0412

2. HEAT cont’d

3. Heat Contents
Temperature and Thermometers:
o Thermal equilibrium and the Zeroth law of
thermodynamics.
o Thermal expansion.
o The Gas laws and absolute temperature.
o The ideal gas law.
o The ideal gas law in terms of molecules.
o Avogadro's number.
o Kinetic theory. Real gases and change of phase.
o Vapour pressure and humidity.
Heat and internal energy.
o Specific heat capacity.
o Latent heat.
o Calorimetry.
o Heat transfer: Conduction, convection and radiation.
o First law of thermodynamics.
o First law applied to simple processes including isobaric
and isothermal processes.

4. Thermal Expansion
Linear Thermal Expansion
• When a material is heated it expands and when it
is cooled it contracts.
• The increases in any one dimension of a solid is
called linear expansion.
• The expansion occurs along a line.

5. Thermal Expansion
Linear Thermal Expansion
• Part (a) of the figure shows two
identical rods. Each has length Lo
and expands ΔL when the
temperature increases by ΔT.
• Part (b) shows the two heated
rods combined into a single rod.
Note that the total expansion is
the sum of the expansions of
each part – namely ΔL + ΔL = 2 ΔL

6. Linear Thermal Expansion
This implies that the amount of
expansion is proportional to its
original length.
ΔL ∞ L0

7. Linear Thermal Expansion
For modest temperature changes it is also found that
ΔL ∞ ΔT
Therefore, using a proportionality constant, we have:
ΔL = α Lo ΔT,
where α = coefficient of linear expansion.

8. Coefficient of Linear Expansion
Determine the unit for α.
  1
1 
 o
o
C
C

9. Egs. Of Coefficient of Linear Expansion for Solids
Substance α (C°)-1
Brass 19 ×10-6
Concrete 12 ×10-6
Copper 17 ×10-6
Steel 12 ×10-6
Glass (Pyrex) 3.3 ×10-6
Quartz 0.5 ×10-6
Aluminium 23 ×10-6
Gold 14 ×10-6
Silver 19 ×10-6

10. 12.4 Linear Thermal Expansion
Example 2.1 The Buckling of a Sidewalk
A concrete sidewalk is constructed between two
buildings on a day when the temperature is 25°C.
As the temperature rises to 38°C, the slabs
expand, but no space is provided for thermal
expansion.
• What would you expect to occur?
• Determine the expand length x of the concrete
slab
• Determine the distance y

11. 12.4 Linear Thermal Expansion
Example 2.1 The Buckling of a Sidewalk
A concrete sidewalk is constructed between two
buildings on a day when the temperature is 25°C.
As the temperature rises to 38°C, the slabs
expand, but no space is provided for thermal
expansion.
• What would you expect to occur?
• Determine the expand length x of the concrete
slab
• Determine the distance y
Expanded length of each slab = original length + ΔL
Once expanded length is known we can use
Pythagoras’ theorem to find vertical distance y
 
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12. 12.4 Linear Thermal Expansion
• Example 2.1 The Buckling of a Sidewalk
• A concrete sidewalk is constructed between two
buildings on a day when the temperature is 25°C. As
the temperature rises to 38°C, the slabs expand, but
no space is provided for thermal expansion.
• What would you expect to occur?
• Determine the expand length x of the concrete
slab
• Determine the distance y

13. THE BIMETALLIC STRIP
A bimetallic strip is made from two strips of metal that have
different coefficients of linear expansion.
Often made from
o Steel [α = 12 × 10-6 (C˚)-1] and one of the following
o Copper [α = 17 × 10-6 (C˚)-1]
o Brass [α = 19 × 10-6 (C˚)-1]
o The two pieces are welded or rivetted together.
o When the strip is heated, the brass (with the larger α value)
expands more than the steel.
o Since the two metals are bonded together, the bimetallic strip bends into
an arc as shown in part (b) with the longer brass having a large radius
than the steel piece.
o If cooled the bimetallic strip bends in the opposite direction (c).

14. THE BIMETALLIC STRIP
• To Control Heating Time (as of a coffee
maker)
• When the bi-metallic strip is cold , current
flows through the heating coil.
• When sufficiently hot, the strip bends away
from the adjustment knob thus turning off
the electricity.
• Electricity stops because it no longer has a
continuous path along which to flow, and the
brewing cycle is shut off.

