HEAT CHAPTER – 11
HEAT DEFINITION:
Total Kinetic energy of a body is known as HEAT.
OR
Transfer of energy from a hot body to a cold one is
termed as Heat.
Heat is measured by using an measurement
centimeter.
UNITS
Since heat is a force of energy therefore its unit is
Joule (J).
TEMPERATURE
DEFINITION
The average kinetic energy of a body is known as
Temperature.
OR
The quantitative determination of degree of hotness
may be termed as Temperature.
SCALES OF TEMPERATURE
There are three main scales of temperature.
1. Celsius Scale
2. Fahrenheit Scale
3. Kelvin Scale
Celsius and Fahrenheit scales are also known as
Scales of Graduation.
1. Celsius Scale
The melting point of ice and boiling point of water at
standard pressure (76cm of Hg) taken to be two
fixed points. On the Celsius (centigrade) scale the
interval between these two fixed points is divided
into hundred equal parts. Each part thus represents
one degree Celsius (1°C). This scale was suggested
by Celsius in 1742.
Mathematically,
°C = K – 273
OR
°C = 5/9 (°F – 32)
2. Fahrenheit Scale
The melting point of ice and boiling of water at
standard pressure (76cm of Hg) are taken to be two
fixed points. On Fahrenheit scale the lower fixed
point is marked 32 and upper fixed point 212. The
interval between them is equally divided into 180
parts. Each part represents one degree Fahrenheit
(1°F).
Mathematically,
°F = 9/5 (°C + 32)
3. Kelvin Scale
The lowest temperature on Kelvin Scale is -273°C.
Thus 0° on Celsius scale will be 273 on Kelvin scale
written as 273K and 100 on Celsius scale will be
373K. The size of Celsius and Kelvin scales are
same.
Mathematically,
K = °C + 273
THERMAL EQUILIBRIUM
Heat flows from hot body to cold body till the
temperature of the bodies becomes same, then they
are said to be in Thermal Equilibrium
.
THERMAL EXPANSION
DEFINITION
The phenomenon due to which solid experience a
change in its length, volume or area on heating is
known as Thermal Expansion.
Explanation
If we supply some amount of heat to any substance
then size or shape of the substance will increase.
This increment is known as Thermal Expansion.
Thermal expansion is due to the increment of the
amplitudes of the molecules.
Types of Thermal Expansion
There are three types of Thermal Expansion.
1. Linear Expansion
2. Superficial Expansion
3. Volumetric Expansion.
1. Linear Expansion.
If we supply some amount of heat to any rod, then
the length of the rod, then the length of the rod will
increase. Such increment is known as Linear
Expansion.
2. Superficial Expansion.
If we apply some amount of heat to any square or
rectangle then area of the square or rectangle will
increase. Such increment is known as Superficial
Expansion.
3. Volumetric Expansion
.
If we apply some amount of heat to any cube, then
the volume of the cube will increase. Such increment
is known as Volumetric Expansion.
COEFFICIENT OF LINEAR EXPANSION
CONSIDERATION
Let Lo be the initial length of rod at t1 °C. If we
increase the temperature from t1 °C to t2 °C, then
length of the rod will increase. This increment in
length is denoted by ΔL. The increment in length
depends upon the following two factors.
1. Original Length (Lo)
2. Difference in temperature Δt
Derivation
The increment in length is directly proportional to
the original length and temperature difference.
Mathematically,
ΔL ∞ Lo —– (I)
ΔL ∞ Δt —– (II)
Combining eq (I) and (II), we get
ΔL ∞ LoΔt
piston is allowed to move upward. When we do so
temperature and pressure of the working substance
will decrease while volume will increase. In order to
keep the temperature constant, we have to supply
required amount of heat from source to cylinder.
Since in this expansion, temperature is constant
therefore it is known as Isothermal Expansion.
ii. Isothermal Compression
In this process, cylinder is placed on a sink and
piston is allowed to move downward. When we do
so temperature and pressure of working substance
will increase while volume will decrease. In order to
maintain the temperature, we have to reject required
amount of heat from cylinder to the sink.
