PHY 101
HEAT ANDTEMPERATURE
BY CYNTHIA MWANSA
OBJECTIVES
• Distinguish between heat and temperature
• Discuss the transfer of heat by various methods.
• Discuss specific heat and latent heats of different substances
• Heat transfer by mixtures and conservation of energy
• Discuss and use the gas law’s
HEAT
Heat is the energy a body has because of the kinetic energy and the potential energy
(p.e.) of its molecules. It is the total energy of particles in a body. Heat is also called
thermal or internal energy; Heat passes from a body at a higher temperature to one at a
lower temperature. Increasing the temperature of a body increases its heat energy because
the k.e. of its molecules increases.
Heat is the sum of KE and PE of particles in a body.
The units of heat are Joules (J).
Other units are calories: 1 Cal = 4.186 J.
UNITS OF HEAT
•
The calorie (cal), is defined as the amount of energy transfer necessary to raise the
temperature of 1 g of water by 1֯ C ( from 14.5°C to 15.5°C).
1 cal = 4.186 J ( mechanical equivalent of heat)
• British thermal unit (Btu), is defined as the amount of energy transfer required to
raise the temperature of 1 lb of water by 1֯ F (from 63°F to 64°F).
EXAMPLE 1
A student eats a dinner rated at 2 000 Calories. He wishes to do an
equivalent amount of work in the gymnasium by lifting a 50.0-kg
barbell. How many times must he raise the barbell to expend this
much energy? Assume that he raises the barbell 2.00 m each time he
lifts it and that he regains no energy when he lowers the barbell.
SOLUTION TO EXAMPLE 1
Because 1 Calorie =1.0 X 103 cal, the total amount of work required to be done on the barbell Earth system is 2.0
X 106 cal. Converting this value to joules, we have
W = (2.0 X 106 cal)(4.186 J/cal) = 8.37 X 106 J
The work done in lifting the barbell a distance h is equal to mgh, and the work done in lifting it n times is nmgh.
We equate this to the total work required:
W =nmgh = 8.37 X106 J
TEMPERATURE
Temperature is the average Kinetic Energy of particles in a body. The greater
the kinetic energy, the faster the molecules move and
the higher the temperature of the body.
The units of temperature are Kelvin (K), Degrees Celsius (OC) and sometimes
Degrees Fahrenheit (OF)
The S.I unit of temperature is Kelvin (K).
Temperature is measured using a thermometer.
TEMPERATURE UNIT CONVERSION
Converting From Degree to Fahrenheit
𝟗
𝑻𝑭 = 𝑻𝑪 + 𝟑𝟐℉
𝟓
Converting From Degree to Kelvin
𝑻𝑲 = 𝟐𝟕𝟑. 𝟓𝑲 + 𝑻𝒄
EXAMPLE 2
Convert 50°F temperature to the temperature in degree
Celsius and in Kelvin?
THERMOMETERS
Liquid in glass thermometer: The thermometer with the liquid in a glass bulb that expands up a
capillary tube when the bulb is heated
Constant Volume - Gas thermometer: The thermometer measures the temperature by the
variation in pressure alone.
Pyrometer: A pyrometer is a type of remote-sensing thermometer used to measure the
temperature of a surface.
Thermocouple : A thermocouple is an electrical device consisting of two dissimilar electrical
conductors forming electrical junctions at differing temperatures.
Bimetallic: Thermometer that uses the difference in expansion of two metals (usually iron and
brass) to measure temperatures between 30°C or 86°F and 300°C or 375F°; it is used especially in
industry.
LIQUID IN GLASS THERMOMETERS
In this type the liquid in a glass bulb expands up a capillary tube when the bulb is
heated.Mercury and coloured alcohol are commonly used in liquid in glass
thermometers. Mercury freezes at −39 ºC and boils at 357 ºC. Alcohol freezes at
−115 ºC and boils at 78 ºC and is therefore more suitable for low temperatures.
Clinical Thermometer
CONSTANT VOLUME GAS THERMOMETERS
Constant volume gas thermometers are used in
calibration of various other thermometers. A
gas thermometer measures temperature with
the variation in pressure or volume of a gas.
