When a body is heated it's temperature rises (except during a change in phase).
(1) Gram specific heat : The amount of heat energy required to raise the temperature of unit mass of a body through \[{{1}^{o}}C\] (or K) is called specific heat of the material of the body.
If Q heat changes the temperature of mass m by \[\Delta \theta \] then specific heat \[c=\frac{Q}{m\Delta \theta }\]
(i) Units : Calorie/gm \[\times {{\,}^{o}}C\] (practical), J/kg \[\times \] K (S.I.)
Dimension : \[[{{L}^{2}}{{T}^{-2}}{{\theta }^{-1}}]\]
(ii) For an infinitesimal temperature change \[d\theta \] and corresponding quantity of heat dQ.
Specific heat \[c=\frac{1}{m}.\frac{dQ}{d\theta }\]
(2) Molar specific heat : Molar specific heat of a substance is defined as the 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.
Molar specific heat (C) \[=M\times \text{Gram specific heat}\](c)
(M = Molecular mass of substance)
\[C=M\frac{Q}{m\Delta \theta }=\frac{1}{\mu }\frac{Q}{\Delta \theta }\] \[\left( \text{where,}\,\text{Number of moles }\mu =\frac{m}{M} \right)\]
Units : calorie/mole \[\times {{\,}^{o}}C\] (practical); J/mole \[\times \] kelvin (S.I.)
Dimension : \[[M{{L}^{2}}{{T}^{-2}}{{\theta }^{-1}}]\]
(1) The form of energy which is exchanged among various bodies or system on account of temperature difference is defined as heat.
(2) We can change the temperature of a body by giving heat (temperature rises) or by removing heat (temperature falls) from body.
(3) The amount of heat (Q) is given to a body depends upon it's mass (m), change in it's temperature \[(\Delta \theta =\Delta \theta )\] and nature of material i.e. \[Q=m.c.\,\Delta \theta \]; where c = specific heat of material.
(4) Heat is a scalar quantity. It's units are joule, erg, cal, kcal etc.
(5) The calorie (cal) is defined as the amount of heat required to raise the temperature of 1 gm of water from \[{{14.5}^{o}}C\] to \[{{15.5}^{o}}C\]. Also 1 kcal = 1000 cal = 4186 J and 1 cal = 4.18 J
(6) British Thermal Unit (BTU) : One BTU is the quantity of heat required to raise the temperature of one pound (\[1\,lb\]) of water from \[{{63}^{o}}F\] to \[{{64}^{o}}F\]
1 BTU = 778 ft. lb = 252 cal = 1055 J
(7) In solids thermal energy is present in the form of kinetic energy, in liquids, in the form of translatory energy of molecules. In gas it is due to the random motion of molecules.
(8) Heat always flows from a body of higher temperature to lower temperature till their temperature becomes equal (Thermal equilibrium).
(9) The heat required for a given temperature increase depends only on how many atoms the sample contains, not on the mass of an individual atom.
Gases have no definite shape, therefore gases have only volume expansion. Since the expansion of container is negligible in comparison to the gases, therefore gases have only real expansion.
(1) Coefficient of volume expansion : At constant pressure, the unit volume of a given mass of a gas, increases with \[{{1}^{o}}C\] rise of temperature, is called coefficient of volume expansion.
\[\alpha =\frac{\Delta V}{{{V}_{0}}}\times \frac{1}{\Delta \theta }\]\[\Rightarrow \]Final volume \[{V}'=V(1+\alpha \Delta \theta )\]
(2) Coefficient of pressure expansion : \[\beta =\frac{\Delta P}{P}\times \frac{1}{\Delta \theta }\]
\[\therefore \] Final pressure \[{P}'=P(1+\beta \Delta \theta )\]
For an ideal gas, coefficient of volume expansion is equal to the coefficient of pressure expansion i.e. \[\alpha =\beta =\frac{1}{273}{}^\circ {{C}^{-1}}\]
Most substances (solid and liquid) expand when they are heated, i.e., volume of a given mass of a substance increases on heating, so the density should decrease \[\left( \text{as }\rho \propto \frac{1}{V} \right)\]. For a given mass
\[\rho \propto \frac{1}{V}\] \[\Rightarrow \]\[\frac{{{\rho }'}}{\rho }=\frac{V}{{{V}'}}=\frac{V}{V+\Delta V}=\frac{V}{V+\gamma V\Delta \theta }=\frac{1}{1+\gamma \,\Delta \theta }\]
\[\Rightarrow \]\[{\rho }'=\frac{\rho }{1+\gamma \,\Delta \theta }=\rho \,{{(1+\gamma \,\Delta \theta )}^{-1}}=\rho \,(1-\gamma \,\Delta \theta )\]
(1) Liquids do not have linear and superficial expansion but these only have volume expansion.