Since in this compression, temperature is kept
constant therefore it is known as isothermal
compression.
SECOND LAW OF THERMODYNAMICS
Introduction
It is inherit tendency of heat that it always flows
from hot reservoir to cold reservoir. Rather than to
flow in both the directions with equal probability.
On the basis of this tendency of heat a law was
proposed that is known as Second Law of
Thermodynamics.
Statement
It is impossible to construct a process which reserves
the natural tendency of heat.
This law is also known as Law of heat and can also
be stated as
Efficiency of heat engine is always less than unity.
Explanation
Many statements of this law has been proposed to
cover similar but different point of vies in which two
are given below.
1. Lord Kelvin Statement
2. Clausius Statement
1. Lord Kelvin Statement
According to this statement,
It is impossible to construct a heat engine which
extract all heat form the source and convert it into
equal amount of work done and no heat is given to
the sink.
Mathematically,
Q1 ≠ W
Q2 ≠ O
2. Clausius Statement
According to Clausius Statement,
Without the performance of external work heat
cannot flow from cold reservoir towards, the hot
reservoir.
Example
In case of refrigerator flow of heat is unnatural but
this unnatural flow of heat is possible only when we
apply electrical power on the pump of the
refrigerator.
Qs. Define the term Entropy and Give its Uses
ENTROPY
Definition
It measures the disorderliness of any system.
Mathematically,
ΔS = ΔQ/T
Where Δs shows change in entropy.
Units
Joule per degree Kelvin – J/°K.
Explanation
As we know that incase of isometric process volume
is constant. In case of Isothermal process
temperature and pressure is constant, but in case of
adiabatic process neither temperature, nor pressure
or volume is constant but one thermal property is
constant which is known as Entropy.
There are two types of Entropy.
1. Positive Entropy
/
2. Negative Entropy
1. Positive Entropy
If heat is supplied to the system the entropy will be
positive.
2. Negative Entropy
When heat is rejected by the system the entropy will
be negative.
Qs. What is carbot engine an carnot cycle?
CARNOT ENGINE
Definition
‘Carnot engine is an ideal heat engine which
converts heat energy into mechanical energy.
Working of Carnot Engine
It consists of a cylinder and a piston. The walls of
the cylinder are non-conducting while the bottom
surface is the conducting one. The piston is also non-
conducting and friction less. It works in four steps.
Which are as follows.
1. Isothermal Expansion
2. Adiabatic Expansion
3. Isothermal Compression
4. Adiabatic Compression
1. Isothermal Expansion
First of all, cylinder is placed on a source and allow
to move upward as a result temperature and pressure
of the working substance decreases, while volume
increases. In order to maintain temperature we have
to supply more amount of heat from source to the
cylinder. Since in this expansion temperature is kept
constant.
2. Adiabatic Expansion
Secondly cylinder is placed on an insulator and
piston is allow to move downward as a result
temperature and pressure of working substance will
decrease. While volume will increase but no heat is
given or taken of the cylinder.
3. Isothermal Compression
In this state cylinder is placed on a sink and piston is
allow to move downward as a result temperature and
pressure of the working substance will increase
while volume will decrease. In order to maintain
temperature we have to reject extra heat from
cylinder to the sink. Since in this compression
temperature is constant.
4. Adiabatic Compression
Finally cylinder is placed on an insulator and piston
is a flow to move downward, when we do so neither
temperature nor pressure or volume is constant. But
no heat is given or taken out of the cylinder.
CARNOT CYCLE
Definition
By combining the four processes Isothermal
Expansion, Adiabatic Expansion, Isothermal
Compression and Adiabatic Compression which are
carried out in carnot engine, then we get a cycle
knows as Carnot cycle.
Qs. How can we increase the efficiency of Heat
Engine?
If we want to increase the efficiency of any heat
engine then for this purpose we have to increase
temperature of source as maximum as possible and
reduce the temperature of sink as minimum as
possible.
Qs. Define Specific Heat and Molar Specific Heat.
SPECIFIC HEAT
Definition
Specific heat is the amount of heat required to raise
the temperature of a unit mass of a substance by one
degree centigrade.
