CBSE Class 12 Physics Thermal Expansion Theory and Examples. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

**1. INTRODUCTION**

Solids are made of atoms and molecules. At a given temperature, the atoms and molecules are placed at some equilibrium distance. When heat is supplied to solid, the interatomic separation increases by which there is an expansion of solids. This expansion can be in terms of length/area/volume.

**2. LINEAR EXPANSION OF SOLID**

(i) Almost all solids expand on heating. On increasing the temperature of a solid, its length increases. This change in length of a solid on heating is called linear expansion.

(ii) **Coefficient of linear expansion** is defined as fractional increase in length per ºC rise in temperature. If l is the length of the rod at T K and as the temperature is changed to T + ΔT its length becomes l+ Δl, so coefficient of linear expansion is given by

(iii) Unit of α is Per Kelvin or Per ºC. It is positive for metals except carbon. The value of α is negative for plastic because in plastic when the temperature increases, length decreases.

(iv)The numerical value of α is same in both the units i.e. in Per Kelvin or Per ºC

(v) If α is coefficient of linear expansion at t1ºC.

l1 = length of the rod at t1ºC

l2 = length of the rod at t2ºC

l2 =l1[1 + α(t2 – t1)]

t may be in any unit ºC or ºK because in the formula there is a difference of temperature which remains same for ºC or ºK.

(vi) If length of the rod is l0 at 0ºC and lt at tºC than

lt = l0 [1 + α (t – 0)]

lt = l0(1 + αt)

where α is temperature coefficient of linear expansion at 0ºC. Here t should be in ºC only because initial temperature is taken as 0ºC.

From the above tree, it is clear that the thermal expansion of solid is classified into three categories.

(1) Linear expansion of solids

(2) Superficial expansion of solids

(3) Cubical expansion of solids

Now we shall discuss these topics one by one.

**3. APPLICATION OF LINEAR EXPANSION**

**3.1 Differential expansion of two solid rod**

(1) Suppose there are two rods of length l1 and l2.The first rod is kept on the other such that the initial separation between the free ends of the

rod is S = l2 – l1

Both the rods are initially at a temperature of t1ºC. On heating the entire system, the temperature increases to t2 such that the length of both the rod increases. So, if the new length of the rod be

**3.2 Radius of Bimetallic strip**

If two strips of different metals are welded together to form a bimetallic strip, when heated uniformly it bends in the form of an arc, the metal with greater coefficient of linear expansion lies on convex side. The radius of arc thus formed by bimetal is

** Differential expansion of two solid rods**

**Ex. 1 The length of the steel rod which would have the same difference in length with a copper rod of length 24cm at all temperatures. ****(αcopper = 18 × 10 ^{–6} k^{–1}, αsteel = 12 × 10^{–6} k^{–1})**

**is –**

**(A) 20 cm (B) 18 cm (C) 24 cm (D) 36 cm**

**Ex. 2 A metal sheet with a circular hole is heated. The hole**

**(A) Gets larger**

**(B) Gets smaller**

**(C) Remains of the same size**

**(D) Gets deformed**

**Sol.** (A) When a body is heated, the distance between any two points on it increases. So due to thermal expansion of solids, the hole gets larger.

**Ex. 3 Two identical rectangular strips one of copper and other of steel are riveted together to form a bimetallic strip (αcopper > αsteel). On heating this strip will**

**(A) Remains straight**

**(B) Bend with copper on convex side**

**(C) Bend with steel on convex side**

**(D) Get twisted**

**Sol.** (B) When a bimetallic strip of different metals is heated, the strip bends due to unequal linear expansion of the two metals. The strip will bend with metal of greater α on the convex side i.e. outer side.

**3.3 Thermal stress**

(1) When a rod is heated or cooled, it expands or contracts. It is turned as free expansion of the rod

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