2. 1. Understanding thermal equilibrium
2. Understanding specific heat capacity
3. Understanding specific latent heat
4. Understanding the gas laws
2007 2008 2009 2010 2011 2012 2013 2014 2015
P1 5 5 5 4 5 6 3 4
P2
A 1 1 1 1 1 1 1 1
B - - - - - - 1 1
C - - 1 - - - - -
P3
A - - - - 1 - - -
B - - - - - 1 - -
Analysis of Past Year Questions
Learning Objectives :
Dear students,
The two basic processes of education are knowing and valuing.
FORM
4
PHYSICS
2016
Chapter 4
Heat
3. Dear students,
Success is the sum of small efforts, repeated day in and
day out.
Heat
Specific Heat
Capacity
Gas Laws
Thermal
Equilibrium
Specific
Latent Heat
Q = mcθ
Specific
latent heat of
fusion
Specific
latent heat of
vaporisation
Charles’
Law
Pressure
Law
Boyle’s
Law
Q = mlf Q = mlv
3
Chapter 4
Heat
Concept Map
4. When an object is
cooled, it will release
heat energy and the
temperature will
decrease.
4
4.1 Thermal Equilibrium
Two objects are in
thermal contact when
heat energy can be
transferred between
them.
A hot object is at a higher
temperature than a cold
object.
• Form of energy
• Measured in
Joules, J
Net heat transferred
from hotter object
(higher temperature)
to colder object (lower
temperature).
When an object is
heated, it will absorb
heat energy and the
temperature will
increase.
The measure of the
degree of hotness of
an object.
SI unit Kelvin, K
Temperature
Heat
Thermal contact
5. Mechanism of Thermal Equilibrium
Heat transfer
When two objects with different degrees of hotness come into ______________________heat
energy is ______________________between the two objects.
• Heat energy is transferred at a _ rate
from the hotter object to the colder object.
Heat energy is also transferred from the
colder object to the hotter one, but at a
________ rate.
• There is a of heat energy
from the hotter object to the colder object.
• The hotter object cools down while the colder
object warms up .
• After some time, heat energy is transferred
at the rate between the two
objects. There is no net heat transfer
between the objects.
• The two objects are said to be in
_________________________________ .
5
Faster rate of heat
transfer from A to B
Slower rate of heat
transfer from B to A
A B
Hot Cold
Heat transferred at
the same rate
between A and B
A B
Net flow of heat
from the hot object
to the cold object
A B A B
No net heat transfer
faster
net flow
same
thermal equilibrium
thermal contact,
transferred
slower
6. Thermal Equilibrium ***
When two objects are in thermal equilibrium, there is no net flow of heat between them.
Two objects in thermal equilibrium have the same temperature.
Examples
1. A wet towel is placed on the forehead of a
person who has high fever.
2. Initially the temperature of the cloth is lower than
the body temperature of the person.
3. Heat energy is transferred from the forehead to
the towel until thermal equilibrium is reached.
4. The towel is rinsed in tap water and the
procedure is repeated.
5. In this way heat energy is removed from the
person.
Cooling drinks
1. A hot drink can be cooled by
adding a few ice cubes to the drink.
2. Heat from the hot drink is
transferred to the colder ice until
thermal equilibrium between the ice
and water is reached.
3. The final temperature of the drink
equal the final temperature of ices.
Strength does not come from physical capacity. It comes
from an indomitable will.
Mahatma Gandhi
“
” 6
7. Liquid-in-glass
Thermometer
The characteristic of the liquid used
in liquid-in-glass thermometer
How a liquid-in-glass
thermometer works?
1. The bulb of the thermometer
contains a fixed mass of
mercury. The volume of the
mercury increases when it
absorbs heat.
2. The mercury expands and
rises in the capillary tube.
The length of the mercury
column in the capillary tube
indicates the magnitude of
the temperature.
How can a thermometer be calibrated?
