Page 1
Physics Class XI
204
THERMOMETRY, THERMAL EXPANSION AND
CALORIEMETRY
8.1 Heat
The ener gy associated with configuration and random motion of the atoms
and molecules with in a body is called heat.
(1) Units : Joule (S.I.) and calorie (Practical unit)
(2) The ratio of work done (W) to heat produced (Q) is constant.
J is called mechanical equivalent of heat and has v alue 4.2 J/cal.
1 calorie = 4.186 Joule = 4.12 Joule
(3) Heat is a path dependent and is taken to be positive if the system absorbs
it and negative if releases it.
8.2 Temperature
T emperature is defined as the degree of hotness or coldness of a body . Heat
flows from higher temperature to lower temperature.
T wo bodies are said to be in thermal equilibrium when both the bodies are
at the same temperature. T emperature a kinetic ener gy
8.3 Scales of Temperature
The K elvin temperature s cale is als o know n as thermodynamic s cale. The S .I.
unit of temper ature is kelvi n and is defined as (1/273.16) of the temperature
of the triple point of water . The triple point of water is that point on a P–T
diagram where the three phases of water , the solid, the liquid and the gas,
Page 2
Physics Class XI
204
THERMOMETRY, THERMAL EXPANSION AND
CALORIEMETRY
8.1 Heat
The ener gy associated with configuration and random motion of the atoms
and molecules with in a body is called heat.
(1) Units : Joule (S.I.) and calorie (Practical unit)
(2) The ratio of work done (W) to heat produced (Q) is constant.
J is called mechanical equivalent of heat and has v alue 4.2 J/cal.
1 calorie = 4.186 Joule = 4.12 Joule
(3) Heat is a path dependent and is taken to be positive if the system absorbs
it and negative if releases it.
8.2 Temperature
T emperature is defined as the degree of hotness or coldness of a body . Heat
flows from higher temperature to lower temperature.
T wo bodies are said to be in thermal equilibrium when both the bodies are
at the same temperature. T emperature a kinetic ener gy
8.3 Scales of Temperature
The K elvin temperature s cale is als o know n as thermodynamic s cale. The S .I.
unit of temper ature is kelvi n and is defined as (1/273.16) of the temperature
of the triple point of water . The triple point of water is that point on a P–T
diagram where the three phases of water , the solid, the liquid and the gas,
can coexist in thermal equilibrium.
T o construct a scale of temperature, two fixed points are taken. First is the
freezing point of water , it is called lower fixed point. The second is the boiling
point of water , it is calle d upper fixed point.
Name of the Symbol for Lower fixed Upper fixed Number of
scale each degree point (LFP) point (UFP) divisions on the
scale
Celsius ºC 0ºC 100ºC 100
Fahrenheit ºF 32ºF 212ºF 180
Reaumer ºR 0ºR 80ºR 80
Rankine ºRa 460 Ra 672 Ra 212
Kelvin K 273.15 K 373.15 K 100
T emperature on one scale can be converted into other scale by using the
following identity .
= Constant for all scales
8.4 Thermal Expansion
When matter is heated, it expands.
(i) Coefficient of linear expansion a =
(ii) Coefficient of superficial expansion ß =
(iii) Coefficient of volume expansion ? =
(iv) The value of a, ß and ? depends upon the nature of material. All have
dimension [?
–1
] a nd unit per ºC.
(v) ? L = La?T, ?A = Aß?T and ?V = V??T
(vi) Final length L ’ = L + ? L = L (1 + a?T)
Final area A ’ = A + ? A = A (1 + ß?T)
Page 3
Physics Class XI
204
THERMOMETRY, THERMAL EXPANSION AND
CALORIEMETRY
8.1 Heat
The ener gy associated with configuration and random motion of the atoms
and molecules with in a body is called heat.
(1) Units : Joule (S.I.) and calorie (Practical unit)
(2) The ratio of work done (W) to heat produced (Q) is constant.
J is called mechanical equivalent of heat and has v alue 4.2 J/cal.
1 calorie = 4.186 Joule = 4.12 Joule
(3) Heat is a path dependent and is taken to be positive if the system absorbs
it and negative if releases it.
8.2 Temperature
T emperature is defined as the degree of hotness or coldness of a body . Heat
flows from higher temperature to lower temperature.
T wo bodies are said to be in thermal equilibrium when both the bodies are
at the same temperature. T emperature a kinetic ener gy
8.3 Scales of Temperature
The K elvin temperature s cale is als o know n as thermodynamic s cale. The S .I.
unit of temper ature is kelvi n and is defined as (1/273.16) of the temperature
of the triple point of water . The triple point of water is that point on a P–T
diagram where the three phases of water , the solid, the liquid and the gas,
can coexist in thermal equilibrium.