When
volume
is
kept
constant,
the
thermometer measures the temperature by the
variation in pressure alone. This is called a
constant volume gas thermometer.
TYPES OF THERMOMETERS
Bimetallic
Pyrometer
Thermocouple
TEMPERATURE SCALES
A scale and unit of temperature are obtained by
choosing two temperatures, called the fixed points,
and dividing the range between them into a number
of equal divisions or degrees.
On the Celsius scale, the lower fixed point is the
temperature of pure melting ice and is taken as 0ºC.
The upper fixed point is the temperature of the steam
above water boiling at normal atmospheric pressure,
105Pa and is taken as 100ºC.
Specific Heat and Calorimetry
• When energy is added to a system and there is no change in the kinetic or potential energy of the
system, the temperature of the system usually rises, except when a system undergoes a change of
state also called a phase transition
• The heat capacity C of a particular sample of a substance is defined as the amount of energy
needed to raise the temperature of that sample by 1°C. If energy Q produces a change ∆T in the
temperature of a sample, then
Q = C∆T
• The specific heat c of a substance is the heat capacity per unit mass. Thus, if energy Q transfers to a
sample of a substance with mass m and the temperature of the sample changes by ∆T, then the
specific heat of the substance is
𝑸
𝑪=
𝒎 ∆𝑻
The energy Q transferred between a sample of mass m of a material and its surroundings to a
temperature change ∆T as
𝐶 = 𝑚𝐶∆𝑇
Conservation of Energy: Calorimetry
• Calorimetry is the science or act of measuring changes in state
variables of a body for the purpose of deriving the heat transfer
associated with changes of its state due, for example, to chemical
reactions, physical changes, or phase transitions under specified
constraints. Calorimetry is performed with a device called calorimeter.
• For example, measuring specific heat involves heating a sample to
some known temperature Tx , placing it in a vessel containing water of
known mass and temperature Tw ‹Tx , and measuring the temperature
of the water after equilibrium has been reached.
• If the system of the sample and the water is isolated, the law of the
conservation of energy requires that the amount of energy that leaves
the sample (of unknown specific heat) equal the amount of energy that
enters the water
Conservation of Energy: Calorimetry
• Conservation of energy allows us to write the mathematical representation of this energy
statement as
𝑸𝒄𝒐𝒍𝒅 = −𝑸𝒉𝒐𝒕
• The negative sign in the equation is necessary to maintain consistency with our sign
convention for heat
𝒎𝒘 𝑪𝒘 (𝑻𝒇 − 𝑻𝒘 ) = −𝒎𝒙 𝑪𝒙 (𝑻𝒇 − 𝑻𝒙 )
𝒎𝒘 𝑪𝒘 (𝑻𝒇 − 𝑻𝒘 )
𝑪𝒙 =
𝒎𝒙 (𝑻𝒙 − 𝑻𝒇 )
SPECIFIC HEAT CAPACITY- DEFINITIONS
Heat Capacity : the amount of heat required to raise temperature of substance by
1 degree Celsius.
Specific Heat Capacity: Heat required to raise the temperature of 1 kg of
substance by 1 degree Celsius
Latent Heat: quantity of heat absorbed or emmited in order to change state of
matter for 1 Kg of substance.
Specific Latent Heat of fusion: quantity of heat required to change 1 kg of solid to
a liquid
Specific Latent Heat of evaporation: quantity of heat required to change 1 kg of
given liquid to vapour
CHANGE OF STATE
SPECIFIC HEAT CAPACITIES
HEAT CAPACITY
Heat Capacity : the amount of heat required to raise temperature of
substance by 1 degree Celsius.
Heat capacity is given:
Q
C
t
Specific Heat Capacity: Heat required to raise the temperature of 1 kg of
substance by 1 degree Celsius.
Specific heat capacity is given as:
Q
c
mt
EXAMPLE 3
How much heat is required to change the temperature of (a) 400g of water
from 18 degrees to 23 degrees ?(b) 400g of copper from 23 degree to 18
degree?