1. A temperature scale is obtained by choosing two temperatures, called the fixed point.
2. Definition of ice point and steam point
Fixed point Definition Value
Lower point:
Ice Point
The temperature of pure melting ice 0°C
Upper point:
Steam point
The temperature of steam from water that is boiling
under standard atmospheric pressure.
100°C
7
1. be easily seen
2. expand and contract rapidly over a
wide range of temperature/ expand
uniformly when heated
3. not stick to the glass wall of the
capillary tube.
8. How can a thermometer be calibrated?
When the two fixed points have been marked on the stem of the
thermometer, the range between them is divided equally into 100
divisions or degrees. The thermometer now has a scale.
8
Ice point Steam point
Ice
Boiling
water
Steam
Water
L0
L100
Ice
point
Steam
point L100
L0
Lθ
Bulb
100 equal
divisions
C
100
L
L
L
L
θ
0
100
0
θ
9. Explain the working principle of a thermometer
1. When the thermometer is placed in contact with hot water,
heat is transferred from hot water to the thermometer.
2. Thermal equilibrium between the thermometer and hot water
is reached when the net rate of heat transfer is zero.
3. The thermometer and the water are at the same temperature.
At this point, the thermometer reading shows the temperature
of the water.
What are characteristics of mercury that makes it suitable as a liquid-in-glass thermometer?
1. It is a good conductor of heat
2. It has a high boiling point, 357°C
3. It expands uniformly when heated
4. It is opaque (does not allow light to pass through) and it can be seen easily.
5. Mercury freezes at a temperature of - 39°C and it is therefore not suitable for measuring
temperatures below this temperature, such at the north pole.
How to increase the sensitivity of a mercury thermometer?
9
Thermometer
1. Thin capillary tube
2. A glass bulb with thinner wall
3. Small bulb
10. Take up one idea. Make
that one idea your life -
think of it, dream of it, live
on that idea. Let the brain,
muscles, nerves, every
part of your body, be full of
that idea, and just leave
every other idea alone.
This is the way to success,
that is way great spiritual
giants are produced
“
”
Swami
Vivekananda
Exercise 4.1
10
1. Which of the following characteristics is used in the
function of a liquid-in-glass thermometer?
A Volume of a fixed mass of liquid
B Boiling point of the liquid
C Resistance of the liquid
D Density of the liquid
2. Which of the following methods can be used to increase
the sensitivity of a mercury thermometer?
A Thick-walled glass bulb
B Thinner capillary tube
C Shorter capillary tube
D Larger glass bulb
3. An alcohol-in-glass thermometer has not been calibrated.
When it is inserted into melting ice and boiling water, its
lengths are 5.2 cm and 13.7 cm respectively.
When it is inserted into a cup of warm water, the alcohol
length is 9.8 cm. Calculate the temperature of the warm
water.
A 44.12 °C
B 52.22 °C
C 20.45 °C
D 54.12 °C
11. 4.2 Specific Heat Capacity
Quantity of heat absorbed or lost by
a substance Q =
What does specific heat of Aluminium
900 Jkg-1°C-1 mean?
900 J of heat needs to be supplied to 1 kg of Aluminium
to produce a 1 °C temperature increase.
What does specific heat of water 4200
Jkg1°C-1 mean?
4 200 J of heat needs to be supplied to 1 kg of water to
produce a 1 °C temperature increase.
SI unit: = J kg-1°C-1
Q = heat absorbed / released, unit J
m = mass of the substance, unit kg
∆θ = temperature difference , unit °C
11
Heat capacity, c
The amount of heat required to change its temperature by one degree.
Specific Heat capacity, c
The amount of heat that must be supplied to increase the temperature by 1 °C for a mass of
1 kg of the substance.
θ
m
Q
c
mc∆θ
12. The physical
meaning of
specific heat
capacity, c
When two objects of equal mass are heated at equal rates, the object with the
smaller specific heat capacity will have a faster temperature.
When two objects of equal mass are left to cool down, the temperature of the
object with smaller heat capacity will drop faster.