Different substances have different specific heat
because number of molecules in one kg is different
in different substances. It is denoted by c.
Mathematical Expression
Consider a substance having mass m at the
temperature t1. The amount of heat supplied is ΔQ,
which raises the temperature to t2. The change in
temperature is Δt.
The quantity of heat is directly proportional to the
mass of the substance.
ΔQ ∞ m
And the temperature difference
ΔQ ∞ Δt
Combining both the equations
ΔQ ∞ mΔt
=> ΔQ = cmΔt
=> c = ΔQ / mΔt —- (I)
Where c is the specific heat of the substance. Its unit
is Joules / Kg°C.
MOLAR SPECIFIC HEAT
Definition
Molar specific heat is the amount of heat required to
raise the temperature of one mole of a substance
through one degree Celsius.
Almost all the substances have the same amount of
molar specific heat because the numbers of
molecules in all substances are same in one mole. It
is denoted by cM.
Mathematical Expression
Mathematically,
No. of Moles = Mass / Molecular Mass
=> n = m / M
=> nM = m
=> nM = ΔQ / nΔt
Where n is the number of moles. The unit of molar
specific heat is J/Kg°C.
Qs. Define Molar Specific Heat at Constant
volume and at Constant Pressure.
MOLAR SPECIFIC HEAT AT CONSTANT
VOLUME
Definition
The amount of heat required to raise the
temperature of one mole of any gas through one
degree centigrade, at constant volume is known as
molar specific heat volume.
It is denoted by Cv.
Mathematical Expression
Mathematically,
ΔQv = nCvΔt
Where ΔQv is the heat supplied at constant volume.
MOLAR SPECIFIC HEAT AT CONSTANT
PRESSURE
Definition
The amount of heat required to raise the
temperature of unit mass of a substance through one
degree centigrade at constant pressure is known as
Molar Specific Heat at Constant Pressure.
It is denoted by Cp.
Mathematical Expression
Mathematically,
ΔQp = nCpΔt
Where ΔQp is the heat supplied at constant volume
Total Kinetic energy of a body is known as HEAT.
OR
Transfer of energy from a hot body to a cold one is
termed as Heat.
Heat is measured by using an measurement
centimeter.
UNITS
Since heat is a force of energy therefore its unit is
Joule (J).
TEMPERATURE
DEFINITION
The average kinetic energy of a body is known as
Temperature.
OR
The quantitative determination of degree of hotness
may be termed as Temperature.
SCALES OF TEMPERATURE
There are three main scales of temperature.
1. Celsius Scale
2. Fahrenheit Scale
3. Kelvin Scale
Celsius and Fahrenheit scales are also known as
Scales of Graduation.
1. Celsius Scale
The melting point of ice and boiling point of water at
standard pressure (76cm of Hg) taken to be two
fixed points. On the Celsius (centigrade) scale the
interval between these two fixed points is divided
into hundred equal parts. Each part thus represents
one degree Celsius (1°C). This scale was suggested
by Celsius in 1742.
Mathematically,
°C = K – 273
OR
°C = 5/9 (°F – 32)
2. Fahrenheit Scale
The melting point of ice and boiling of water at
standard pressure (76cm of Hg) are taken to be two
fixed points. On Fahrenheit scale the lower fixed
point is marked 32 and upper fixed point 212. The
interval between them is equally divided into 180
parts. Each part represents one degree Fahrenheit
(1°F).
Mathematically,
°F = 9/5 (°C + 32)
3. Kelvin Scale
The lowest temperature on Kelvin Scale is -273°C.
Thus 0° on Celsius scale will be 273 on Kelvin scale
written as 273K and 100 on Celsius scale will be
373K. The size of Celsius and Kelvin scales are
same.
Mathematically,
K = °C + 273
THERMAL EQUILIBRIUM
Heat flows from hot body to cold body till the
temperature of the bodies becomes same, then they
are said to be in Thermal Equilibrium
.
THERMAL EXPANSION
DEFINITION
The phenomenon due to which solid experience a
change in its length, volume or area on heating is
known as Thermal Expansion.
