Some bodies are colder as compared to a given body. For example a piece of ice is colder than burning charcoal. The coldness or hotness of a body can be measured interms of temperature. When a body is heated, various types of physical changes, such as expansion, contraction, change of state, change of electrical properties, chemical properties are observed.
Heat is a form of energy, it can change into mechanical energy, electrical energy, etc. Heat flows from one body to another body due to temperature difference. It flows from a body at high temperature to a body at low temperature. SI unit of heat is Joule (J). SI unit of temperature is Kelvin (K). Temperature is a property, which determines the nature of the body which is hot (or) cold. "Temperature may be defined as the thermal condition of a body which determine its ability to transfer heat to other bodies". It is a scalar quantity.
Thermal Equillibrium:
Two systems are said to be in thermal equilibrium with each other, if they are at same temperature. Temperature determines whether the two systems will be in thermal equilibrium or not.
Measurement of Temperature:
Measurement of temperature requires the construction of an instrument called thermometer. Many physical properties of materials change sufficiently with temperature to be used as basis for constructing thermometers. The commonly used property is variation of volume of liquid with temperature. The branch of heat that deals with measurement of temperature is called "thermometry".
Thermometers require calibration, which depends on fixing certain points on thermometers. The fixed points are the ice-point, corresponding to the temperature of melting point of ice and steam point, corresponding to the temperature of boiling point of water under normal atmospheric pressure. Ice-point is taken as Lower Fixed Point (L.F.P.) and steam point is taken as Upper Fixed Point (U.F.P.). The interval between U.F.P. and L.F.P. is called fundamental interval. This interval divided into equal parts. These are given arbitrary numerical values of temperature known as thermometric scale. e.g.,: Celsius, Fahrenheit, Reaumur, Kelvin, Rankines.
Thermal Expansion:
Some times sealed bottles with metallic lids are so tightly screwed that one has to put the lid in hot water for some time to open the lid. This would allow the metallic cover to expand, there by loosing it to unscrew easily.
In general, all substances expand on heating. Expansion of solids is less compared to liquid and gases. Since in solids molecules are closely packed. Few substances contract on heating. e.g.: Cast Iron, Bismuth, Leather, Indian rubber ...etc.,. Change in temperature of the body causes change in its dimensions. The increase in dimensions of the body due to increase in its temperature is called ''thermal expansion''.
Since solids have a definite shape and size, their expansion can be considered in terms of their Length (linear), Area (areal expansion), Volume (cubical expansion). Different materials expand to different extents for same raise of temperature. The quantity which will be a measure of expansion of given material is coefficient of expansion.
The coefficient of expansion of solids are three types.
1. Linear expansion:
This is expansion in length. The increase in length of solid per unit original length per unit raise in temperature, is called coefficient of linear expansion.
Units: /0ºC , /K 
Units: /0ºC, /K
D.F. : [Mº Lº Tº K−1]
Thermal expansion of solids is rather small, few materials like Pyrex glass and Invar steel having particularly low values of expansion. Expansion for Alcohol is more than Mercury and it expands more than Mercury for the same rise in temperature.
Anomalous Expansion: Generally liquids expand on heating and contract on cooling. But water contracts on heating from 0ºC to 4ºC and expands with further rise in temperature. Below 4ºC the volume increases, density decreases. This means water has maximum density at 4ºC. This peculiar behaviour of water is called Anomalous Expansion. 
The curve (a) shows that volume of water decrease from 0ºC to 4ºC and then increases. At 4ºC volume of water is minimum. The curve (b) shows that the density of water increases from 0ºC to 4ºC and then decreases. At 4ºC water has maximum density.
Relation between α, γ :
Ideal gas and Ideal gas Equation:
A gas which obeys Boyle's law and Charles law strictly at all temperatures and pressures is called a perfect or an ideal gas. At absolute zero, an ideal gas remains, in gaseous state. Total internal energy (U) of an ideal gas = Σ KE of all the gas molecules. The ideal gas has point size molecules.
onsider, 1 mole of an ideal gas of mass 'm' having pressure P1, volume V1 and absolute temperature T. Final values of pressure, volume and temperature are P2, V2, T2.