T o construct a scale of temperature, two fixed points are taken. First is the
freezing point of water , it is called lower fixed point. The second is the boiling
point of water , it is calle d upper fixed point.
Name of the Symbol for Lower fixed Upper fixed Number of
scale each degree point (LFP) point (UFP) divisions on the
scale
Celsius ºC 0ºC 100ºC 100
Fahrenheit ºF 32ºF 212ºF 180
Reaumer ºR 0ºR 80ºR 80
Rankine ºRa 460 Ra 672 Ra 212
Kelvin K 273.15 K 373.15 K 100
T emperature on one scale can be converted into other scale by using the
following identity .
= Constant for all scales
8.4 Thermal Expansion
When matter is heated, it expands.
(i) Coefficient of linear expansion a =
(ii) Coefficient of superficial expansion ß =
(iii) Coefficient of volume expansion ? =
(iv) The value of a, ß and ? depends upon the nature of material. All have
dimension [?
–1
] a nd unit per ºC.
(v) ? L = La?T, ?A = Aß?T and ?V = V??T
(vi) Final length L ’ = L + ? L = L (1 + a?T)
Final area A ’ = A + ? A = A (1 + ß?T)
Final volu me V’ = V + ? V = V (1 + ??T)
(vii) ß = 2 a and ? = 3 a
8.5 Anomalous Expansion of Water
(1) In case of water , it expands on heating if its tempe rature is greater than
4ºC. In the range 0ºC to 4ºC water contracts on heatin g and expands on
cooling, i.e., negative.
(2) At 4ºC, density of water is maximum while its specific volume is
minimum.
8.6 Expansion of Gases
Gases have no definite shape, therefore gases have only volume expansion.
8.7 Thermal Capacity and Water Equivalent
(1) Thermal capacity : It is defined as the amount of heat required to raise
the temperature of the whole body (mass, m ) through 1ºC or 1 K.
Thermal c apacity = m c = µ C =
Dimension : [ML
2
T
–2
?
–1
], Unit : call ºC (practical) Joule K (S.I.)
(2) Water Equivalent : W ater equivalent of a body is defined as the mass of
water which would absorb or evolve the same amount of heat as is done
by the body in rising or falling through the same range of temperature.
It is represented by W .
If m = Mass of the body , c = Specific heat of body
? W ater equivalent ( W) = mc gm
8.8 Specific Heat
(1) Gram specific heat : The heat required to raise the temperature of one
gram mass of a body through 1ºC (or 1 K) is called gram specific heat
of the material of the body .
specific heat, c =
Page 4
Physics Class XI
204
THERMOMETRY, THERMAL EXPANSION AND
CALORIEMETRY
8.1 Heat
The ener gy associated with configuration and random motion of the atoms
and molecules with in a body is called heat.
(1) Units : Joule (S.I.) and calorie (Practical unit)
(2) The ratio of work done (W) to heat produced (Q) is constant.
J is called mechanical equivalent of heat and has v alue 4.2 J/cal.
1 calorie = 4.186 Joule = 4.12 Joule
(3) Heat is a path dependent and is taken to be positive if the system absorbs
it and negative if releases it.
8.2 Temperature
T emperature is defined as the degree of hotness or coldness of a body . Heat
flows from higher temperature to lower temperature.
T wo bodies are said to be in thermal equilibrium when both the bodies are
at the same temperature. T emperature a kinetic ener gy
8.3 Scales of Temperature
The K elvin temperature s cale is als o know n as thermodynamic s cale. The S .I.
unit of temper ature is kelvi n and is defined as (1/273.16) of the temperature
of the triple point of water . The triple point of water is that point on a P–T
diagram where the three phases of water , the solid, the liquid and the gas,
can coexist in thermal equilibrium.
T o construct a scale of temperature, two fixed points are taken. First is the
freezing point of water , it is called lower fixed point. The second is the boiling
point of water , it is calle d upper fixed point.
Name of the Symbol for Lower fixed Upper fixed Number of
scale each degree point (LFP) point (UFP) divisions on the
scale
Celsius ºC 0ºC 100ºC 100
Fahrenheit ºF 32ºF 212ºF 180
Reaumer ºR 0ºR 80ºR 80
Rankine ºRa 460 Ra 672 Ra 212
Kelvin K 273.15 K 373.15 K 100
T emperature on one scale can be converted into other scale by using the
following identity .
= Constant for all scales
8.4 Thermal Expansion
When matter is heated, it expands.
(i) Coefficient of linear expansion a =
(ii) Coefficient of superficial expansion ß =
(iii) Coefficient of volume expansion ? =
(iv) The value of a, ß and ? depends upon the nature of material. All have
dimension [?