( Specific heat capacity for water = 4184J/kg C; Specific heat capacity for
copper = 390J/kg C )
LATENT HEAT -DEFINITIONS

Latent Heat of a substance is the invisible heat that is involved in change of state. (Unit
are J)

Specific Latent heat(L) of fusion for a given substance is the amount of heat required
to change state from solid to liquid of 1 kg of substance at the melting point. (Units
are J/Kg).

Latent heat of vapourisation is the term used to refer to the heat in phase change of
substance from liquid to vapour (Units are 𝐽/𝑘𝑔)
LATENT HEAT
Latent Heat: quantity of heat absorbed or emmited in order to change state of
matter for 1 Kg of substance.
Specific Latent Heat of fusion: quantity of heat required to change 1 kg of solid
to a liquid
The formula for latent heat is
The S.I unit is J/Kg
Q
L
m
Example 4
A 0.050 kg ingot is heated to 200⁰C and then dropped in beaker containing
0.400 kg of water initially at 20 ⁰C. If the equilibrium temperature of the
mixture is then 22.4 ⁰C, what is the specific heat of the metal?
EXAMPLE 5
A cowboy fires a silver bullet with a muzzle speed of 200 m/s into the pine
wall of a saloon. Assume that all the internal energy generated by the
impact remains with the bullet.
What is the temperature change of the bullet?
Example 6
What mass of steam initially at 130 ⁰C is required to warm 200g of water
initially in 100g glass container from 20 ⁰C to 50 ⁰C?
Lv water = 2.26 x 106 J/kg
specific heat capacity of water is 4184 J/kg. ⁰C
Specific heat capacity of steam 2.01x 103 J/kg. ⁰C
Specific heat capacity of glass 837 J/kg. ⁰C
EXAMPLE 7
How much heat is released from 50g water as it changes (a) liquid
to the crystalline state (b) steam to liquid water at 100 degrees?
(Specific heat of fusion for water = 80 cal/g; Specific heat
vapourisation for water = 539cal/g )
SOME LATENT HEATS OF SOME SUBSTANCES
CHANGE OF STATE DIAGRAM FOR WATER
EFFECTS OF HEAT
Temperature change
Linear expansion
Heat Transfer
Chemical effects
THERMAL EXPANSION
Thermal expansion is the fractional increase in size when the temperature of a substance
changes. Thermal expansion is the tendency of matter to change its shape, area, and
volume in response to a change in temperature. Thermal expansion is a consequence of
the change in the average separation between the atoms in an object.
Types of Expansion
1. Linear expansion
2. Area Expansion
3 . volume expansion
APPLICATIONS OF EXPANSION
(a) Thermal-expansion joints are used to separate sections of roadways on
bridges. Without these joints, the surfaces would buckle due to thermal
expansion on very hot days or crack due to contraction on very cold days. (b)
The long, vertical joint is filled with a soft material that allows the wall to expand
and contract as the temperature of the bricks changes.
APPLICATIONS OF EXPANSION
(a) A bimetallic strip bends as the temperature changes because the twometals
have different expansion coefficients. (b) A bimetallic strip used in a thermostat to
break or make electrical contact.
LINEAR EXPANSION
The change in length due to a temperature change is given by
𝑳𝒇 − 𝑳𝒊 = 𝜶𝑳𝒊 (𝑻𝒇 − 𝑻𝒊 )
where coefficient of heat expansion is
∆𝑳/𝑳𝒊
𝜶=
∆𝑻
AREA EXPANSION
Changes in area compared to original area (ΔA/Ai) called areal
expansion or superficial expansion.