A substance with
a small value of
specific heat
capacity
1. Heats up and cools at a faster rate. For example, metal like iron, steel,
copper and Aluminium is used as pots and pans because they can be
quickly heated up when there is only small heat absorption.
2. Sensitive to temperature changes a thermometer has low specific heat
capacities so it enables heat to be easily absorbed and released even
when small quantities of heat are involved.
A substance with
a high value of
specific heat
capacity
1. Heats up and cools at slower rate. Require more heat to raise its
temperature by a specific amount. Poor conductor of heat – handle of pot
2. Can absorb a great amount of heat without a high increase in
temperature. For example, water acts a heat reservoir as it can absorb a
great amount of heat before it boils. Water is used as a cooling agent in a
car radiator.
When one makes the mind stick to one
thought, the mind becomes rock-steady and
the energy is conserved.
“
” Ramana Maharshi 12
13. Applications of Specific Heat Capacity
1. Low specific heat capacity. The pot
becomes hot very quickly. This enables
quick cooking of the food in the pot.
2. High density. _____________________
__________________________________
__________________________________
Cooking pot
Copper base
Handle
Aluminium body
1. Large specific heat capacity.
_____________________________
_____________________________
_____________________________
2. Poor conductor of heat.
1. Relatively low specific
heat capacity. The pot
becomes hot quickly.
2. Low density so it will
be lighter
3. Does not react with
the food in the pot
13
The handle will not become too hot
when heat is absorbed.
base ensures that the pot is stable
and will not topple over easily.
The heavier
14. • Land has a smaller specific heat capacity than
sea. Temperature of land increase faster than
sea. Therefore, land is warmer than the sea at
day time.
• Air above the land is heated up and rises.
• Cooler air from the sea moves from towards the
land as sea breeze.
Sea Breeze
• At night, heat is lost from the land and sea.
• Sea has a larger specific heat capacity so sea is
warmer than land.
• Warmer air above the sea rises
• Cooler air from the land moves towards the sea
as land breeze.
Land Breeze
14
15. 1. Calculate the total heat that is absorbed by a copper block of mass 500 g and which has been
heated from 31 °C to 80°C. (specific heat capacity of copper = 390 Jkg-1°C-1).
2. When an electric heater is supplied with an electric power of 2 kW to heat 4 kg of water for 1
minute, calculate the increase in temperature of the water. [specific heat capacity of water =
4 200 Jkg-1°C-1) .Assume there is no heat loss to the surroundings.
15
Tips : Electric Energy, E = Pt = VIt Heat Energy, Q = mcθ
Exercise 4.2
Ans : 7.15°C
Ans : 38220 J
16. 3. A lead bullet moves horizontally with a velocity of 130 ms-1 and embedded into a cement wall
after collision. If the specific heat capacity of lead = 130 Jkg-1°C-1 and all heat produces is
absorbed by the bullet, what is the increase in temperature of the bullet?
4. An aluminium block of mass 1 kg is heated by an electric heater for 3 minutes and a
temperature rise of 15 °C is recorded. If the electric heater is connected to a voltmeter which
gives a reading of 30 V and an ammeter which gives a reading of 2.5A, calculate the specific
heat capacity of the aluminium.
16
Tips : Kinetic Energy, E = ½ mv2 Heat Energy, Q = mcθ
Ans : 65°C
Ans : 900 JKg-1°C-1
17. 5. 300 g of water at temperature 40 °C is mixed with 900 g of water at temperature 80°C. If there
is no heat loss to the surroundings, what is the final temperature when thermal equilibrium is
achieved by the mixture of water?
17
Tips : Heat Energy Released = Heat Energy Absorbed
Ans : 70°C
18. The heat absorbed or the heat released at constant temperature during change of phase.
Latent heat
4.3 Specific Latent Heat
1. When a solid melts at its melting point, latent heat of fusion is absorbed
2. For a liquid to solidify at its freezing point, latent heat of fusion is released.
3. When a liquid is boiling at its boiling point, latent heat of vaporization is
absorbed.