Step - I
Keeping temperature of the gas as constant, pressure is changed from P1 to P2, volume changes from, V1 to V
According to Boyle's Law
Step -II
Now keeping the pressure of gas constant, if temperature is chaged from T1 to T2, volume changes from V to V2 then apply Charles law.
Density of a gas interms of Boltzman constant (K) is
Specific heat Capacity: Take some water in a vessel and start heating on a burner, bubbles begin to move upward. As the temperature is raised the motion of water particles increases till it becomes turbulent as water starts "boiling".
Heat a given quantity of water to raise its temperature by tºC (say 20ºC), note the time taken. Again heat the same quantity of water to raise its temperature by 2tºC
(say 40ºC), by using same source, and note the time taken, observe both the cases. Double the quantity of heat required raising twice the temperature of same substance. In the second step, double the quantity of substance and heat it using same source. In this case time become twice that required in the first case.
In the third step, in place of water, heat the same quantity of some oil, raise the temperature again by tºC (say 20ºC) we observe that the time taken will be shorter, the quantity of heat required would be less than that required by the same amount of water for same raise in temperature. Specific heat depends only on nature of the substance. It does not depends on mass of the substance. If amount of substance is specified in terms of moles (µ) then heat capacity per mole of the substance is known as molar heat capacity (C)
'C' depends on nature of the substance and its temperature.
SI unit is J − mole−1 −K−1
Water equivalent:
The mass of water whose thermal capacity is equal to that of a given body is called water equivalent of that body.
Water equivalent = mass × specific heat = ms
In C.G.S. system the unit for water equivalent is 'gm'.
In SI system the unit for water equivalent is 'kg'.
Dimensional formula is [MLº Tº]
e.g.: Find the water equivalent of a Copper block of mass 200 gm. The specific heat of Copper is 0.09 cal/ gm − ºC
Solution: Water equivalent = ms = 200 × 0.09 = 18 gm Specific heat capacity of some substances at room temperature and atmospheric pressure.
Specific heat of gases:
When heat is supplied to a solid or liquid, it produces an increase in temperature only without causing any practical change in its volume or pressure. When a gas is heated, the volume and pressure also change with increase in temperature. Here heat energy will be required not only to increase the temperature of the gas but also to do mechanical work in overcoming external pressure during expansion. The specific heat of a gas depends upon the conditions under which it is being heated. Heat energy may be given to a gas keeping one of them (Pressure or Volume) constant and allowing the other to change with temperature. Thus gas has two specific heats.
(i) Specific heat at constant pressure (Cp): The amount of heat required to raise the temperature of 1 gm of gas through 1ο C at constant pressure.
At constant pressure, the quantity of heat required to increase the temperature of one mole of a gas through 1 degree is called molar specific heat capacity of a gas at constant pressure.
Specific heat of a gas at Constant Volume (CV):
At constant volume, the quantity of heat required to increase the temperature of one mole of a gas through one degree is called "Molar specific heat" of the gas at Constant Volume (Cv).
¤ Water has the highest specific heat capacity compared to other substances. For this reason water is used as a coolant in automobile radiators as well as a heater in hot water bags.
¤ Water warms up much more slowly than the land during summer and consequently wind from the sea has a cooling effect.
Calorimetry:
Hot water is mixed with cold water, the resultant temperature of water (mixture) is different from hot water/ cold water temperature. Why? If a hot solid metalic sphere is immersed in cold water, the resultant temperature of mixture is different from their individual temperature. Why?
The above questions are explained by the branch of science called "Calorimetry", which deals with the measurement of heat. When a body at higher temperature is brought in contact with another body at lower temperature, then heat lost by the hot body is equal to the heat gained by the colder body, provided no heat is allowed to escape to the surroundings. A device in which heat measurement can be made is called "Calorimeter". It consists of a metallic vessel and stirrer of the same material like Aluminium (or) Copper.
The vessel kept inside a wooden jacket, which contains heat insulating materials like grass, wool.. etc to prevent loss of heat. There is an opening in the lid, through which a mercury thermometer can be inserted into calorimeter.
Principle of method of mixtures (Principle of Calorimetry):
If two bodies at two different temperatures are brought into thermal contact, then heat lost by the hot body is equal to the heat gained by the cold body. Heat transfer from hot body to cold body until they attain a common resultant temperature (no heat lost to the surroundings).
