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Kinetic Theory of Gases: Thermal Energy and Heat Capacity and Specific Heat

Thermal Energy

Thermal Energy is the energy possess by a body due to its temperature.

Heat Capacity and Specific Heat

  • Specific heat is the amount of heat Q is required to raise the temperature of a mass m of the solid (or liquid) through, thus specific heat is expressed as .
  • SI unit of specific heat is .
  • When heat is supplied to a solid (or liquid) , its temperature increases.
  • The rise in the temperature of a solid, when a certain amount of heat is supplied to it, depends upon the nature of the material of the solid.
  • The amount of heat required to raise the temperature of a substance is given by .

Calorimetry

  • When two bodies at different temperatures are kept in contact, transfer of heat takes place from the body at higher temperature to the body at lower temperature till both the bodies acquire the same temperature .
  • The Specific heat of a material and other physical quantize related to this heat transfer are measured with the help of a device called calorimeter and the process of measurement is called Calorimetry

Principle of Calorimetry

  • The principle of calorimetry is the law of conservation of energy.
  • Let two substances of mass and , of specific heat capacities and and at temperatures and , respectively be kept in contact.
  • Heat will be transferred from the higher to the lower temperature and the substances will acquire the same temperature .
  • Assuming that no energy loss takes place to the surroundings and applying the law of conservation of energy , we can write Heat loss = Heat gained.

By knowing , and the specific heat capacity of a substance can be determined if the specific heat capacity of other substance is known.

Thermal Expansion

  • When heat is given to a substance it expands in length, area or volume, this is called Thermal Expansion.
  • The expansion in length, area and volume are called linear, superficial and cubical expansion, respectively.
  • In linear expansion, the change in length is directly proportional to the original length and change in temperature.

is the coefficient of linear expansion or temperature coefficient of linear expansion. It is given by

If and Then

  • Coefficient of linear expansion is defined as the change in length of unit length of the substance whose temperature is increased by .
  • In superficial expansion, the change in area is directly proportional to the original area and change in temperature.

is the temperature coefficient of superficial expansion.

In cubical expansion, the change in volume is directly proportional to the change in temperature and original volume:

is the temperature coefficient of cubical expansion.

If and , then

Coefficient of cubical expansion is defined as the change in volume of a unit volume of a substance whose temperature is increased by .

Relation between, Ξ’ and Ξ“

Let there be a cube of side l whose temperature is increased by . The change in length:

New Length,

Illustration: Relation between, Ξ’ and Ξ“

=

=

is very small therefore may be neglected, Thus

=

is very small, the term and may be neglected, Thus, .