4. When vapour condenses back into the liquid phase, latent heat of
vaporization is released.
The common characteristics of the four processes in the change of phase
1. A Substance undergoes a change of phase at a particular temperature.
2. Heat energy is transferred during change of phase
3. During change of phase, the temperature remains ___________ even though there is
transfer of heat. 18
MELTING
Latent heat
absorbed
BOILING
Latent heat
absorbed
Latent heat
released
SOLIDIFICATION
Latent heat
released
CONDENSATION
GAS
LIQUID
SOLID
4 main
Changes of
phase
constant
19. 19
A
B C
D E
F
Time
Melting Point
Boiling Point
Temperature
State : Solid
Temperature : Increases
Solid heated to its melting
point
State : Liquid
Temperature : Increases
Liquid heated to its boiling
point
State : Gaseous
Temperature : Increases
The temperature of the
gas will increase to the
temperature of the source
State : Solid and liquid
Temperature : Unchanged
B : Solid start melting
B – C : Solid melting
C : Solid melted completely
State : Liquid and gas
Temperature : Unchanged
D : Liquid start boiling
D – E : Liquid boiling
F : Liquid boiled completely
Heating Curve
20. 20
P
Q R
S T
U
Time
Freezing Point
Boiling Point
Temperature
State : Gaseous
Temperature : Decreases
The temperature decreases as
heat is released to the
surrounding.
State : Solid and liquid
Temperature : Unchanged
S : The solid start freezing
S – T : The liquid freezing
T : The liquid freezes completely
Draw a cooling curve.
State : Liquid
Temperature : Decreases
The liquid is cooled to its
freezing point.
State : Liquid and gas
Temperature : Unchanged
Q : The gas start condensing
Q – R : The gas condensing
R : The gas condenses completely
State : Solid
Temperature : Decreases
The solid is cooled to the room
temperature.
Cooling Curve
21. Why does the temperature remains constant during change of phase?
1. During change of phase, the transfer of heat does not cause a change in the kinetic energy of
the molecules.
2. During melting, the heat absorbed is used to break up the bonds between the particles. The
particles are freed from their fixed positions and are able to vibrate and move among each
other.
3. When a liquids boils, the heat absorbed is used to completely break the bonds between the
particles and also to do work against atmospheric pressure when the gaseous vapour expands
into the atmosphere.
Specific Latent Heat, l
The amount of heat required to change the phase of 1 kg of the substance at a constant
temperature.
Specific latent heat of fusion
21
Unit : J kg-1
Q = latent heat absorbed or released by the substance
m = mass of the substance
The amount of heat required to change 1 kg of the substance from solid to liquid phase
without a change in temperature.
m
Q
l
22. Specific latent heat of vaporization
22
Specific latent heat of fusion of ice is
336 000 Jkg-1
Specific latent heat of vaporization of water
is 2.26 x 106 Jkg-1
336 000 J of latent heat is needed for 1 kg ice
to melt to become water at 0 °C
2.26 x 106 J of latent heat is needed for 1 kg
water to boil to become vapour at 100°C
Formula to
calculate
HEAT
Condition
Q = mcθ
The heat added or
removed changes the
temperature of an
object, the heat is
calculated using
as
Q = Pt = ml
If heat is supplied
electrically
Q = ml
When the heat added
or removed changes
the phase of an object
at constant
temperature, the heat is
calculated using
P = power of the heater, unit in W,
t = time , unit is seconds
as
The amount of heat required to change 1 kg of the substance from the liquid to gaseous
phase without a change in temperature.
23. 1. The specific latent heat of fusion of ice is
336 000 Jkg-1. What is the quantity of heat
required to melt 2.5 kg of ice at 0 °C?
2. An electric kettle contains 3kg of water.
Calculate the amount of heat required to
boil away all the water after the boiling
point has been reached.