–1
] a nd unit per ºC.
(v) ? L = La?T, ?A = Aß?T and ?V = V??T
(vi) Final length L ’ = L + ? L = L (1 + a?T)
Final area A ’ = A + ? A = A (1 + ß?T)
Final volu me V’ = V + ? V = V (1 + ??T)
(vii) ß = 2 a and ? = 3 a
8.5 Anomalous Expansion of Water
(1) In case of water , it expands on heating if its tempe rature is greater than
4ºC. In the range 0ºC to 4ºC water contracts on heatin g and expands on
cooling, i.e., negative.
(2) At 4ºC, density of water is maximum while its specific volume is
minimum.
8.6 Expansion of Gases
Gases have no definite shape, therefore gases have only volume expansion.
8.7 Thermal Capacity and Water Equivalent
(1) Thermal capacity : It is defined as the amount of heat required to raise
the temperature of the whole body (mass, m ) through 1ºC or 1 K.
Thermal c apacity = m c = µ C =
Dimension : [ML
2
T
–2
?
–1
], Unit : call ºC (practical) Joule K (S.I.)
(2) Water Equivalent : W ater equivalent of a body is defined as the mass of
water which would absorb or evolve the same amount of heat as is done
by the body in rising or falling through the same range of temperature.
It is represented by W .
If m = Mass of the body , c = Specific heat of body
? W ater equivalent ( W) = mc gm
8.8 Specific Heat
(1) Gram specific heat : The heat required to raise the temperature of one
gram mass of a body through 1ºC (or 1 K) is called gram specific heat
of the material of the body .
specific heat, c =
Units : Calorie/gm ºC (Practical), J/kg K(S.I.)
Dimension : [L
2
T
–2
?
–1
]
(2) Molar specific heat : Amount of heat required to raise the temperature
of one gram mole of the substance through a unit degree it is represented
by (capital) C.
? C =
Units : Cal mol
–1
ºC
–1
(Practical), J mol
–1
K
–1
(S.I.)
Dimension : [ML
2
T
–2
?
–1
µ
–1
]
8.9 Specific Heat of Solids
Specific heat of a solid is specific heat at constant volume C
v
.
W ith rise in temperature, C
v
increases and becomes co nstant = 3R
Dulong and Petit law : A verage molar specific heat of all metals at room
temperature is constant and is equal to 3R. This statement is known as Dulong
and Petit law .
8.10 Latent Heat
(1) When a substance changes from one state to another state then ener gy
is either absorbed or liber ated. This heat ener gy is called latent heat.
(2) No change in tempera ture is involved when the substance changes its
state.
(3) ? Q = m L, where L is the latent heat.
(4) Unit : cal/gm or J kg and Dimension : [L
2
T
–2
]
(5) Any material has two types of latent heats
(i) Latent heat of fusion : The heat required to change 1 kg of the
material in its solid state to its liquid state, latent heat of fusion (or
latent heat of ice) is L
F
= L
ice
˜ 80 cal/g.
Page 5
Physics Class XI
204
THERMOMETRY, THERMAL EXPANSION AND
CALORIEMETRY
8.1 Heat
The ener gy associated with configuration and random motion of the atoms
and molecules with in a body is called heat.
(1) Units : Joule (S.I.) and calorie (Practical unit)
(2) The ratio of work done (W) to heat produced (Q) is constant.
J is called mechanical equivalent of heat and has v alue 4.2 J/cal.
1 calorie = 4.186 Joule = 4.12 Joule
(3) Heat is a path dependent and is taken to be positive if the system absorbs
it and negative if releases it.
8.2 Temperature
T emperature is defined as the degree of hotness or coldness of a body . Heat
flows from higher temperature to lower temperature.
T wo bodies are said to be in thermal equilibrium when both the bodies are
at the same temperature. T emperature a kinetic ener gy
8.3 Scales of Temperature
The K elvin temperature s cale is als o know n as thermodynamic s cale. The S .I.
unit of temper ature is kelvi n and is defined as (1/273.16) of the temperature
of the triple point of water . The triple point of water is that point on a P–T
diagram where the three phases of water , the solid, the liquid and the gas,
can coexist in thermal equilibrium.
T o construct a scale of temperature, two fixed points are taken. First is the
freezing point of water , it is called lower fixed point. The second is the boiling
point of water , it is calle d upper fixed point.
Name of the Symbol for Lower fixed Upper fixed Number of
scale each degree point (LFP) point (UFP) divisions on the
scale
Celsius ºC 0ºC 100ºC 100
Fahrenheit ºF 32ºF 212ºF 180
Reaumer ºR 0ºR 80ºR 80
Rankine ºRa 460 Ra 672 Ra 212
Kelvin K 273.15 K 373.15 K 100
T emperature on one scale can be converted into other scale by using the
following identity .
