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Expansion of Solid

Expansion of Solids:

  • Increase in dimension of solid on heating,
  • Linear Expansion: The expansion in length of an object.
  • Superficial Expansion: The expansion in length and breadth of an object.
  • Cubical Expansion: The expansion in three dimension.

Linear Expansion or One dimension expansion:

  • Coefficient of linear expansion or linear expansivity{) is the change in length per unit original length per degree change in temperature. It's value is constant for a matter.
  • or


Pendulum Clock

  • The time period of a pendulum clock is given by
  • When a pendulum clock keep correct time then time period of it must be 2 sec.
  • During summer season, temperature increases so the length of pendulum clock also increase and it lose time or becomes late.
  • During winter length of pendulum clock decrease so it gain time or becomes fast.
  • To keep correct time at all temperature pendulum clock is made by invar, since value of linear expansivity for it is least
  • Change in time per sec =

Differential expansion:

  • The difference in expansions of different substances when they are heated through the same range of temperature is called the differential expansion.


If the length of material chosen that then


Force due to expansion or contraction:

  • When a rod placed between two rigid supports is not free to expand on heating and not free to contract on cooling then the force or tension is developed along it.
  • Force(F) = YA where Y is young's modulus of rigidity.
  • Thermal Stress
  • Thermal Strain
  • Energy Density

Bimetallic Thermostat:

  • When two different metal strip are welded together then on heating, it bends towards one of lower linear expansivity.
  • It is used in automatic electric switch to control temperature. Most popularly in heat sensor.
  • Metal of higher linear expansivity lies on convex side and lower lines on concave side
  • Radius of curvature (R)=

Superficial Expansion or Two dimension expansion:

  • Coefficient of superficial expansion or superficial expansivity() is the change in area per unit original area per degree change in temperature . It's value is constant for a matter.
  • or

Three dimensional Expansion or Cubical Expansion:

  • Coefficient of cubical expansion or cubical expansivity() is the change in volume per unit original volume per degree change in temperature . It's value is constant for a matter.
  • or

Relation between

For an isotropic body

For anisotropic body