Specific latent heat of fusion of ice is 336 000 Jkg-1
Specific latent heat of vaporization of water is 2.26 x 106 Jkg-1
Specific heat capacity of water is 4.2 x 103 J kg-1°C-1 23
Exercise 4.3
Ans : 840000 J
Ans : 6.78 x 106 J
24. 3. What is the quantity of heat that is required to convert 4g of ice into steam at 100°C.
Specific latent heat of fusion of ice is 336 000 Jkg-1
Specific latent heat of vaporization of water is 2.26 x 106 Jkg-1
Specific heat capacity of water is 4.2 x 103 J kg-1°C-1 24
Ans : 12064 J
25. Drinks can be cooled by adding
in several cubes of ice. When
ice melts a large amount of heat
is absorbed and this lowers the
temperature of the drink.
The freshness of fish and meat can be maintained
by placing them in contact with ice. With its larger
latent heat, ice is able to absorb a large quantity of
heat from the fish as it melts. Thus, food can be
kept at a low temperature for an
extended period of time.
Water has a large specific latent
heat of vaporization. This property
enables steam to be used for
cooking by the method of
steaming. When steam
condenses on the food, the latent
heat is released directly onto the
food enables the food to be
cooked at a faster rate.
1
2
3
4 Always be very careful when
opening the lid of a pot when the
water in it is boiling. Water has a
large specific latent heat of
vaporization. When steam
condenses on the skin of your
arm, the very large amount of
latent heat released can cause a
serious burn.
Applications of Specific
Latent Heat
25
26. 4.4 Gas Laws
Boyle’s Law
states that for a fixed mass
of gas, the pressure of the
gas, P is inversely
proportional to its volume,
V when the temperature, T
is kept constant.
states that for a fixed mass
of gas, the volume of the
gas, V is directly
proportional to its absolute
temperature, T when its
pressure, P is kept
constant.
states that for a fixed mass
of gas, the pressure of the
gas, P is directly
proportional to its absolute
temperature, T when its
volume, V is kept constant.
Charles’ law Pressure Law
P
V
1
P
V
V
T
P
T
PV
PV
V P
V/T
V/T
V T
P/T
P/T
P T
26
V
1
P T
V T
P
2
2
1
1 V
P
V
P
2
2
1
1
T
V
T
V
2
2
1
1
T
P
T
P
28. 1. When the volume of a
gas is decreased, the
number of molecules
per unit volume
increases .
2. The same number of
molecules moves in a
smaller space.
3. The molecules collide
more frequently
with the walls of the
container.
4. This increase in the
rate of collision results
in an increase in
the pressure exerted by
the gas.
1. When a gas is heated, the
average kinetic energy of
the molecules increases .
Temperature of the gas
increases.
2. Rate of collision between
the molecules and the
walls will increase if
the volume is constant.
3. If the gas is allowed to
expand, the faster
molecules now move in a
bigger space.
4. Therefore, the rate of
collision between the
molecules and the walls
remain constant and
thus the pressure is
constant.
1. When a gas is heated,
the average kinetic
energy increases .
The temperature of the
gas increases.
2. The faster moving
molecules strike the
walls of the container
more frequently .
3. Thus, the pressure of
the gas increases .
28
Boyle’s Law Charles’ law Pressure Law
29. Convert °C to Kelvin:
θ + 273
The lowest possible temperature
which is ________________________.
At this point:
1. Voume and pressure of gas is zero
2. Kinetic energy of the gas molecules is zero
3. Gas molecules are stationary.
Convert Kelvin to °C :
T – 273
V
T/K
V
θ / °C
P
T/K
P
θ / °C
Temperatures measured in the Kelvin, K
29
Human beings unlike plants and animals have the capacity to choose what they want to
be. I belief that if a child elects to be a brilliant and successful person he has the innate,
God-given talents to achieve whatever he desires. There are absolutely no obstacles to
his ambition except himself.