Explanation
If we supply some amount of heat to any substance
then size or shape of the substance will increase.
This increment is known as Thermal Expansion.
Thermal expansion is due to the increment of the
amplitudes of the molecules.
Types of Thermal Expansion
There are three types of Thermal Expansion.
1. Linear Expansion
2. Superficial Expansion
3. Volumetric Expansion.
1. Linear Expansion.
If we supply some amount of heat to any rod, then
the length of the rod, then the length of the rod will
increase. Such increment is known as Linear
Expansion.
2. Superficial Expansion.
If we apply some amount of heat to any square or
rectangle then area of the square or rectangle will
increase. Such increment is known as Superficial
Expansion.
3. Volumetric Expansion
.
If we apply some amount of heat to any cube, then
the volume of the cube will increase. Such increment
is known as Volumetric Expansion.
COEFFICIENT OF LINEAR EXPANSION
CONSIDERATION
Let Lo be the initial length of rod at t1 °C. If we
increase the temperature from t1 °C to t2 °C, then
length of the rod will increase. This increment in
length is denoted by ΔL. The increment in length
depends upon the following two factors.
1. Original Length (Lo)
2. Difference in temperature Δt
Derivation
The increment in length is directly proportional to
the original length and temperature difference.
Mathematically,
ΔL ∞ Lo —– (I)
ΔL ∞ Δt —– (II)
Combining eq (I) and (II), we get
ΔL ∞ LoΔt
piston is allowed to move upward. When we do so
temperature and pressure of the working substance
will decrease while volume will increase. In order to
keep the temperature constant, we have to supply
required amount of heat from source to cylinder.
Since in this expansion, temperature is constant
therefore it is known as Isothermal Expansion.
ii. Isothermal Compression
In this process, cylinder is placed on a sink and
piston is allowed to move downward. When we do
so temperature and pressure of working substance
will increase while volume will decrease. In order to
maintain the temperature, we have to reject required
amount of heat from cylinder to the sink.
Since in this compression, temperature is kept
constant therefore it is known as isothermal
compression.
SECOND LAW OF THERMODYNAMICS
Introduction
It is inherit tendency of heat that it always flows
from hot reservoir to cold reservoir. Rather than to
flow in both the directions with equal probability.
On the basis of this tendency of heat a law was
proposed that is known as Second Law of
Thermodynamics.
Statement
It is impossible to construct a process which reserves
the natural tendency of heat.
This law is also known as Law of heat and can also
be stated as
Efficiency of heat engine is always less than unity.
Explanation
Many statements of this law has been proposed to
cover similar but different point of vies in which two
are given below.
1. Lord Kelvin Statement
2. Clausius Statement
1. Lord Kelvin Statement
According to this statement,
It is impossible to construct a heat engine which
extract all heat form the source and convert it into
equal amount of work done and no heat is given to
the sink.
Mathematically,
Q1 ≠ W
Q2 ≠ O
2. Clausius Statement
According to Clausius Statement,
Without the performance of external work heat
cannot flow from cold reservoir towards, the hot
reservoir.
Example
In case of refrigerator flow of heat is unnatural but
this unnatural flow of heat is possible only when we
apply electrical power on the pump of the
refrigerator.
Qs. Define the term Entropy and Give its Uses
ENTROPY
Definition
It measures the disorderliness of any system.
Mathematically,
ΔS = ΔQ/T
Where Δs shows change in entropy.
Units
Joule per degree Kelvin – J/°K.
Explanation
As we know that incase of isometric process volume
is constant. In case of Isothermal process
temperature and pressure is constant, but in case of
adiabatic process neither temperature, nor pressure
or volume is constant but one thermal property is
constant which is known as Entropy.
There are two types of Entropy.
1. Positive Entropy
/
2. Negative Entropy
1. Positive Entropy
If heat is supplied to the system the entropy will be
positive.
2. Negative Entropy
When heat is rejected by the system the entropy will
be negative.
Qs. What is carbot engine an carnot cycle?