(2) Since liquids are always to be heated along with a vessel which contains them so initially on heating the system (liquid + vessel), the level of liquid in vessel falls (as vessel expands more since it absorbs heat and liquid expands less) but later on, it starts rising due to faster expansion of the liquid.
PQ \[\to \] represents expansion of vessel
QR \[\to \] represents the real expansion of liquid
PR \[\to \] Represent the apparent expansion of liquid
(3) The actual increase in the volume of the liquid = The apparent increase in the volume of liquid + the increase in the volume of the vessel.
(4) Liquids have two coefficients of volume expansion.
(i) Co-efficient of apparent expansion \[({{\gamma }_{a}})\]: It is due to apparent (that appears to be, but is not) increase in the volume of liquid if expansion of vessel containing the liquid is not taken into account.
\[{{\gamma }_{a}}=\frac{\text{Apparent expansion in volume}}{\text{Initial volume }\times \text{ }\Delta \theta }=\frac{{{(\Delta V)}_{a}}}{V\times \Delta \theta }\]
(ii) Co-efficient of real expansion \[({{\gamma }_{r}})\] : It is due to the actual increase in volume of liquid due to heating. \[{{\gamma }_{r}}=\frac{\text{Real increase in volume}}{\text{Initial volume }\times \Delta \theta }=\frac{{{(\Delta V)}_{r}}}{V\times \Delta \theta }\]
(iii) Also coefficient of expansion of flask \[{{\gamma }_{Vessel}}=\frac{{{(\Delta V)}_{Vessel}}}{V\times \Delta \theta }\]
(iv) \[{{\gamma }_{\operatorname{Re}al}}={{\gamma }_{Apparent}}+{{\gamma }_{Vessel}}\]
(v) Change (apparent change) in volume in liquid relative to vessel is
\[\Delta {{V}_{app}}=V\,{{\gamma }_{app}}\,\Delta \theta =V({{\gamma }_{Real}}-{{\gamma }_{Vessel}})\Delta \theta =V({{\gamma }_{r}}-3\alpha )\Delta \theta \]
\[\alpha =\] Coefficient of linear expansion of the vessel. Different level of liquid in vessel
(1) Bi-metallic strip : Two strips of equal lengths but of different materials (different coefficient of linear expansion) when join together, it is called "bi-metallic strip", and can be used in thermostat to break or make electrical contact. This strip has the characteristic property of bending on heating due to unequal linear expansion of the two metal. The strip will bend with metal of greater \[\alpha \] on outer side i.e. convex side.
(2) Effect of temperature on the time period of a simple pendulum : A pendulum clock keeps proper time at temperature \[\theta \]. If temperature is increased to \[\theta '(>\theta )\] then due to linear expansion, length of pendulum and hence its time period will increase.
Fractional change in time period \[\frac{\Delta T}{T}=\frac{1}{2}\alpha \,\Delta \theta \]
(i) Due to increment in its time period, a pendulum clock becomes slow in summer and will lose time.