 A  2 Ai  T
VOLUME EXPANSION
Changes in volume compared to original volume (ΔV/V0) called volumetric
expansion or cubical expansion
V   Vi T
Where;
β - average coefficient of volume expansion
Vi - initial volume
∆T - change in temperature
The average coefficient of volume expansion is three times the average linear expansion
coefficient:
V
 3T
Vi
1 V
3 
Vi T
  3
COEFFICIENTS OF THERMAL EXPANSION
Equations of thermal expansion
equation
Δℓ
=
ΔA
=
ΔV
=
solids
ℓ0αΔT linear expansion
A02αΔT
areal (or superficial) expansion
V03αΔT
volumetric (or cubical) expansion
equation
ΔV
=
liquids
V0βΔT
equation
PV
=
gases
nRT ideal gas law
volumetric (or cubical) expansion
EXAMPLE 8
The segment of steel railroad track has a length of 30.000 m,
when the temperature is 0.0°C. What is the length when
temperature is 40°C?
SOLUTION TO EXAMPLE 8
For the values
∆𝑳 = 𝜶𝑳𝒊 ∆𝑻 = (𝟏𝟏 × 𝟏𝟎−𝟔 × 𝟑𝟎. 𝟎𝟎 × 𝟒𝟎)
∆𝑳 = 𝟎. 𝟎𝟏𝟑𝒎
New length
𝑳𝒇 = 𝑳𝒊 + ∆𝑳
∴ 𝑳𝒇 = 𝟑𝟎. 𝟎𝟏𝟑𝒎
Example 9
An electronic device has been poorly designed so that two bolts of different
parts of the devices nearly touch each other in the interior. The brass and
steel bolts are at different electric potentials and if they touch there will be a
short circuit, and this will damage the devices. If the initial gap between the
ends is 5.0µm at 28 °C . At what temperature will the bolts touch?
GAS LAWS
CHARLES LAW
The volume of a fixed mass of gas is directly proportional to its absolute temperature if the
pressure is kept constant.
PRESSURE LAW
The pressure of a fixed mass of gas is directly proportional to its absolute temperature if the
volume is kept constant.
BOYLES LAW
The pressure of a fixed mass of gas is inversely proportional to
its volume if its temperature is kept constant.
CHARLES LAW
At constant pressure, the volume of a fixed mass of gas is directly proportional to
temperature
VT
V  cons tan t  T
V
 cons tan t
T
V1
V2

T1
T2
PRESSURE LAW
At constant volume, the pressure of a fixed mass of gas is directly proportional
to its change in temperature.
p T
p  cons tan t  T
p
 cons tan t
T
p1
p2

T1
T2
BOYLES LAW
If the volume of a fixed mass of gas is halved by halving the volume of the container, the
number of molecules per cm3 will be doubled. There will be twice as many collisions per
second with the walls, i.e. the pressure is doubled.
p1V1  p2V2
SUMMARY ON GAS LAWS
PRESSURE’S LAW
CHARLSE’ LAW
BOYLE’S LAW
NOTE: Use kelvin temperatures when solving problems on gas laws.
IDEAL GAS LAW
An ideal gas is one for which PV/nT is constant
Combining above laws
The Universal gas law
Where
are pressure, volume, temperature, number of moles of gas and universal
gas constant respectively.
EXAMPLE 10
An ideal gas occupies a volume of 100 cm3 at 20°C
and 100 Pa. Find the number of moles of gas in the
container.
EXAMPLE 11
A spray can containing a propellant gas at twice atmospheric pressure (202 kPa)
and having a volume of 125.00 cm3 is at 22°C. It is then tossed into an open
fire. When the temperature of the gas in the can reaches 195°C, what is the
pressure inside the can?
(a) Assume any change in the volume of the can is negligible.
(b) Suppose we include a volume change due to thermal expansion of the steel
can as the temperature increases. linear expansion coefficient is 11x 10-6 /֯ C.
EXAMPLE 12
Standard atmospheric pressure and temperature are 1.01325X105 Pa and
0˚C. Find the volume that one mole of ideal gas occupies at these values
of P and T.
Note :
HEAT TRANSFER
Conduction – mode heat transfer in solids by contact of neighbouring
atoms/molecules
Convection – mode heat transfer prominent in fluid due to collisions of
molecules
Radiation – Heat transfer in vacuum
HEAT TRANSFER BY CONDUCTION
The rate of heat flow between surfaces in contact at different
temperatures
i.e.