15. EXPANSION OF HOLES
Assume you have grid of tiles as arranged in the figure
shown. Note the centre tile is missing and all tiles are
unheated.
o If the tiles are heated, they expand individually.
o The hole expands just as if it is filled with the same
material.
o If the ninth (9th) tile is heated it would fit into the
hole.
o Similarly, a hole in a piece of solid material expands
when heated and contracts when cooled, just as if it
were filled with the material that surrounds it.
Hole
Heated
Unheated
9’th tile heated
Expanded Hole

16. Example 3.1 A heated Engagement Ring
A gold engagement ring has an inner diameter
of 1.5 × 10-2 m and a temperature of 27 ˚C.
•The ring falls into a sink of hot water whose
temperature is 49 ˚C.
•What is the change in diameter of the hole in
the ring?
Reasoning: The hole expands as if it were filled
with gold, so the change in diameter is given by
T
L
L o

 
The change in the ring’s diameter is:

17. Example 3.1 A heated Engagement Ring
A gold engagement ring has an inner diameter
of 1.5 × 10-2 m and a temperature of 27 ˚C.
•The ring falls into a sink of hot water whose
temperature is 49 ˚C.
•What is the change in diameter of the hole in
the ring?
Reasoning: The hole expands as if it were filled
with gold, so the change in diameter is given by
T
L
L o

 
The change in the ring’s diameter is:

18. VOLUME EXPANSION
• The change in volume ΔV over modest temperature changes is proportional
to the change in temperature ΔT, as well as the initial volume V0
ΔV = βV0ΔT,
β is the coefficient of volume expansion ;units:  1

o
C

19. Volume Expansion
Material Coefficient of Volume Expansion (C°)-1
Water 207× 10-6
Gasoline 9.50 × 10-6
Mercury 182 × 10-6
o Liquids do not have fixed shapes so α is not defined for them.
o Values of α and β pertain to a temperature near 20°C.

20. Example
A small coolant reservoir is attached to a copper
radiator. The radiator is filled to its 15-quart
capacity when the engine is “cold” (6.0 °C).
How much overflow from the radiator will spill into
the reservoir when the coolant reaches its
operating temperature of 92°C?
• β - coolant = 410 × 10-6 (C°)-1
• β - copper = 51 × 10-6 (C°)-1

21. Example
A small coolant reservoir is attached to a copper
radiator. The radiator is filled to its 15-quart
capacity when the engine is “cold” (6.0 °C).
How much overflow from the radiator will spill into
the reservoir when the coolant reaches its
operating temperature of 92°C?
• β - coolant = 410 × 10-6 (C°)-1
• β - copper = 51 × 10-6 (C°)-1
• Reasoning:
• When the temperature increases, both the coolant and the
radiator expand.
• If they were to expand by the same amount there would be
no overflow.
• However liquid coolant expands more that the radiator,
and the overflow volume is the amount of coolant
expansion minus the amount of the radiator expansion.
T
V
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 
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Liquids generally expand more than solids
for the same change in temperature.

22. Summary
• Thermometers
•The operation of any thermometer is based on changes
in some physical property with temperature; this
physical property is called a
•Examples are:
• Thermal Expansion
• Resistance of a metal or thermistor
• EMF of a thermocouple
thermometric property

23. Summary
• Kelvin Temperature Scale
• For scientific work, the Kelvin temperature scale is the
scale of choice. One Kelvin (K) is equal in size to 1
Celsius degree. However, we can convert from
temperature Tc on the Celsius scale to temperature T
on the Kelvin scale by:
15
.
273

 c
T
T

24. Summary
• Zeroth Law of
Thermodynamics
• The zeroth low of thermodynamics states that two
systems individually in thermal equilibrium with a
third system are in thermal equilibrium with each
other.

25. Summary
• Linear Thermal Expansion
• Most substances expand when heated. For linear
expansion, an object of length Lo experiences a
change ΔL in length when the temperature changes
by ΔT:
T
L
L o

 

26. Summary
• How a hole in a plate expands or
contracts
• When temperature changes, a hole in a plate of solid
material expands or contracts as if the hole were filled
with the surrounding material.

27. Summary
• Volume thermal expansion
• For volume expansion, the change ΔV in the volume
of an object of volume Vo is given by:
T
V
V o

 

28. GAS LAWS

29. The Gas Laws
•The equation
cannot be used to describe the expansion of gases because gases
usually expand to fill ‘the container they are in. It is meaningful only if
the pressure is kept constant.
T
V
V o

 

30. Equation of State
• It is possible to determine the relation between the volume,
the pressure, the absolute temperature, and the mass of a
gas. This relation is referred to as the “Equation of State”
• The results of the equation are only accurate for gases that
are not too dense (i.e., the pressure is in the order of 1atm.
or less).