Loss of time in a time period \[\Delta T=\frac{1}{2}\alpha \,\,\Delta \theta \,\,T\]
(ii) Time lost by the clock in a day (t = 86400 sec)
\[\Delta t=\frac{1}{2}\alpha \,\,\Delta \theta \,\,t=\frac{1}{2}\alpha \,\,\Delta \theta \,\,(86400)=43200\,\alpha \,\,\Delta \theta \,\,sec\]
(iii) The clock will lose time i.e. will become slow if \[{\theta }'>\theta \] (in summer) and will gain time i.e. will become fast if \[{\theta }'
The centigrade \[{{(}^{o}}C),\] Farenheite \[{{(}^{o}}F),\] Kelvin (K), Reaumer (R), Rankine (Ra) are commonly used temperature scales. (1) To construct a scale of temperature, two fixed points are taken. First fixed point is the freezing point (ice point) of water, it is called lower fixed point (LFP). The second fixed point is the boiling point (steam point) of water, it is called upper fixed point (UFP). (2) Celsius scale : In this scale LFP (ice point) is taken \[{{0}^{o}}\] and UFP (steam point) is taken \[{{100}^{o}}\]. The temperature measured on this scale all in degree Celsius \[{{(}^{o}}C)\]. (3) Farenheite scale : This scale of temperature has LFP as \[{{32}^{o}}F\] and UFP as \[{{212}^{o}}F\]. The change in temperature of \[{{1}^{o}}F\] corresponds to a change of less than \[{{1}^{o}}\]on Celsius scale. (4) Kelvin scale : The Kelvin temperature scale is also known as thermodynamic scale. The triple point of water is also selected to be the zero of scale of temperature. The temperature measured on this scale are in Kelvin (K). 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 equilibrium. Different measuring scales
Scale
Symbol for each degree
LFP
UFP
Number of divisions on the scale
Celsius
\[^{o}C\]
\[{{0}^{o}}C\]
\[{{100}^{o}}C\]
100
Fahrenheit
\[^{o}F\]
\[{{32}^{o}}F\]
\[{{212}^{o}}F\]
180
Reaumer
\[^{o}R\]
\[{{0}^{o}}R\]
\[{{80}^{o}}R\]
80
Rankine
\[^{o}Ra\]
460 Ra
672 Ra
212
Kelvin
K
273.15 K
373.15 K
100
(5) Temperature on one scale can be converted into other scale by using the following identity. \[\frac{\text{Reading on any scale }-\text{LFP}}{\text{UFP}-\,\text{LFP}}\] = Constant for all scales (6) All these temperatures are related to each other by the following relationship \[\frac{C-0}{100}=\frac{F-32}{212-32}=\frac{K-273.15}{373.15-273.15}=\frac{R-0}{80-0}=\frac{Ra-460}{672-460}\] or \[\frac{C}{5}=\frac{F-32}{9}=\frac{K-273}{5}=\frac{R}{4}=\frac{Ra-460}{10.6}\] (7) The Celsius and Kelvin scales have different zero points but the same size degrees. Therefore any temperature difference is the same on the Celsius and Kelvin scales \[{{({{T}_{1}}-{{T}_{2}})}^{o}}C=({{T}_{2}}-{{T}_{1}})K\].
When matter is heated without any change in it's state, it usually expands. According to atomic theory of matter, a symmetry in potential energy curve is responsible for thermal expansion. As with rise in temperature the amplitude of vibration and hence energy of atoms increases, hence the average distance between the atoms increases. So the matter as a whole expands.
(1) Thermal expansion is minimum in case of solids but maximum in case of gases because intermolecular force is maximum in solids but minimum in gases.
(2) Solids can expand in one dimension (linear expansion), two dimension (superficial expansion) and three dimension (volume expansion) while liquids and gases usually suffers change in volume only.
(3) Linear expansion : When a solid is heated and it's length increases, then the expansion is called linear expansion.
(i) Change in length \[\Delta L={{L}_{0}}\alpha \Delta T\]
(\[{{L}_{0}}=\] Original length, \[\Delta T=\] Temperature change)
(ii) Final length \[L={{L}_{0}}(1+\alpha \Delta T)\]
(iii) Co-efficient of linear expansion \[\alpha =\frac{\Delta L}{{{L}_{0}}\Delta T}\]
(iv) Unit of \[\alpha \] is \[^{o}{{C}^{-1}}\] or \[{{K}^{-1}}.\] It's dimension is \[[{{\theta }^{-1}}]\]
(4) Superficial (areal) expansion : When the temperature of a 2D object is changed, it's area changes, then the expansion is called superficial expansion.