= Constant for all scales
8.4 Thermal Expansion
When matter is heated, it expands.
(i) Coefficient of linear expansion a =
(ii) Coefficient of superficial expansion ß =
(iii) Coefficient of volume expansion ? =
(iv) The value of a, ß and ? depends upon the nature of material. All have
dimension [?
–1
] a nd unit per ºC.
(v) ? L = La?T, ?A = Aß?T and ?V = V??T
(vi) Final length L ’ = L + ? L = L (1 + a?T)
Final area A ’ = A + ? A = A (1 + ß?T)
Final volu me V’ = V + ? V = V (1 + ??T)
(vii) ß = 2 a and ? = 3 a
8.5 Anomalous Expansion of Water
(1) In case of water , it expands on heating if its tempe rature is greater than
4ºC. In the range 0ºC to 4ºC water contracts on heatin g and expands on
cooling, i.e., negative.
(2) At 4ºC, density of water is maximum while its specific volume is
minimum.
8.6 Expansion of Gases
Gases have no definite shape, therefore gases have only volume expansion.
8.7 Thermal Capacity and Water Equivalent
(1) Thermal capacity : It is defined as the amount of heat required to raise
the temperature of the whole body (mass, m ) through 1ºC or 1 K.
Thermal c apacity = m c = µ C =
Dimension : [ML
2
T
–2
?
–1
], Unit : call ºC (practical) Joule K (S.I.)
(2) Water Equivalent : W ater equivalent of a body is defined as the mass of
water which would absorb or evolve the same amount of heat as is done
by the body in rising or falling through the same range of temperature.
It is represented by W .
If m = Mass of the body , c = Specific heat of body
? W ater equivalent ( W) = mc gm
8.8 Specific Heat
(1) Gram specific heat : The heat required to raise the temperature of one
gram mass of a body through 1ºC (or 1 K) is called gram specific heat
of the material of the body .
specific heat, c =
Units : Calorie/gm ºC (Practical), J/kg K(S.I.)
Dimension : [L
2
T
–2
?
–1
]
(2) Molar specific heat : Amount of heat required to raise the temperature
of one gram mole of the substance through a unit degree it is represented
by (capital) C.
? C =
Units : Cal mol
–1
ºC
–1
(Practical), J mol
–1
K
–1
(S.I.)
Dimension : [ML
2
T
–2
?
–1
µ
–1
]
8.9 Specific Heat of Solids
Specific heat of a solid is specific heat at constant volume C
v
.
W ith rise in temperature, C
v
increases and becomes co nstant = 3R
Dulong and Petit law : A verage molar specific heat of all metals at room
temperature is constant and is equal to 3R. This statement is known as Dulong
and Petit law .
8.10 Latent Heat
(1) When a substance changes from one state to another state then ener gy
is either absorbed or liber ated. This heat ener gy is called latent heat.
(2) No change in tempera ture is involved when the substance changes its
state.
(3) ? Q = m L, where L is the latent heat.
(4) Unit : cal/gm or J kg and Dimension : [L
2
T
–2
]
(5) Any material has two types of latent heats
(i) Latent heat of fusion : The heat required to change 1 kg of the
material in its solid state to its liquid state, latent heat of fusion (or
latent heat of ice) is L
F
= L
ice
˜ 80 cal/g.
208
(ii) Latent heat of vaporisation : The heat ener gy required to change 1
kg of the material in its liquid to 1 kg of the material in its gaseous
state. Latent heat of vaporisation (latent heat of steam) is L
v
= L
steam
˜ 540 cal/gm.
8.11 Principle of Caloriemetry
Heat lost = Heat gained
i.e., principle of caloriemetry represents the law of conservation of heat
ener gy .
8.12 Heating Curve
Thermodynamic Processes
(1) Thermodynamics : It is a branch of science which deals with exchange
of heat ener gy between bodies and conversion of the heat ener gy into
mechanical ener gy and vice versa.
(2) Thermodynamic system : A collection of an extremely lar ge number
of atoms or molecules confi ned w ith in certain boundaries s uch that
it has a certai n value of pressure, volume and temperature is called a
thermodynamic system. Anything outside the thermodynamic system to
which ener gy or matter is exchanged is called its surroundings.
Thermodynamic system may be of three types :
(i) Open system : It exchange both energy and matter with the
surrounding.
(ii) Closed system : It e xc ha ng e onl y e ne r gy (not m a t t e r ) wi t h t he
surroundings.
(iii) Isolated system : It exchange neither ener gy nor matter with the
surrounding.
Heat (Q)
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