CARNOT ENGINE
Definition
‘Carnot engine is an ideal heat engine which
converts heat energy into mechanical energy.
Working of Carnot Engine
It consists of a cylinder and a piston. The walls of
the cylinder are non-conducting while the bottom
surface is the conducting one. The piston is also non-
conducting and friction less. It works in four steps.
Which are as follows.
1. Isothermal Expansion
2. Adiabatic Expansion
3. Isothermal Compression
4. Adiabatic Compression
1. Isothermal Expansion
First of all, cylinder is placed on a source and allow
to move upward as a result temperature and pressure
of the working substance decreases, while volume
increases. In order to maintain temperature we have
to supply more amount of heat from source to the
cylinder. Since in this expansion temperature is kept
constant.
2. Adiabatic Expansion
Secondly cylinder is placed on an insulator and
piston is allow to move downward as a result
temperature and pressure of working substance will
decrease. While volume will increase but no heat is
given or taken of the cylinder.
3. Isothermal Compression
In this state cylinder is placed on a sink and piston is
allow to move downward as a result temperature and
pressure of the working substance will increase
while volume will decrease. In order to maintain
temperature we have to reject extra heat from
cylinder to the sink. Since in this compression
temperature is constant.
4. Adiabatic Compression
Finally cylinder is placed on an insulator and piston
is a flow to move downward, when we do so neither
temperature nor pressure or volume is constant. But
no heat is given or taken out of the cylinder.
CARNOT CYCLE
Definition
By combining the four processes Isothermal
Expansion, Adiabatic Expansion, Isothermal
Compression and Adiabatic Compression which are
carried out in carnot engine, then we get a cycle
knows as Carnot cycle.
Qs. How can we increase the efficiency of Heat
Engine?
If we want to increase the efficiency of any heat
engine then for this purpose we have to increase
temperature of source as maximum as possible and
reduce the temperature of sink as minimum as
possible.
Qs. Define Specific Heat and Molar Specific Heat.
SPECIFIC HEAT
Definition
Specific heat is the amount of heat required to raise
the temperature of a unit mass of a substance by one
degree centigrade.
Different substances have different specific heat
because number of molecules in one kg is different
in different substances. It is denoted by c.
Mathematical Expression
Consider a substance having mass m at the
temperature t1. The amount of heat supplied is ΔQ,
which raises the temperature to t2. The change in
temperature is Δt.
The quantity of heat is directly proportional to the
mass of the substance.
ΔQ ∞ m
And the temperature difference
ΔQ ∞ Δt
Combining both the equations
ΔQ ∞ mΔt
=> ΔQ = cmΔt
=> c = ΔQ / mΔt —- (I)
Where c is the specific heat of the substance. Its unit
is Joules / Kg°C.
MOLAR SPECIFIC HEAT
Definition
Molar specific heat is the amount of heat required to
raise the temperature of one mole of a substance
through one degree Celsius.
Almost all the substances have the same amount of
molar specific heat because the numbers of
molecules in all substances are same in one mole. It
is denoted by cM.
Mathematical Expression
Mathematically,
No. of Moles = Mass / Molecular Mass
=> n = m / M
=> nM = m
=> nM = ΔQ / nΔt
Where n is the number of moles. The unit of molar
specific heat is J/Kg°C.
Qs. Define Molar Specific Heat at Constant
volume and at Constant Pressure.
MOLAR SPECIFIC HEAT AT CONSTANT
VOLUME
Definition
The amount of heat required to raise the
temperature of one mole of any gas through one
degree centigrade, at constant volume is known as
molar specific heat volume.
It is denoted by Cv.
Mathematical Expression
Mathematically,
ΔQv = nCvΔt
Where ΔQv is the heat supplied at constant volume.
MOLAR SPECIFIC HEAT AT CONSTANT
PRESSURE
Definition
The amount of heat required to raise the
temperature of unit mass of a substance through one
degree centigrade at constant pressure is known as
Molar Specific Heat at Constant Pressure.
It is denoted by Cp.
Mathematical Expression
Mathematically,
ΔQp = nCpΔt
Where ΔQp is the heat supplied at constant volume
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