(i) Change in area is \[\Delta A={{A}_{0}}\beta \Delta T\]
(\[{{A}_{0}}=\] Original area, \[\Delta T=\] Temperature change)
(ii) Final area \[A={{A}_{0}}(1+\beta \Delta T)\]
(iii) Co-efficient of superficial expansion \[\beta =\frac{\Delta A}{{{A}_{0}}\Delta T}\]
(iv) Unit of \[\beta \] is \[^{o}{{C}^{-1}}\] or \[{{K}^{-1}}\].
(5) Volume or cubical expansion : When a solid is heated and it's volume increases, then the expansion is called volume or cubical expansion.
(i) Change in volume is \[\Delta V={{V}_{0}}\gamma \Delta T\]
(\[{{V}_{0}}=\] Original volume, \[\Delta T=\] change in temperature)
(ii) Final volume \[V={{V}_{0}}(1+\gamma \Delta T)\]
(iii) Volume co-efficient of expansion \[\gamma =\frac{\Delta V}{{{V}_{0}}\Delta T}\]
(iv) Unit of \[\gamma \] is \[^{o}{{C}^{-1}}\] or \[{{K}^{-1}}\].
(6) More about \[\alpha ,\,\,\beta \] and \[\gamma \] : The co-efficient \[\alpha ,\,\beta \] and \[\gamma \] for a solid are related to each other as follows
\[\alpha =\frac{\beta }{2}=\frac{\gamma }{3}\]\[\Rightarrow \] \[\alpha :\beta :\gamma =1:2:3\]
(i) Hence for the same rise in temperature
Percentage change in area \[=2\times \] percentage change in length. Percentage change in volume \[=3\times \] percentage change in length.
(ii) The three coefficients of expansion are not constant for a given solid. Their values depend on the temperature range in which they are measured.
(iii) The values of \[\alpha ,\,\,\beta ,\,\gamma \] are independent of the units of length, area and volume respectively.
(iv) For anisotropic solids \[\gamma ={{\alpha }_{x}}+{{\alpha }_{y}}+{{\alpha }_{z}}\] where \[{{\alpha }_{x}},\,\,{{\alpha }_{y}},\] and \[{{\alpha }_{z}}\] represent the mean coefficients of linear expansion along three mutually perpendicular directions.
(7) Contraction on heating : Some rubber like substances contract with rising temperature, because transverse vibration of atoms of substance dominate more...
An instrument used to measure the temperature of a body is called a thermometer.
It works by absorbing some heat from the body, so the temperature recorded by it is lesser than the actual value unless the body is at constant temperature. Some common types of thermometers are as follows
(1) Liquid (mercury) thermometers : In liquid thermometers mercury is preferred over other liquids as its expansion is large and uniform and it has high thermal conductivity and low specific heat.
(i) Range of temperature : \[\underset{\text{(freezing point)}}{\mathop{-\,50{}^\circ C}}\,\text{ to }\underset{\text{(boiling point)}}{\mathop{350{}^\circ C}}\,\]
(ii) Upper limit of range of mercury thermometer can be raised upto \[{{550}^{o}}C\] by filling nitrogen in space over mercury under pressure (which elevates boiling point of mercury).
(iii) Mercury thermometer with cylindrical bulbs are more sensitive than those with spherical bulbs.