31. Boyle’s Law
• Robert Boyle demonstrated experimentally
that if the pressure on a gas is doubled its
volume is reduced to half its original
volume.
• Thus, for a given quantity of gas the volume
of the gas is inversely proportional to the
pressure applied to it when the
temperature is kept constant.
• V ∝ 1/P (at constant temperature)
• Or P ∝ 1/V (at constant temperature)
• This is Boyles law, and it can also be written
:
PV = constant (at constant T)

32. Boyle’s Law
• Practical Implication
• This means that, at constant temperature, if
either the pressure or volume of the gas is
allowed to vary, the other variable also
changes so that the product PV remains
constant.
• This is shown by the following plot:
PV Graph

33. Charles Law
• Jacques Charles also demonstrated
experimentally that the temperature
also affects the volume of a gas.
• He found that if the pressure is
moderate and is kept constant, the
volume of a gas increases with
temperature at a nearly constant rate.
• i.e. V ∝ T (at constant pressure)
If a gas could be cooled to -273.15C
it would have zero volume
VT graph

34. Gay–Lussac’s Law (Pressure Law)
• Joseph Gay-Lussac discovered a third
principle which states that:
• “At constant volume, the pressure of a gas
is directly proportional to its Absolute
Temperature”.
• i.e., P ∝ T (at constant volume)

35. The Ideal Gas Law
• The three laws can be combined
into a single more general relation
PV ∝ T
• When a gas balloon is blown up it can
be seen that the more air is forced into
the balloon, the bigger it gets:
• the volume increases in direct proportion
to the mass m of the gas present.
• Instead of mass ‘m’ we can use the number
of moles, n
• 1 mole is that number of grams of
substance numerically equal to the
molecular mass of the substance
• (e.g. 1 mole of CO2 has a molecular mass of
[12+ (32)]g = 44g
• Also, in general the number of moles, n, in
a given sample of a pure substance is equal
to its mass in grams divided by its
molecular mass
n (mole) = mass (grams) ÷ molecular mass(grams/mol)

36. The Ideal Gas Law
• The three laws can be combined
into the a single more general
relation
PV ∝ T
• Therefore we can write the ideal gas law relation as
PV ∝ nT
PV = nRT
where n is the number of moles, and R is the constant
of proportionality and is called the Universal Gas
Constant because its value is found experimentally
to be the same for all gases.
• R = 8.315J/(mol.K) = 1.99calories/(mol.K)
• So, PV =nRT is called the “Ideal Gas Law” or the
equation of state for an ideal gas.

37. The Ideal Gas Law
• Definition of Ideal
o The term ideal is used because real gases do not follow the equation of state precisely:
i. Particularly at high pressures (and density)
ii. Where the gas is near the liquefaction point (boiling point)
Standard Temperature and Pressure (STP) Conditions
This simply means that
i. T = 273.15K (0°C)
ii. P = 1 atm = 1.013 x 10 5 Nm-2 or 1.013 x 10 5 Pa

38. E.g.
• Determine the volume of 1mol of any gas at STP assuming it
behaves like an ideal gas.
nRT
PV 
P
nRT
V 
   
5
10
013
.
1
273
31
.
8
1


3
3
10
4
.
22 m




39. Many Gases (fixed volume)
• In many cases, when the problem involves a change in the pressure,
temperature and volume of a fixed amount of gas we have
• PV = nRT or PV/T = nR = constant
• If P1, V1 and T1 represent the initial variable and P2, V2 and T2 represent
the variable after the change is made, then we write:
P1V1/T1 = P2V2/T2

40. E.g.
• An automobile tire is filled to a gauge
pressure of 200kPa at 10°C. If after
driving 100km, the temperature within
the tire rises to 40°C.
• What is the pressure within the tire
now?
Reasoning: Volume is constant
P1 = 200 kPa;
T1 = 10˚C = 283.15 K;
T2 = 40˚C = 313.15 K;
2
2
1
1
T
P
T
P

  
K
K
Pa
T
T
P
P
15
.
283
15
.
313
10
200 3
1
2
1
2


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kPa
Pa 221
10
21
.
2 5


