# Calorimetry And Change Of Phase

Heat is defined as the thermal energy that flows from a system to its surroundings or the other way round solely as a result of the difference between their temperatures. The flow always takes place from a higher temperature to a lower temperature, and never in the reverse direction. The CGS unit of heat is calorie (cal); a larger unit kilocalorie is also used. Since heat is now recognised as a form of energy, CGPM insists that we use the SI unit of energy, joule (J), as the unit of heat. 1 cal = 4.186 J.

The specific heat capacity, or simply specific heat, of a substance is defined as the amount of heat required to raise the temperature of unit mass by one degree. Its SI unit is J/kg-K. If Q is the heat supplied to raise temperature of a body of mass m and specific heat capacity c from θ1 to θ2 then:

` Q = cm (θ2 - θ1) `

The molar heat capacity or molar specific heat of a substance is defined as the amount of heat required to raise the temperature of one mole of the substance by one degree. Its SI unit is J/mol-K. If Q is the heat required to raise temperature of n moles of a substance of molar heat capacity C from θ1 to θ2 then:

``` Q = Cn (θ2 - θ1) ```

The heat capacity of a body is defined as the amount of heat required to raise its temperature by one degree. Its SI unit is J/K. Once you distinguish heat capacity from molar heat capacity and specific heat capacity, you should be able to deduce the relation between any two of them.

The water equivalent of a body is the mass of water which has the same heat capacity as the body itself.

When a hot body is brought into contact with comparatively cold surroundings, heat flows from the body to the surroundings until their temperatures become equal. The experiments of calorimetry are usually carried out inside a properly insulated metal vessel known as a calorimeter. The hot body placed in the vessel is the "system"; the calorimeter and calorimetric liquid together are the "surroundings". Assuming no heat enters or exits the calorimeter and no chemical reaction takes place inside it:

Heat lost by hotter system = heat gained by colder surroundings

This is the fundamental principle of calorimetry.

The term phase means the state in which a substance exists, i.e. solid, liquid or gas. For example, the chemical substance H2O exists as ice in the solid phase, water in the liquid phase and water vapour or steam in the gas phase.

When a substance changes phase, the process does not take place abruptly. It happens at a constant temperature, even though heat is either supplied to or withdrawn from the system. The amount of heat required to change the phase of unit mass of a substance is known as the latent heat, L, of the substance. If Q is the amount of heat required to change the phase of mass m of a substance then:

`Q = mL`

The SI unit of latent heat is J/kg. If the phase changes from solid to liquid, we use the term latent heat of fusion. If the change happens from liquid to gas, the term used is latent heat of vaporisation. There are standard calorimetric experiments to determine latent heat of fusion of ice and latent heat of vaporisation of water. The first one is 3.33 x 105 J/kg, while the latter is 2.26 x 106 J/kg.

The equivalence between mechanical work and heat was established in the 19th century chiefly through the efforts of Robert Mayer and Helmholtz in Germany and James Joule in England. If W is the mechanical work which produces the same rise in temperature of a system as does the flow of heat Q then:

` W = JQ`

The quantity J is a constant of proportionality known as the mechanical equivalent of heat. The best modern value of J is 4.186 J/cal.

Let us touch upon various types of phase change. The change of phase from solid to liquid is called fusion or melting. The reverse process in which a substance changes from liquid to solid phase is called freezing or solidification. The temperature at which melting takes place under a pressure of 1 atm is called the normal melting point of the substance. The temperature at which freezing takes place under 1 atm pressure is called the normal freezing point of the substance. For a crystalline substance, these two temperatures are usually the same.

The change of phase from liquid to vapour is called vaporisation. The reverse process in which a substance changes from vapour to liquid is called condensation. Vaporisation can take place in two ways: evaporation and boiling. Evaporation is a slow process which happens at any temperature from the surface of a liquid. Shallow ponds dry up in summer due to evaporation. Boiling is a rapid, vigourous process that takes place throughout the mass of the liquid. The temperature at which boiling takes place under a pressure of 1 atm is called the normal boiling point of the substance.

Substances like iodine, camphor and naphthalene change directly from solid to vapour phase on heating. This type of phase change is called sublimation. The amount of heat absorbed by unit mass of a substance to sublimate is called the latent heat of sublimation.

#### Basic level videos

Definition Of Heat And Types Of Heat Capacity 1:03:22 Basic
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Problems On Heat Capacity 1:09:48 Basic
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Principle Of Calorimetry, And Determination Of Specific Heat By Method Of Mixtures 1:19:05 Basic
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Sources Of Error In Experiments Of Calorimetry 1:27:14 Basic
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More Problems On Calorimetry And Error Correction 41:55 Basic
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Latent Heat And Its Experimental Determination 1:20:15 Basic
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Problems On Latent Heat 1:04:33 Basic
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Equivalence Between Mechanical Work And Heat, And Determination Of Mechanical Equivalent Of Heat 1:27:21 Basic
400 3
Various Types Of Phase Change 1:07:4 Basic
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#### Advanced level Videos Note: (CE) Stands for Problems from Competitive Examination Papers

Advanced-level Problems On Calorimetry I 1:37:34
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Advanced-level Problems On Calorimetry II 1:14:50
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