(iv) If alcohol is used instead of mercury then range of temperature measurement becomes \[-{{80}^{o}}C\] to \[{{350}^{o}}C\]
(v) Formula : \[t=\frac{l-{{l}_{0}}}{{{l}_{100}}-{{l}_{0}}}\times 100{}^\circ C\]
(2) Gas thermometers : These are more sensitive and accurate than liquid thermometers as expansion of gases is more than that of liquids. The thermometers using a gas as thermoelectric substance are called ideal gas thermometers. These are of two types
(i) Constant pressure gas thermometers
(a) Principle \[V\propto T\] (if P = constant)
(b) Formula : \[t=\frac{V-{{V}_{0}}}{{{V}_{100}}-{{V}_{0}}}\times 100{}^\circ C\] or \[T=273.16\frac{V}{{{V}_{Tr}}}K\]
(ii) Constant volume gas thermometers
(a) Principle \[P\propto T\] (if V = constant)
(b) Formula : \[t=\frac{P-{{P}_{0}}}{{{P}_{100}}-{{P}_{0}}}\times 100{}^\circ C\] or \[T=273.16\frac{P}{{{P}_{Tr}}}K\]
(c) Range of temperature :
Hydrogen gas thermometer : \[-{{200}^{o}}C\] to \[{{500}^{o}}C\]
Nitrogen gas thermometer : \[-{{200}^{o}}C\] to \[{{1600}^{o}}C\]
Helium gas thermometer : \[-{{268}^{o}}C\] C to \[{{500}^{o}}C\]
(3) Resistance thermometers : Usually platinum is used in resistance thermometers due to high melting point and large value of temperature coefficient of resistance.
Resistance of metals varies with temperature according to relation. \[R={{R}_{0}}(1+\alpha t)\] where \[\alpha \] is the temperature coefficient of resistance and t is change in temperature.
(i) Formula : \[t=\frac{R-{{R}_{0}}}{{{R}_{100}}-{{R}_{0}}}\times 100{}^\circ C\] or \[T=273.16\frac{R}{{{R}_{Tr}}}K\]
(ii) Temperature range : For Platinum resistance thermometer it is \[-{{200}^{o}}C\] to \[{{1200}^{o}}C\]
For Germanium resistance thermometer it is 4 to 77 K.
(4) Thermoelectric thermometers : These are based on ?Seebeck effect? according to which when two distinct metals are joined to form a closed circuit called thermocouple and the difference in temperature is maintained between their junctions, an emf is developed. The emf is called thermo-emf and if one junction is at \[{{0}^{o}}C,\] thermoelectric emf varies with temperature of hot junction (t) according to \[e=at+b{{t}^{2}};\] where a and b are constants.
Thermoelectric thermometers have low thermal capacity and high thermal conductivity, so can be used to measure quickly changing temperature Different temperature range
The centigrade \[{{(}^{o}}C),\] Farenheite \[{{(}^{o}}F),\] Kelvin (K), Reaumer (R), Rankine (Ra) are commonly used temperature scales.
(1) To construct a scale of temperature, two fixed points are taken. First fixed point is the freezing point (ice point) of water, it is called lower fixed point (LFP). The second fixed point is the boiling point (steam point) of water, it is called upper fixed point (UFP).
(2) Celsius scale : In this scale LFP (ice point) is taken \[{{0}^{o}}\] and UFP (steam point) is taken \[{{100}^{o}}\]. The temperature measured on this scale all in degree Celsius \[{{(}^{o}}C)\].
(3) Farenheite scale : This scale of temperature has LFP as \[{{32}^{o}}F\] and UFP as \[{{212}^{o}}F\]. The change in temperature of \[{{1}^{o}}F\] corresponds to a change of less than \[{{1}^{o}}\]on Celsius scale.
(4) Kelvin scale : The Kelvin temperature scale is also known as thermodynamic scale. The triple point of water is also selected to be the zero of scale of temperature. The temperature measured on this scale are in Kelvin (K).
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 equilibrium. Different measuring scales
Scale
Symbol for each degree
LFP
UFP
Number of divisions on the scale
Celsius
\[^{o}C\]
\[{{0}^{o}}C\]
\[{{100}^{o}}C\]
100
Fahrenheit
\[^{o}F\]
\[{{32}^{o}}F\]
\[{{212}^{o}}F\]
180
Reaumer
\[^{o}R\]
\[{{0}^{o}}R\]
\[{{80}^{o}}R\]
80
Rankine
\[^{o}Ra\]
460 Ra
672 Ra
212
Kelvin
K
273.15 K
373.15 K
100
(5) Temperature on one scale can be converted into other scale by using the following identity.