Absolute temperature
-273
0 K
-273
0 K
Absolute zero
-273°C or 0 K
30. Question 1
The air in a foot pump has an initial volume
of 2800 cm3 and pressure 100 kPa. The
outlet of the pump is closed and the piston
pushed inwards until the volume of the air
becomes 700 cm3. What is the pressure of
the compressed air in the pump?
Question 2
The pressure of a bubble under the sea is 120
cm Hg. When the bubble rises to the surface
of the sea, its volume becomes 25.0 cm3.
Assuming that the atmospheric pressure is 76
cm Hg, what is the original volume of the
bubble?
30
Exercise 4.4
Ans : 400 kPa Ans : 15.83 cm3
31. Question 3
A cylinder contains 200 cm3 of gas at a
temperature of 27°C. The gas is heated until
its temperature increases by 30°C. If the
piston of the cylinder expands under constant
pressure, what is the final volume of the gas?
Question 4
A fixed mass of gas in an enclosed metal
container has a pressure of 2.5 x 105 Pa. If the
gas is heated from 27°C to 87°C, calculate the
final pressure of the gas.
31
Ans : 220 cm3
Ans : 300 kPa
32. 1. As shown in Figure 1 , block P of mass 7 kg at 90°C and block Q of mass 3 kg at 30°C . Given
that the specific heat capacity of P is 4 900 J kg-1°C-1 and the specific heat capacity of Q is
3800 J kg-1°C-1 .Block P and Q are contact with each other. Assume that there is no energy loss
to the surroundings.
Challenge Zone
32
7 kg
P
90°C 30°C
Q
3 kg
Figure 1
(a) What is the final temperature of P and Q if they
are in thermal equilibrium?
(b) Find the energy given by P during the process.
Give the answer in unit of kJ.
(c) Find the energy absorbed by Q during the
process. Give the answer in unit of kJ.
Ans : (a) 75.03C (b) 513.47kJ (c) 513.34kJ
33. 33
2. There are two beakers of water each with mass 500 g and 1 200 g respectively. The water is
then mixed together by pouring the water into another beaker. If the initial temperature of 500g
water and 1 200g water are 38°C and 88°C respectively.
(a) Determine the final temperature of the mixture of water after achieved equilibrium.
(b) State the assumption used in your calculation.
Ans : (a) 73.29 °C (b) No heat loss to the surroundings
34. 3. The graph of temperature-time in Figure 2 is
obtained when a solid is heated by a heater of
power 500 W. Determine
(a) the melting point of the solid.
(b) the latent heat of fusion of the substance.
34
t/s
75
0 0.2 2.0
Graph of temperature
against time
T/°C
Figure 2
Ans : (a) 75 °C (b) 900 J
35. 35
4. Figure 3 shows a gas trapped inside a tube by 7 cm of
mercury. The length of the gas column at 20°C is 23 cm.
Determine the length of the air column at temperature
90°C.
Mercury
Gas
7 cm
23 cm at
20°C
Figure 3
Ans : 28.49 cm
36. Diagram 4 shows an ice cream container used by an ice cream seller using his
motorcycle.
5.
Table 1 shows the specification of four types of ice cream containers P, Q, R and S, that can
be used by an ice cream seller to carry ice cream.
You are required to determine the most suitable ice cream container to carry ice cream.
Study the specification of the four types of ice cream container based on the given aspects.
Explain the suitability of the each aspects.
[10 marks]
Diagram 4
36
37. Table 1
Characteristics Explanation
Low specific heat capacity of ice
cream box
Easy get cold // becomes cool quickly
Smaller size of ice cream box Easier to carry // easy too become cold
Plastic PVC Poor conductor of heat
Bright colour of outer box Does not absorb heat from surrounding quickly
R is chosen because Low specific heat capacity of ice cream
box, Smaller size of ice cream box, Plastic PVC,
Bright colour of outer box
Answer : 37
Box P Q R S
Specific heat capacity of ice cream box High High Low Low
Size of ice cream box Large Small Small Large
Material of outer box Copper PVC PVC Aluminium
Colour of outer box Dark Bright Bright Dark