So that
𝑸
∆𝑻
∝𝑨
∆𝒕
∆𝒙
𝑻𝒉 − 𝑻𝒄
𝑷 = 𝒌𝑨
𝑳
HEAT TRANSFER COEFFICIENTS
EXAMPLE 13
Find the difference in temperature across the surfaces of an iron
plate 5 cm thick, through every 100 sq. m. of which heat flows at
the rate of 96 x 104 J /s . (K=96J/smK)
HEAT TRANSFER BY CONVECTION
Convection is energy transferred by the movement of fluids. It is the flow due to
convection currents in fluids i.e.
Liquids
Gases
When the movement results from differences in density, as with air around a fire, it is
referred to as natural convection. Air flow at a beach is an example of natural
convection, as is the mixing that occurs as surface water in a lake cools and sinks.
When the heated substance is forced to move by a fan or pump, as in some hot-air and
hot-water heating systems, the
process is called forced convection
HEAT TRANSFER BY RADIATION
The heat flow in vacuum or empty space. This is transfer of heat by infrared waves.
It is governed by Stefan
where
A - area of the objects surface,
T - is its absolute temperature,
є - emissivity of the body,
σ - is Stefan – Boltzmann’s constant.
DEFINITIONS RELATED TO RADIATION
Blackbody is a body which absorbs all heat radiation reaching its surface of all possible
wavelengths. Emissivity = 1, hence a black body is called an ideal absorber. An ideal absorber
is also an ideal radiator of energy
Emissive power is the radiant energy emitted per second per unit surface area.
Absorptive power is the radiant energy absorbed per second per unit surface area of body.
Ideal reflector: absorbs none of the energy incident on it. The object reflects all the incident
energy that falls on it, hence emissivity = 0
Stefan – Boltzmann constant
STEFAN - BOLTZMANN’S LAW
Stefan- Boltzmann's Law states that the total radiant heat energy emitted from a surface is
proportional to the fourth power of its absolute temperature.
For two bodies at different temperature, the heat radiated per unit area is
e   (T  T )
4
2
where
T1 - is absolute temperature of cooler body
T2 - is absolute temperature of hot body,
є - emissivity of the body,
σ - is Stefan – Boltzmann’s constant.
4
1
EXAMPLE 14
An unclothed person whose body has a surface area 0f 1.40 m2 with an
emissivity of 0.85 has a skin temperature of 37˚C and stands in a 20˚C room.
How much heat does the person lose per minute?
NEWTON’S LAW OF COOLING
Statement of Law;
A body at temperature above that of the surroundings reduces exponentially according to
the cooling curve below
DEWER’S FLASK
The Dewar flask is a container designed to minimize energy losses by conduction, convection,
and radiation. Dewar flasks are commonly used to store liquid nitrogen (boiling point: 77 K)
and liquid oxygen (boiling point: 90 K).
APPLICATIONS OF THE THERMOS FLASK
A Thermos bottle is a common household equivalent of a Dewar flask. The standard
construction consists of a double-walled Pyrex glass vessel with silvered walls, vacuum and
stopper.
Vacuum: The space between the walls is evacuated to minimize energy transfer by conduction
and convection.
Silvered glass vessel: The silvered surfaces minimize energy transfer by radiation because
silver is a very good reflector and has very low emissivity.
A further reduction in energy loss is obtained by reducing the size of the neck
READING ASSIGNMENT
1. Explain how a thermos flask is capable of keeping its contents at a constant
temperature in with respect to the three modes of heat transfer.
2. Explain the principle of thermograms.
3. Why is it that two pairs of cloth blankets will keep you warmer than a single
blanket with the combined thickness of the two?
4. Can heat be added to something without its temperature changing? What if
that something is a gas? liquid? solid?
REFERENCES
• Serway and Faughn,(1999), College Physics,5ed., Brooks/Cole- Thompson
Learning.
• Serway, Physics for Scientists and Engineers, e- Book.
• Maholtra Stalin,(2007), Numerical Problems in Physics For Class IX, Tata
Macgraw Publishing Company, Limited