\[\frac{\text{Reading on any scale }-\text{LFP}}{\text{UFP}-\,\text{LFP}}\] = Constant for all scales
(6) All these temperatures are related to each other by the following relationship
\[\frac{C-0}{100}=\frac{F-32}{212-32}=\frac{K-273.15}{373.15-273.15}=\frac{R-0}{80-0}=\frac{Ra-460}{672-460}\]
or \[\frac{C}{5}=\frac{F-32}{9}=\frac{K-273}{5}=\frac{R}{4}=\frac{Ra-460}{10.6}\]
(7) The Celsius and Kelvin scales have different zero points but the same size degrees. Therefore any temperature difference is the same on the Celsius and Kelvin scales \[{{({{T}_{1}}-{{T}_{2}})}^{o}}C=({{T}_{2}}-{{T}_{1}})K\].
PQ \[\to \] represents expansion of vessel
QR \[\to \] represents the real expansion of liquid
PR \[\to \] Represent the apparent expansion of liquid
(3) The actual increase in the volume of the liquid = The apparent increase in the volume of liquid + the increase in the volume of the vessel.
(4) Liquids have two coefficients of volume expansion.
(i) Co-efficient of apparent expansion \[({{\gamma }_{a}})\]: It is due to apparent (that appears to be, but is not) increase in the volume of liquid if expansion of vessel containing the liquid is not taken into account.
\[{{\gamma }_{a}}=\frac{\text{Apparent expansion in volume}}{\text{Initial volume }\times \text{ }\Delta \theta }=\frac{{{(\Delta V)}_{a}}}{V\times \Delta \theta }\]
(ii) Co-efficient of real expansion \[({{\gamma }_{r}})\] : It is due to the actual increase in volume of liquid due to heating. \[{{\gamma }_{r}}=\frac{\text{Real increase in volume}}{\text{Initial volume }\times \Delta \theta }=\frac{{{(\Delta V)}_{r}}}{V\times \Delta \theta }\]
(iii) Also coefficient of expansion of flask \[{{\gamma }_{Vessel}}=\frac{{{(\Delta V)}_{Vessel}}}{V\times \Delta \theta }\]
(iv) \[{{\gamma }_{\operatorname{Re}al}}={{\gamma }_{Apparent}}+{{\gamma }_{Vessel}}\]
(v) Change (apparent change) in volume in liquid relative to vessel is
\[\Delta {{V}_{app}}=V\,{{\gamma }_{app}}\,\Delta \theta =V({{\gamma }_{Real}}-{{\gamma }_{Vessel}})\Delta \theta =V({{\gamma }_{r}}-3\alpha )\Delta \theta \]
\[\alpha =\] Coefficient of linear expansion of the vessel. Different level of liquid in vessel
(2) Effect of temperature on the time period of a simple pendulum : A pendulum clock keeps proper time at temperature \[\theta \]. If temperature is increased to \[\theta '(>\theta )\] then due to linear expansion, length of pendulum and hence its time period will increase.
Fractional change in time period \[\frac{\Delta T}{T}=\frac{1}{2}\alpha \,\Delta \theta \]
(i) Due to increment in its time period, a pendulum clock becomes slow in summer and will lose time.
Loss of time in a time period \[\Delta T=\frac{1}{2}\alpha \,\,\Delta \theta \,\,T\]
(ii) Time lost by the clock in a day (t = 86400 sec)
\[\Delta t=\frac{1}{2}\alpha \,\,\Delta \theta \,\,t=\frac{1}{2}\alpha \,\,\Delta \theta \,\,(86400)=43200\,\alpha \,\,\Delta \theta \,\,sec\]
(iii) The clock will lose time i.e. will become slow if \[{\theta }'>\theta \] (in summer) and will gain time i.e. will become fast if \[{\theta }' 
The centigrade \[{{(}^{o}}C),\] Farenheite \[{{(}^{o}}F),\] Kelvin (K), Reaumer (R), Rankine (Ra) are commonly used temperature scales. (1) To construct a scale of temperature, two fixed points are taken. First fixed point is the freezing point (ice point) of water, it is called lower fixed point (LFP). The second fixed point is the boiling point (steam point) of water, it is called upper fixed point (UFP). (2) Celsius scale : In this scale LFP (ice point) is taken \[{{0}^{o}}\] and UFP (steam point) is taken \[{{100}^{o}}\]. The temperature measured on this scale all in degree Celsius \[{{(}^{o}}C)\]. (3) Farenheite scale : This scale of temperature has LFP as \[{{32}^{o}}F\] and UFP as \[{{212}^{o}}F\]. The change in temperature of \[{{1}^{o}}F\] corresponds to a change of less than \[{{1}^{o}}\]on Celsius scale. (4) Kelvin scale : The Kelvin temperature scale is also known as thermodynamic scale. The triple point of water is also selected to be the zero of scale of temperature. The temperature measured on this scale are in Kelvin (K). 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 equilibrium. Different measuring scales
When matter is heated without any change in it's state, it usually expands. According to atomic theory of matter, a symmetry in potential energy curve is responsible for thermal expansion. As with rise in temperature the amplitude of vibration and hence energy of atoms increases, hence the average distance between the atoms increases. So the matter as a whole expands.
