.
Consider the following data for a car running head-on into an immovable object.
initial velocity of car
final velocity of car
car front crumple distance
distance from head to windscreen
(a)
= 54 km hr–1
=0
= 1.25m
= 0.96m
Show that the car’s speed in m s–1 just before hitting the object is 15 m s–1.
[2]
Ambrose College
6
(b)
Calculate
(i)
the deceleration of the car during the collision (assumed to be constant)
deceleration = ....................................... m s–2
[2]
(ii)
the time taken for the car to crumple to rest.
time = ....................................... s
[2]
(c)
The data for a ball and spring sensor is given below.
mass of ball
spring constant
distance to be compressed
= 0.12 kg
= 30 N m–1
= 3.6 cm
Calculate
(i)
the force necessary to compress the spring by 3.6 cm
force = ....................................... N
[2]
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(ii)
the deceleration which the force in (c)(i) would cause in a mass of 0.12 kg.
deceleration = ....................................... m s–2
[1]
(d)
When the airbag was fully inflated from a storage cylinder, the bag had a volume
of 0.060 m3, with the gas inside at a pressure of 250 kPa. If the storage cylinder
had a volume of 3.0 × 10–4 m3, calculate the stored gas pressure, assuming the
gas was ideal and at constant temperature.
pressure = ....................................... Pa
[2]
(e)
Suppose that the pressure inside the cylinder dropped by 20% over a period of 4
weeks.
Assuming the mean temperature of the cylinder is 17 °C, calculate the average
number of gas molecules leaving per second during this time.
number leaving per second = .......................................
[4]
Ambrose College
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(f)
The data for a modern airbag is given below.
energy required for reaction to start
heater wire cross sectional area
heater wire length
resistivity of heater wire
battery voltage
(i)
= 0.96 J
= 2.75 × 10–8 m2
= 2.2 cm
= 1.5 × 10–6 Ωm
= 12V
Show that the resistance of the heater filament is 1.2Ω.
[2]
(ii)
Hence calculate the time taken for the heater to start the chemical reaction.
time to start = ....................................... s
[3]
[Total 20 marks]
Ambrose College
9
7.
Flow occurs in many different aspects of physics. For example, flow of electrons is an
electric current, heat flow takes place as a result of a temperature gradient and flow of
water or gas along a pipe is a common experience. The dimensions of the material
through which flow occurs, together with the properties of the material and the cause of
flow, determine the amount of flow which takes place.
(a)
Why is one pipe necessary for the supply of gas to a house but two cables are
necessary for the supply of electricity?
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[3]
(b)
The amount of heat energy flowing per unit time through the wall of a room is
given by
   1 
Q

 kA 2
t
 d 
where
and
(i)
Q is the quantity of heat energy which flows in time t,
k is called the thermal conductivity,
A is the surface area of the wall,
d is the thickness of the wall
2 and 1 are the inside and outside temperatures respectively.
Deduce the SI unit of k, the thermal conductivity.
unit of k ..............................
[3]
Ambrose College
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(ii)
Calculate the rate at which heat energy is lost through the wall of the room
under the following conditions.
k = 0.35 in SI units
A = 12.0 m2
2 = 22.0 °C
1 = 8.0 °C
d = 0.10 m
Q 
rate at which heat energy is lost   = .............................. W
t 
[2]
(c)
(i)
Write a corresponding equation to that in (b) for charge flow per unit time,
Q
through a wire, in terms of
t
the potential difference across the wire V
the resistivity of the material of which the wire is made 
and the length l and area of cross-section A of the wire.
[2]
Ambrose College
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(ii)
Compare the equations in (c)(i) and (b).
1
State which thermal property corresponds with V in the electrical
case.
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[1]
2
State which thermal property corresponds with  in the electrical
case.
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[1]
(d)
(i)
Flow of gas through a pipe follows the same pattern as for electron flow
and heat flow. Suggest an equation for gas flow. State the meaning of any
symbols you introduce.
[3]
Ambrose College
12
(ii)
160 cm3 of gas flow per second through a pipe of internal diameter 15 mm.
How much gas will flow per second through a pipe of internal diameter
22 mm under the same conditions?
volume per second = .............................. cm3 s–1
[2]
[Total 17 marks]
8.
Consider a 2.0 kg block of aluminium. Assume that the heat capacity of aluminium is
independent of temperature and that the internal energy is zero at absolute zero. Also
assume that the volume of the block does not change over the range of temperature
from 0 K to 293 K.
(i)
Show that the internal energy of this block of aluminium at 20 °C is 540 kJ.
specific heat capacity of aluminium = 920 J kg–1 K–1
[2]
Ambrose College
13
(ii)
Hence show that the mean energy per atom in the 2.0 kg aluminium block at
20 °C is about 1.2 × 10–20 J.
molar mass of aluminium = 0.027 kg mol–1
[3]
(iii)
In 1819, Dulong and Petit measured the heat capacities of bodies made of
different substances, and found that for one mole of each substance the molar
heat capacity was about 25 J mol–1 K–1. Starting from any of the data in (i) or (ii)
show that this is true for aluminium.
[2]
[Total 7 marks]
9.
(a)
The equation of state of an ideal gas is pV = nRT. Explain why the temperature
must be measured in kelvin.
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[2]
Ambrose College
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(b)
A meteorological balloon rises through the atmosphere until it expands to a
volume of 1.0 × 106 m3, where the pressure is 1.0 × 103 Pa. The temperature
also falls from 17 °C to –43 °C.
The pressure of the atmosphere at the Earth’s surface = 1.0 × 105 Pa.
Show that the volume of the balloon at take off is about 1.3 × 104 m3.
[3]
(c)
The balloon is filled with helium gas of molar mass 4.0 × 10–3 kg mol–1 at 17 °C at
a pressure of 1.0 × 105 Pa. Calculate
(i)
the number of moles of gas in the balloon
number of moles = ……………..
[2]
(ii)
the mass of gas in the balloon.
mass = ................kg
[1]
Ambrose College
15
(d)
The internal energy of the helium gas is equal to the random kinetic energy of all
of its molecules. When the balloon is filled at ground level at a temperature of
17 °C the internal energy is 1900MJ. Estimate the internal energy of the helium
when the balloon has risen to a height where the temperature is –43 °C.
internal energy = ................MJ
[2]
(e)
The upward force on the filled balloon at the Earth’s surface is 1.3 × 105 N. The
initial acceleration of the balloon as it is released is 27 m s–2. The total mass of
the filled balloon and its load is M.
(i)
On the diagram below draw and label suitable arrows to represent the
forces acting on the balloon immediately after lift off.
[2]
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(ii)
Calculate the value of M.
M = ...............kg
[3]
[Total 15 marks]
Ambrose College
17