Explanation: Consider a hot body of mass m1, specific heat s1 at t1ºC is kept in thermal contact with another cold body of mass m2, specific heat s2 at temperature t2ºC. t3ºC be the common temperature of the mixture.
Change of State (Three phases of matter):
The substance can exist in three states (phases) called solid, liquid & gaseous phases at different temperatures and pressures. Any phase of a substance can be changed into another Phase by heating or cooling it.
"A transition from one of these states to another called a change of state" or "The process of converting one phase of a substance into another phase of a substance is called Phase change" or "Change of state".
Take some cubes of ice in a beaker. Start heating slowly on a constant heat source. Ice melts at 0ºC and converts into water (solid phase changes to liquid). If heat is taken out of water or water is cooled it freezes at 0ºC and converts into ice.
The process of changing solid phase into the liquid phase is known as melting and from liquid to solid phase is called fusion. It is observed that the temperature remains constant until the entire amount of solid substance melts, corresponding temperature is called "melting point of substance".At this point of temperature both solid and liquid states of the substance coexist in thermal equilibrium during the change of states from solid to liquid.
Similarly if water is heated, it boils at 100ºC at normal pressure and converts into steam, (liquid phase changes to gaseous phase). If heat is taken out of steam, steam converts into water.
The process of changing liquid phase into gaseous phase is known as "vapourisation", gaseous phase to liquid phase is called "condensation". The temperature at which liquid and vapour states of the substance coexist is called its "boiling point".
Newton's Law of Cooling: When a cup of hot coffee is placed on a table and left it. Now coffee begins to cool gradually and finally it attains the temperature of surroundings. When temperature of a body is greater than that of surroundings, the body radiates more heat than what it gains from the surroundings.
Then the body experiences a net loss of heat and cools down."The rate of loss of heat energy of a hot body is directly proportional to the temperature difference between the body and its surroundings''. This law holds good for small temperature differences about 30ºC only.
Let T1, T2 be the temperatures of a hot body and surroundings respectively.
−ve sign indicates loss of energy (heat)
k is +ve constant depends on area and nature of the body.
If m is mass of the body, 's' is its specific heat then dQ = m s dT
Assume that the body cools from T1ºC to T2ºC in the time 't' then temperature of the body is taken as their average.
Ts is temperature of surroundings (or) in terms of 'θ'.
'C' is called cooling constant.
Unit: sec−1, Dimensional Formula: = [T−1]
Newton's law of cooling is applicable when
* Temperature of the body is uniformly distributed over it.
* Loss of heat occurs in a stream lined flow of air.
Loss of heat is neglible by conduction, and only when it is due to convection and radiation.
* Temperature difference is moderate i.e., upto 30º.
* As body cools its rate of cooling goes on decreasing.
* It is a special case of "Stefan's - Boltzman Law".
Example Problem
1. A body is found to cool from 50ºC to 40ºC in 5 min. from 45ºC to 40ºC in next 6 min. Calculate the temperature of surroundings.
Experimental verification
Newton's law of cooling can be verified with the help of a setup contains a vessel (v) containing water in between two walls. A Copper Calorimeter (C) containing hot water is placed inside double walled vessel. Two thermometers are used to measure temperatures of water in Calorimeter (T2) and water in between double walls. A graph is plotted between loge(T2 − T1) and time (t). Then nature of graph is observed to be a straight line having negative slope.
Greenhouse effect:
The earth's surface is source of thermal radiation as it absorbs energy received from the Sun.
The wavelength of this radiation lies in the long wavelength region (IR). But large portion of this radiation absorbed by green house gases. They are Carbon dioxide (CO2), Methane (CH4), Nitrous oxide (N2O), ChlorofluoroCarbon (CFx Clx). This heats up the atmosphere, gives more energy to earth resulting in warmer surface. This increases the intensity of radiation from the surface. This cyclic process is repeated until no radiaton is available for absorption. The net result is heating up of earth's surface and atmosphere. This is known as Green House effect.
Concentration of Green house gasses has enhanced due to human activities, making earth warmer. Because of enhancement temperature of earth is increased by 0.3 to 0.6º C. In future it may reach to 3ºC (higher than today). This global warming may cause problems for human life, plants and animals. Because of global warming ice caps are melting and sea level is raising, weather pattern is changing. All over the world, efforts are being made to minimise the effect of global warming.