(1) Thermal expansion is minimum in case of solids but maximum in case of gases because intermolecular force is maximum in solids but minimum in gases.
(2) Solids can expand in one dimension (linear expansion), two dimension (superficial expansion) and three dimension (volume expansion) while liquids and gases usually suffers change in volume only.
(3) Linear expansion : When a solid is heated and it's length increases, then the expansion is called linear expansion.
(i) Change in length \[\Delta L={{L}_{0}}\alpha \Delta T\]
(\[{{L}_{0}}=\] Original length, \[\Delta T=\] Temperature change)
(ii) Final length \[L={{L}_{0}}(1+\alpha \Delta T)\]
(iii) Co-efficient of linear expansion \[\alpha =\frac{\Delta L}{{{L}_{0}}\Delta T}\]
(iv) Unit of \[\alpha \] is \[^{o}{{C}^{-1}}\] or \[{{K}^{-1}}.\] It's dimension is \[[{{\theta }^{-1}}]\]
(4) Superficial (areal) expansion : When the temperature of a 2D object is changed, it's area changes, then the expansion is called superficial expansion.
(i) Change in area is \[\Delta A={{A}_{0}}\beta \Delta T\]
(\[{{A}_{0}}=\] Original area, \[\Delta T=\] Temperature change)
(ii) Final area \[A={{A}_{0}}(1+\beta \Delta T)\]
(iii) Co-efficient of superficial expansion \[\beta =\frac{\Delta A}{{{A}_{0}}\Delta T}\]
(iv) Unit of \[\beta \] is \[^{o}{{C}^{-1}}\] or \[{{K}^{-1}}\].
(5) Volume or cubical expansion : When a solid is heated and it's volume increases, then the expansion is called volume or cubical expansion.
(i) Change in volume is \[\Delta V={{V}_{0}}\gamma \Delta T\]
(\[{{V}_{0}}=\] Original volume, \[\Delta T=\] change in temperature)
(ii) Final volume \[V={{V}_{0}}(1+\gamma \Delta T)\]
(iii) Volume co-efficient of expansion \[\gamma =\frac{\Delta V}{{{V}_{0}}\Delta T}\]
(iv) Unit of \[\gamma \] is \[^{o}{{C}^{-1}}\] or \[{{K}^{-1}}\].
(6) More about \[\alpha ,\,\,\beta \] and \[\gamma \] : The co-efficient \[\alpha ,\,\beta \] and \[\gamma \] for a solid are related to each other as follows
\[\alpha =\frac{\beta }{2}=\frac{\gamma }{3}\]\[\Rightarrow \] \[\alpha :\beta :\gamma =1:2:3\]
(i) Hence for the same rise in temperature
Percentage change in area \[=2\times \] percentage change in length. Percentage change in volume \[=3\times \] percentage change in length.
(ii) The three coefficients of expansion are not constant for a given solid. Their values depend on the temperature range in which they are measured.
(iii) The values of \[\alpha ,\,\,\beta ,\,\gamma \] are independent of the units of length, area and volume respectively.
