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- 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.

**Coefficient of linear expansion or linear expansivity{**$α$**)**is the change in length per unit original length per degree change in temperature. It's value is constant for a matter.- $α=lΔθΔl $ or $l_{θ}=l_{o}(1+αΔθ)$

**Note:**

**Pendulum Clock**

- The time period of a pendulum clock is given by $T=2πgl $
- 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 =$21 αΔθ$

**Differential expansion:**

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

When,

$d_{2}−d_{1}=(l_{1}α−l_{1}α_{′})Δθ$

If the length of material chosen that then

$l_{1}α−l_{1}α_{′}=0$

**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$αΔθ$ where Y is young's modulus of rigidity.
- Thermal Stress $(AF )=YαΔθ$
- Thermal Strain $(lΔl )=αΔθ$
- Energy Density $(VE )=21 stress×strain=21 Y(αΔθ)_{2}$

**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)=$(α_{2}−α_{1})Δθd $

**Coefficient of superficial expansion or superficial expansivity(**$β$) is the change in area per unit original area per degree change in temperature . It's value is constant for a matter.- $β=AΔθΔA $ or $A_{θ}=A_{o}(1+βΔθ)$

**Coefficient of cubical expansion or cubical expansivity(**$γ$) is the change in volume per unit original volume per degree change in temperature . It's value is constant for a matter.- $γ=VΔθΔV $ or $V_{θ}=V_{o}(1+γΔθ)$

**Relation between **$α,β,γ$** **

For an isotropic body

$α=2β =3γ $

$∴α:β:γ=1:2:3$

For anisotropic body

$β=α_{1}+α_{2}$ and $γ=α_{1}+α_{2}+α_{3}$