(iv) For anisotropic solids \[\gamma ={{\alpha }_{x}}+{{\alpha }_{y}}+{{\alpha }_{z}}\] where \[{{\alpha }_{x}},\,\,{{\alpha }_{y}},\] and \[{{\alpha }_{z}}\] represent the mean coefficients of linear expansion along three mutually perpendicular directions.
(7) Contraction on heating : Some rubber like substances contract with rising temperature, because transverse vibration of atoms of substance dominate more... 
An instrument used to measure the temperature of a body is called a thermometer.
It works by absorbing some heat from the body, so the temperature recorded by it is lesser than the actual value unless the body is at constant temperature. Some common types of thermometers are as follows
(1) Liquid (mercury) thermometers : In liquid thermometers mercury is preferred over other liquids as its expansion is large and uniform and it has high thermal conductivity and low specific heat.
(i) Range of temperature : \[\underset{\text{(freezing point)}}{\mathop{-\,50{}^\circ C}}\,\text{ to }\underset{\text{(boiling point)}}{\mathop{350{}^\circ C}}\,\]
(ii) Upper limit of range of mercury thermometer can be raised upto \[{{550}^{o}}C\] by filling nitrogen in space over mercury under pressure (which elevates boiling point of mercury).
(iii) Mercury thermometer with cylindrical bulbs are more sensitive than those with spherical bulbs.
(iv) If alcohol is used instead of mercury then range of temperature measurement becomes \[-{{80}^{o}}C\] to \[{{350}^{o}}C\]
(v) Formula : \[t=\frac{l-{{l}_{0}}}{{{l}_{100}}-{{l}_{0}}}\times 100{}^\circ C\]
(2) Gas thermometers : These are more sensitive and accurate than liquid thermometers as expansion of gases is more than that of liquids. The thermometers using a gas as thermoelectric substance are called ideal gas thermometers. These are of two types
(i) Constant pressure gas thermometers
(a) Principle \[V\propto T\] (if P = constant)
(b) Formula : \[t=\frac{V-{{V}_{0}}}{{{V}_{100}}-{{V}_{0}}}\times 100{}^\circ C\] or \[T=273.16\frac{V}{{{V}_{Tr}}}K\]
(ii) Constant volume gas thermometers
(a) Principle \[P\propto T\] (if V = constant)
(b) Formula : \[t=\frac{P-{{P}_{0}}}{{{P}_{100}}-{{P}_{0}}}\times 100{}^\circ C\] or \[T=273.16\frac{P}{{{P}_{Tr}}}K\]
(c) Range of temperature :
Hydrogen gas thermometer : \[-{{200}^{o}}C\] to \[{{500}^{o}}C\]
Nitrogen gas thermometer : \[-{{200}^{o}}C\] to \[{{1600}^{o}}C\]
Helium gas thermometer : \[-{{268}^{o}}C\] C to \[{{500}^{o}}C\]
(3) Resistance thermometers : Usually platinum is used in resistance thermometers due to high melting point and large value of temperature coefficient of resistance.
Resistance of metals varies with temperature according to relation. \[R={{R}_{0}}(1+\alpha t)\] where \[\alpha \] is the temperature coefficient of resistance and t is change in temperature.
(i) Formula : \[t=\frac{R-{{R}_{0}}}{{{R}_{100}}-{{R}_{0}}}\times 100{}^\circ C\] or \[T=273.16\frac{R}{{{R}_{Tr}}}K\]
(ii) Temperature range : For Platinum resistance thermometer it is \[-{{200}^{o}}C\] to \[{{1200}^{o}}C\]
For Germanium resistance thermometer it is 4 to 77 K.
(4) Thermoelectric thermometers : These are based on ?Seebeck effect? according to which when two distinct metals are joined to form a closed circuit called thermocouple and the difference in temperature is maintained between their junctions, an emf is developed. The emf is called thermo-emf and if one junction is at \[{{0}^{o}}C,\] thermoelectric emf varies with temperature of hot junction (t) according to \[e=at+b{{t}^{2}};\] where a and b are constants.
Thermoelectric thermometers have low thermal capacity and high thermal conductivity, so can be used to measure quickly changing temperature Different temperature range
